{"id":186411,"date":"2025-06-15T13:12:37","date_gmt":"2025-06-15T13:12:37","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/186411\/"},"modified":"2025-06-15T13:12:37","modified_gmt":"2025-06-15T13:12:37","slug":"barren-plateaus-in-variational-quantum-computing","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/186411\/","title":{"rendered":"Barren plateaus in variational quantum computing"},"content":{"rendered":"
  • \n

    Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3<\/b>, 625\u2013644 (2021). Review on variational quantum algorithms presents details for newcomers to the field.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bharti, K. et al. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94<\/b>, 015004 (2022). Review on variational quantum algorithms presents details for newcomers to the field.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Endo, S., Cai, Z., Benjamin, S. C. & Yuan, X. Hybrid quantum-classical algorithms and quantum error mitigation. J. Phys. Soc. Jpn. 90<\/b>, 032001 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schuld, M., Sinayskiy, I. & Petruccione, F. An introduction to quantum machine learning. Contemp. Phys. 56<\/b>, 172\u2013185 (2015). Pedagogical introduction to quantum machine learning.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Biamonte, J. et al. Quantum machine learning. Nature 549<\/b>, 195\u2013202 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, L. & Coles, P. J. Challenges and opportunities in quantum machine learning. Nat. Comput. Sci. https:\/\/www.nature.com\/articles\/s43588-022-00311-3<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Di Meglio, A. et al. Quantum computing for high-energy physics: state of the art and challenges. PRX Quantum 5<\/b>, 037001 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9<\/b>, 4812 (2018). Seminal work in which the barren plateaus phenomenon is discovered.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Qi, H., Wang, L., Zhu, H., Gani, A. & Gong, C. The barren plateaus of quantum neural networks: review, taxonomy and trends. Quantum Inf. Process. 22<\/b>, 435 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Arrasmith, A., Holmes, Z., Cerezo, M. & Coles, P. J. Equivalence of quantum barren plateaus to cost concentration and narrow gorges. Quantum Sci. Technol. 7<\/b>, 045015 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cerezo, M. et al. Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing. Preprint at https:\/\/arxiv.org\/abs\/2312.09121<\/a> (2023). This work presents a deep connection between absence of barren plateaus and classical simulability.<\/b><\/p>\n<\/li>\n

  • \n

    Bittel, L. & Kliesch, M. Training variational quantum algorithms is NP-hard. Phys. Rev. Lett. 127<\/b>, 120502 (2021). In this work, it is shown that training variational quantum algorithms can be, in the worst case, NP-hard.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fontana, E., Cerezo, M., Arrasmith, A., Rungger, I. & Coles, P. J. Non-trivial symmetries in quantum landscapes and their resilience to quantum noise. Quantum 6<\/b>, 804 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Anschuetz, E. R. & Kiani, B. T. Beyond barren plateaus: quantum variational algorithms are swamped with traps. Nat. Commun. 13<\/b>, 7760 (2022). This work showcases the problems of local m\u00ednima in variational quantum computing.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Anschuetz, E. R. Critical points in quantum generative models. In International Conference on Learning Representations https:\/\/openreview.net\/forum?id=2f1z55GVQN<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Larocca, M. et al. Diagnosing barren plateaus with tools from quantum optimal control. Quantum 6<\/b>, 824 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bermejo, P., Aizpurua, B. & Or\u00fas, R. Improving gradient methods via coordinate transformations: applications to quantum machine learning. Phys. Rev. Res. 6<\/b>, 023069 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    N\u00e1dori, J., Morse, G., Majnay-Tak\u00e1cs, Z., Zimbor\u00e1s, Z. & Rakyta, P. Line search strategy for navigating through barren plateaus in quantum circuit training. Preprint at https:\/\/arxiv.org\/abs\/2402.05227<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Sim, S., Johnson, P. D. & Aspuru-Guzik, A. Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Adv. Quantum Technol. 2<\/b>, 1900070 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Akshay, V., Philathong, H., Morales, M. E. & Biamonte, J. D. Reachability deficits in quantum approximate optimization. Phys. Rev. Lett. 124<\/b>, 090504 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Miao, Q. & Barthel, T. Equivalence of cost concentration and gradient vanishing for quantum circuits: an elementary proof in the Riemannian formulation. Quantum Sci. Technol. 9<\/b>, 045039 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cerezo, M. & Coles, P. J. Higher order derivatives of quantum neural networks with barren plateaus. Quantum Sci. Technol. 6<\/b>, 035006 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Puig, R., Drudis, M., Thanasilp, S. & Holmes, Z. Variational quantum simulation: a case study for understanding warm starts. PRX Quantum 6<\/b>, 010317 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, S. et al. Noise-induced barren plateaus in variational quantum algorithms. Nat. Commun. 12<\/b>, 6961 (2021). Here, it is shown that noise can induce barren plateaus and deterministic exponential concentration.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Diaz, N. L., Garc\u00eda-Mart\u00edn, D., Kazi, S., Larocca, M. & Cerezo, M. Showcasing a barren plateau theory beyond the dynamical lie algebra. Preprint at https:\/\/arxiv.org\/abs\/2310.11505<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Leone, L., Oliviero, S. F., Cincio, L. & Cerezo, M. On the practical usefulness of the hardware efficient ansatz. Quantum 8<\/b>, 1395 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Thanasilp, S., Wang, S., Nghiem, N. A., Coles, P. & Cerezo, M. Subtleties in the trainability of quantum machine learning models. Quant. Mach. Intell. 5<\/b>, 21 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cybulski, J. L. & Nguyen, T. Impact of barren plateaus countermeasures on the quantum neural network capacity to learn. Quantum Inf. Process. 22<\/b>, 442 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    P\u00e9rez-Salinas, A., Wang, H. & Bonet-Monroig, X. Analyzing variational quantum landscapes with information content. npj Quantum Inf. 10<\/b>, 27 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, H.-K., Zhu, C. & Wang, X. Predicting quantum learnability from landscape fluctuation. Preprint at https:\/\/arxiv.org\/abs\/2406.11805<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Sack, S. H., Medina, R. A., Michailidis, A. A., Kueng, R. & Serbyn, M. Avoiding barren plateaus using classical shadows. PRX Quantum 3<\/b>, 020365 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Okumura, S. & Ohzeki, M. Fourier coefficient of parameterized quantum circuits and barren plateau problem. Preprint at https:\/\/arxiv.org\/abs\/2309.06740<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Nemkov, N. A., Kiktenko, E. O. & Fedorov, A. K. Fourier expansion in variational quantum algorithms. Phys. Rev. A 108<\/b>, 032406 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    St\u0119ch\u0142y, M., Gao, L., Yogendran, B., Fontana, E. & Rudolph, M. Connecting the Hamiltonian structure to the QAOA energy and Fourier landscape structure. Preprint at https:\/\/arxiv.org\/abs\/2305.13594<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Dankert, C., Cleve, R., Emerson, J. & Livine, E. Exact and approximate unitary 2-designs and their application to fidelity estimation. Phys. Rev. A 80<\/b>, 012304 (2009).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sharma, K., Cerezo, M., Cincio, L. & Coles, P. J. Trainability of dissipative perceptron-based quantum neural networks. Phys. Rev. Lett. 128<\/b>, 180505 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Patti, T. L., Najafi, K., Gao, X. & Yelin, S. F. Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3<\/b>, 033090 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Marrero, C. O., Kieferov\u00e1, M. & Wiebe, N. Entanglement-induced barren plateaus. PRX Quantum 2<\/b>, 040316 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Holmes, Z. et al. Barren plateaus preclude learning scramblers. Phys. Rev. Lett. 126<\/b>, 190501 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ragone, M. et al. A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits. Nat. Commun. 15<\/b>, 7172 (2024). This is one of the two concurrent works that present a general theory for characterizing barren plateaus.<\/b><\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fontana, E. et al. Characterizing barren plateaus in quantum ans\u00e4tze with the adjoint representation. Nat. Commun. 15<\/b>, 7171 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schatzki, L., Larocca, M., Nguyen, Q. T., Sauvage, F. & Cerezo, M. Theoretical guarantees for permutation-equivariant quantum neural networks. npj Quantum Inf. 10<\/b>, 12 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, J., Lin, Z. & Jiang, L. Laziness, barren plateau, and noise in machine learning. Mach. Learn. Sci. Technol. 5<\/b>, 015058 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    West, M. T., Heredge, J., Sevior, M. & Usman, M. Provably trainable rotationally equivariant quantum machine learning. PRX Quantum 5<\/b>, 030320 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Garc\u00eda-Mart\u00edn, D., Larocca, M. & Cerezo, M. Deep quantum neural networks form Gaussian processes. Preprint at https:\/\/arxiv.org\/abs\/2305.09957<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Mele, A. A. Introduction to Haar measure tools in quantum information: a beginner\u2019s tutorial. Quantum 8<\/b>, 1340 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ragone, M. et al. Representation theory for geometric quantum machine learning. Preprint at https:\/\/arxiv.org\/abs\/2210.07980<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun. 12<\/b>, 1791 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Uvarov, A. & Biamonte, J. D. On barren plateaus and cost function locality in variational quantum algorithms. J. Phys. A Math. Theor. 54<\/b>, 245301 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Pesah, A. et al. Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11<\/b>, 041011 (2021).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Heyraud, V., Li, Z., Donatella, K., Boit\u00e9, A. L. & Ciuti, C. Efficient estimation of trainability for variational quantum circuits. PRX Quantum 4<\/b>, 040335 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, Z., Yu, L.-W., Duan, L.-M. & Deng, D.-L. The presence and absence of barren plateaus in tensor-network based machine learning. Phys. Rev. Lett. 129<\/b>, 270501 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Barthel, T. & Miao, Q. Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states. Preprint at https:\/\/arxiv.org\/abs\/2304.00161<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Miao, Q. & Barthel, T. Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus. Phys. Rev. A 109<\/b>, L050402 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Garcia, R. J., Zhao, C., Bu, K. & Jaffe, A. Barren plateaus from learning scramblers with local cost functions. J. High Energy Phys. 2023<\/b>, 1\u201379 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Letcher, A., Woerner, S. & Zoufal, C. Tight and efficient gradient bounds for parameterized quantum circuits. Quantum 8<\/b>, 1484 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Arrazola, J. M. et al. Universal quantum circuits for quantum chemistry. Quantum 6<\/b>, 742 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, H.-K., Liu, S. & Zhang, S.-X. Absence of barren plateaus in finite local-depth circuits with long-range entanglement. Phys. Rev. Lett. 132<\/b>, 150603 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Garc\u00eda-Mart\u00edn, D., Braccia, P. & Cerezo, M. Architectures and random properties of symplectic quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2405.10264<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Deneris, A. E., Bermejo, P., Braccia, P., Cincio, L. & Cerezo, M. Exact spectral gaps of random one-dimensional quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2408.11201<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Napp, J. Quantifying the barren plateau phenomenon for a model of unstructured variational ans\u00e4tze. Preprint at https:\/\/arxiv.org\/abs\/2203.06174<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Braccia, P., Bermejo, P., Cincio, L. & Cerezo, M. Computing exact moments of local random quantum circuits via tensor networks. Quant. Mach. Intell. 6<\/b>, 54 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hu, H.-Y. et al. Demonstration of robust and efficient quantum property learning with shallow shadows. Preprint at https:\/\/arxiv.org\/abs\/2402.17911<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Zhao, C. & Gao, X.-S. Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus. Quantum 5<\/b>, 466 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, K., Liu, L., Hsieh, M.-H. & Tao, D. Escaping from the barren plateau via Gaussian initializations in deep variational quantum circuits. Adv. Neural Inf. Process. Syst. https:\/\/openreview.net\/forum?id=jXgbJdQ2YIy<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Wang, Y., Qi, B., Ferrie, C. & Dong, D. Trainability enhancement of parameterized quantum circuits via reduced-domain parameter initialization. Phys. Rev. Appl. 22<\/b>, 054005 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Park, C.-Y. & Killoran, N. Hamiltonian variational ansatz without barren plateaus. Quantum 8<\/b>, 1239 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Park, C.-Y., Kang, M. & Huh, J. Hardware-efficient ansatz without barren plateaus in any depth. Preprint at https:\/\/arxiv.org\/abs\/2403.04844<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Sannia, A., Tacchino, F., Tavernelli, I., Giorgi, G. L. & Zambrini, R. Engineered dissipation to mitigate barren plateaus. npj Quantum Inf. 10<\/b>, 81 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, J., Wilde, F., Mele, A. A., Jiang, L. & Eisert, J. Stochastic noise can be helpful for variational quantum algorithms. Preprint at https:\/\/arxiv.org\/abs\/2210.06723<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Schumann, M., Wilhelm, F. K. & Ciani, A. Emergence of noise-induced barren plateaus in arbitrary layered noise models. Quantum Sci. Technol. 9<\/b>, 045019 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Singkanipa, P. & Lidar, D. A. Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and fixed points. Quantum 9<\/b>, 1617 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bremner, M. J., Mora, C. & Winter, A. Are random pure states useful for quantum computation? Phys. Rev. Lett. 102<\/b>, 190502 (2009).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gross, D., Flammia, S. T. & Eisert, J. Most quantum states are too entangled to be useful as computational resources. Phys. Rev. Lett. 102<\/b>, 190501 (2009).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yang, G. et al. Tensor programs v: tuning large neural networks via zero-shot hyperparameter transfer. Adv. Neural Inf. Process. Syst. 34<\/b>, 17084\u201317097 (2021).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).<\/p>\n<\/li>\n

  • \n

    Horgan, J. Scott Aaronson answers every ridiculously big question throw at him. Sci. Am. https:\/\/blogs.scientificamerican.com\/cross-check\/scott-aaronson-answers-every-ridiculously-big-question-i-throw-at-him<\/a> (2016).<\/p>\n<\/li>\n

  • \n

    Liu, Y., Arunachalam, S. & Temme, K. A rigorous and robust quantum speed-up in supervised machine learning. Nat. Phys. https:\/\/www.nature.com\/articles\/s41567-021-01287-z<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    J\u00e4ger, J. & Krems, R. V. Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines. Nat. Commun. 14<\/b>, 576 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Holmes, Z., Sharma, K., Cerezo, M. & Coles, P. J. Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3<\/b>, 010313 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Friedrich, L. & Maziero, J. Quantum neural network cost function concentration dependency on the parametrization expressivity. Sci. Rep. 13<\/b>, 9978 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Abbas, A. et al. The power of quantum neural networks. Nat. Comput. Sci. 1<\/b>, 403\u2013409 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Haug, T., Bharti, K. & Kim, M. S. Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2<\/b>, 040309 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Larocca, M., Ju, N., Garc\u00eda-Mart\u00edn, D., Coles, P. J. & Cerezo, M. Theory of overparametrization in quantum neural networks. Nat. Comput. Sci. 3<\/b>, 542\u2013551 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Somma, R., Ortiz, G., Barnum, H., Knill, E. & Viola, L. Nature and measure of entanglement in quantum phase transitions. Phys. Rev. A 70<\/b>, 042311 (2004).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Somma, R. D. Quantum computation, complexity, and many-body physics. Preprint at https:\/\/arxiv.org\/abs\/quant-ph\/0512209<\/a> (2005).<\/p>\n<\/li>\n

  • \n

    Khatri, S. et al. Quantum-assisted quantum compiling. Quantum 3<\/b>, 140 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Uvarov, A., Biamonte, J. D. & Yudin, D. Variational quantum eigensolver for frustrated quantum systems. Phys. Rev. B 102<\/b>, 075104 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kashif, M. & Al-Kuwari, S. The impact of cost function globality and locality in hybrid quantum neural networks on NISQ devices. Mach. Learn. Sci. Technol. 4<\/b>, 015004 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Leadbeater, C., Sharrock, L., Coyle, B. & Benedetti, M. F-divergences and cost function locality in generative modelling with quantum circuits. Entropy 23<\/b>, 1281 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cerezo, M., Sharma, K., Arrasmith, A. & Coles, P. J. Variational quantum state eigensolver. npj Quantum Inf. 8<\/b>, 1\u201311 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kiani, B. T., De Palma, G., Marvian, M., Liu, Z.-W. & Lloyd, S. Learning quantum data with the quantum earth mover\u2019s distance. Quantum Sci. Technol. 7<\/b>, 045002 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zambrano, L., Mu\u00f1oz-Moller, A. D., Mu\u00f1oz, M., Pereira, L. & Delgado, A. Avoiding barren plateaus in the variational determination of geometric entanglement. Quantum Sci. Technol. 9<\/b>, 025016 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ogunkoya, O., Morris, K. & K\u00fcrk\u00e7\u00fcoglu, D. M. Investigating parameter trainability in the snap-displacement protocol of a qudit system. Preprint at https:\/\/arxiv.org\/abs\/2309.14942<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Zhang, B. & Zhuang, Q. Energy-dependent barren plateau in bosonic variational quantum circuits. Quantum Sci. Technol. 10<\/b>, 015009 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wiersema, R., Zhou, C., Carrasquilla, J. F. & Kim, Y. B. Measurement-induced entanglement phase transitions in variational quantum circuits. SciPost Phys. 14<\/b>, 147 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Shaydulin, R. & Wild, S. M. Importance of kernel bandwidth in quantum machine learning. Phys. Rev. A 106<\/b>, 042407 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kashif, M. & Al-Kuwari, S. The unified effect of data encoding, ansatz expressibility and entanglement on the trainability of HQNNs. Int. J. Parallel Emergent Distrib. Syst. 38<\/b>, 362\u2013400 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das, S., Martina, S. & Caruso, F. The role of data embedding in equivariant quantum convolutional neural networks. Quant. Mach. Intell. 6<\/b>, 82 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mhiri, H. et al. Constrained and vanishing expressivity of quantum Fourier models. Preprint at https:\/\/arxiv.org\/abs\/2403.09417<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Stilck Fran\u00e7a, D. & Garcia-Patron, R. Limitations of optimization algorithms on noisy quantum devices. Nat. Phys. 17<\/b>, 1221\u20131227 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    De Palma, G., Marvian, M., Rouz\u00e9, C. & Fran\u00e7a, D. S. Limitations of variational quantum algorithms: a quantum optimal transport approach. PRX Quantum 4<\/b>, 010309 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Crognaletti, G., Grossi, M. & Bassi, A. Estimates of loss function concentration in noisy parametrized quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2410.01893<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Mele, A. A. et al. Noise-induced shallow circuits and absence of barren plateaus. Preprint at https:\/\/arxiv.org\/abs\/2403.13927<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Fefferman, B., Ghosh, S., Gullans, M., Kuroiwa, K. & Sharma, K. Effect of non-unital noise on random circuit sampling. PRX Quantum 5<\/b>, 030317 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Deshpande, A. et al. Dynamic parameterized quantum circuits: expressive and barren-plateau free. Preprint at https:\/\/arxiv.org\/abs\/2411.05760<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Wilde, M. M. Quantum Information Theory (Cambridge Univ. Press, 2013).<\/p>\n<\/li>\n

  • \n

    Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549<\/b>, 242\u2013246 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    He, Z., Li, L., Zheng, S., Li, Y. & Situ, H. Variational quantum compiling with double q-learning. N. J. Phys. 23<\/b>, 033002 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Moro, L., Paris, M. G. A., Restelli, M. & Prati, E. Quantum compiling by deep reinforcement learning. Commun. Phys. 4<\/b>, 178 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Beer, K. et al. Training deep quantum neural networks. Nat. Commun. 11<\/b>, 808 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Buonaiuto, G., Gargiulo, F., De Pietro, G., Esposito, M. & Pota, M. The effects of quantum hardware properties on the performances of variational quantum learning algorithms. Quant. Mach. Intell. 6<\/b>, 9 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, X., Liu, G., Zhang, H.-K., Huang, J. & Wang, X. Mitigating barren plateaus of variational quantum eigensolvers. IEEE Trans. Quant. Eng. 1\u201319 https:\/\/ieeexplore.ieee.org\/abstract\/document\/10485449<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Zhang, H.-K., Zhu, C., Liu, G. & Wang, X. Exponential hardness of optimization from the locality in quantum neural networks. In Proc. AAAI Conference on Artificial Intelligence Vol. 38, 16741\u201316749 https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/29614<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Wecker, D., Hastings, M. B. & Troyer, M. Progress towards practical quantum variational algorithms. Phys. Rev. A 92<\/b>, 042303 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wiersema, R. et al. Exploring entanglement and optimization within the Hamiltonian variational ansatz. PRX Quant. 1<\/b>, 020319 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5<\/b>, 4213 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wiersema, R., K\u00f6kc\u00fc, E., Kemper, A. F. & Bakalov, B. N. Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies. npj Quantum Inf. 10<\/b>, 110 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https:\/\/arxiv.org\/abs\/1411.4028<\/a> (2014).<\/p>\n<\/li>\n

  • \n

    Hadfield, S. et al. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms 12<\/b>, 34 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    B\u00e4rtschi, A. & Eidenbenz, S. Grover mixers for QAOA: shifting complexity from mixer design to state preparation. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 72\u201382 https:\/\/www.computer.org\/csdl\/proceedings-article\/qce\/2020\/896900a072\/1p2VnUCmpYA<\/a> (IEEE, 2020).<\/p>\n<\/li>\n

  • \n

    Fuchs, F. G., Lye, K. O., M\u00f8ll Nilsen, H., Stasik, A. J. & Sartor, G. Constraint preserving mixers for the quantum approximate optimization algorithm. Algorithms 15<\/b>, 202 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tate, R., Moondra, J., Gard, B., Mohler, G. & Gupta, S. Warm-started QAOA with custom mixers provably converges and computationally beats Goemans\u2013Williamson\u2019s max-cut at low circuit depths. Quantum 7<\/b>, 1121 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, B., Sone, A. & Zhuang, Q. Quantum computational phase transition in combinatorial problems. npj Quantum Inf. 8<\/b>, 87 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kazi, S. et al. Analyzing the quantum approximate optimization algorithm: ans\u00e4tze, symmetries, and Lie algebras. Preprint at https:\/\/arxiv.org\/abs\/2410.05187<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Crooks, G. E. Performance of the quantum approximate optimization algorithm on the maximum cut problem. Preprint at https:\/\/arxiv.org\/abs\/1811.08419<\/a> (2018).<\/p>\n<\/li>\n

  • \n

    Boulebnane, S. & Montanaro, A. Solving Boolean satisfiability problems with the quantum approximate optimization algorithm. PRX Quantum 5<\/b>, 030348 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Montanaro, A. & Zhou, L. Quantum speedups in solving near-symmetric optimization problems by low-depth QAOA. Preprint at https:\/\/arxiv.org\/abs\/2411.04979<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Herrman, R., Lotshaw, P. C., Ostrowski, J., Humble, T. S. & Siopsis, G. Multi-angle quantum approximate optimization algorithm. Sci. Rep. 12<\/b>, 1\u201310 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Aguilar, G., Cichy, S., Eisert, J. & Bittel, L. Full classification of Pauli Lie algebras Preprint at https:\/\/arxiv.org\/abs\/2408.00081<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Chapman, A. & Flammia, S. T. Characterization of solvable spin models via graph invariants. Quantum 4<\/b>, 278 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    K\u00f6kc\u00fc, E., Wiersema, R., Kemper, A. F. & Bakalov, B. N. Classification of dynamical Lie algebras generated by spin interactions on undirected graphs. Preprint at https:\/\/arxiv.org\/abs\/2409.19797<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Haah, J., Liu, Y. & Tan, X. Efficient approximate unitary designs from random Pauli rotations. In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS) 463\u2013475 (IEEE, 2024).<\/p>\n<\/li>\n

  • \n

    Zhou, N.-R., Liu, X.-X., Chen, Y.-L. & Du, N.-S. Quantum k-nearest-neighbor image classification algorithm based on K-L transform. Int. J. Theor. Phys. 60<\/b>, 1209\u20131224 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chai, Y. et al. Shortcuts to the quantum approximate optimization algorithm. Phys. Rev. A 105<\/b>, 042415 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chandarana, P. et al. Digitized-counterdiabatic quantum approximate optimization algorithm. Phys. Rev. Res. 4<\/b>, 013141 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Vizzuso, M., Passarelli, G., Cantele, G. & Lucignano, P. Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters. N. J. Phys. 26<\/b>, 013002 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Shaydulin, R., Lotshaw, P. C., Larson, J., Ostrowski, J. & Humble, T. S. Parameter transfer for quantum approximate optimization of weighted maxcut. ACM Trans. Quantum Comput. 4<\/b>, 115 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Farhi, E., Goldstone, J., Gutmann, S. & Zhou, L. The quantum approximate optimization algorithm and the Sherrington\u2013Kirkpatrick model at infinite size. Quantum 6<\/b>, 759 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Taube, A. G. & Bartlett, R. J. New perspectives on unitary coupled-cluster theory. Int. J. Quantum Chem. 106<\/b>, 3393\u20133401 (2006).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lee, J., Huggins, W. J., Head-Gordon, M. & Whaley, K. B. Generalized unitary coupled cluster wave functions for quantum computation. J. Chem. Theory Comput. 15<\/b>, 311\u2013324 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mao, R., Tian, G. & Sun, X. Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms. Commun. Phys. 7<\/b>, 342 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bermejo, P. et al. Quantum convolutional neural networks are (effectively) classically simulable. Preprint at https:\/\/arxiv.org\/abs\/2408.12739<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Cichy, S., Faehrmann, P. K., Khatri, S. & Eisert, J. Perturbative gadgets for gate-based quantum computing: nonrecursive constructions without subspace restrictions. Phys. Rev. A 109<\/b>, 052624 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kiani, B. T., Lloyd, S. & Maity, R. Learning unitaries by gradient descent. Preprint at https:\/\/arxiv.org\/abs\/2001.11897<\/a> (2020).<\/p>\n<\/li>\n

  • \n

    Rajakumar, J., Golden, J., B\u00e4rtschi, A. & Eidenbenz, S. Trainability barriers in low-depth QAOA landscapes. In Proc. 21st ACM International Conference on Computing Frontiers, CF \u201924, 199\u2013206 https:\/\/doi.org\/10.1145\/3649153.3649204<\/a> (Association for Computing Machinery, 2024).<\/p>\n<\/li>\n

  • \n

    Marshall, S. C., Gyurik, C. & Dunjko, V. High dimensional quantum machine learning with small quantum computers. Quantum 7<\/b>, 1078 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, K., Hsieh, M.-H., Liu, L. & Tao, D. Toward trainability of quantum neural networks. Preprint at https:\/\/arxiv.org\/abs\/2011.06258<\/a> (2020).<\/p>\n<\/li>\n

  • \n

    Larocca, M. et al. Group-invariant quantum machine learning. PRX Quantum 3<\/b>, 030341 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Nguyen, Q. T. et al. Theory for equivariant quantum neural networks. PRX Quantum 5<\/b>, 020328 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Meyer, J. J. et al. Exploiting symmetry in variational quantum machine learning. PRX Quantum 4<\/b>, 010328 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Skolik, A., Cattelan, M., Yarkoni, S., B\u00e4ck, T. & Dunjko, V. Equivariant quantum circuits for learning on weighted graphs. npj Quantum Inf. 9<\/b>, 47 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Volkoff, T. & Coles, P. J. Large gradients via correlation in random parameterized quantum circuits. Quantum Sci. Technol. 6<\/b>, 025008 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sauvage, F., Larocca, M., Coles, P. J. & Cerezo, M. Building spatial symmetries into parameterized quantum circuits for faster training. Quantum Sci. Technol. 9<\/b>, 015029 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kazi, S., Larocca, M. & Cerezo, M. On the universality of sn-equivariant k-body gates. N. J. Phys. 26<\/b>, 053030 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Monbroussou, L., Landman, J., Grilo, A. B., Kukla, R. & Kashefi, E. Trainability and expressivity of Hamming-weight preserving quantum circuits for machine learning. Preprint at https:\/\/arxiv.org\/abs\/2309.15547<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Raj, S. et al. Quantum deep hedging. Quantum 7<\/b>, 1191 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lee, J., Magann, A. B., Rabitz, H. A. & Arenz, C. Progress toward favorable landscapes in quantum combinatorial optimization. Phys. Rev. A 104<\/b>, 032401 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jozsa, R. & Miyake, A. Matchgates and classical simulation of quantum circuits. Proc. R. Soc. A Math. Phys. Eng. Sci. 464<\/b>, 3089\u20133106 (2008).<\/p>\n

    ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wan, K., Huggins, W. J., Lee, J. & Babbush, R. Matchgate shadows for fermionic quantum simulation. Commun. Math. Phys. 404<\/b>, 629 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    De Melo, F., \u0106wikli\u0144ski, P. & Terhal, B. M. The power of noisy fermionic quantum computation. N. J. Phys. 15<\/b>, 013015 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Oszmaniec, M., Dangniam, N., Morales, M. E. & Zimbor\u00e1s, Z. Fermion sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states. PRX Quantum 3<\/b>, 020328 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Matos, G., Self, C. N., Papi\u0107, Z., Meichanetzidis, K. & Dreyer, H. Characterization of variational quantum algorithms using free fermions. Quantum 7<\/b>, 966 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Diaz, N. L. et al. Parallel-in-time quantum simulation via Page and Wootters quantum time. Preprint at https:\/\/arxiv.org\/abs\/2308.12944<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    K\u00f6kc\u00fc, E. et al. Fixed depth Hamiltonian simulation via Cartan decomposition. Phys. Rev. Lett. 129<\/b>, 070501 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Volkoff, T. J. Efficient trainability of linear optical modules in quantum optical neural networks. J. Russ. Laser Res. 42<\/b>, 250\u2013260 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Volkoff, T., Holmes, Z. & Sornborger, A. Universal compiling and (no-)free-lunch theorems for continuous-variable quantum learning. PRX Quantum 2<\/b>, 040327 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Arjovsky, M., Shah, A. & Bengio, Y. Unitary evolution recurrent neural networks. In International Conference on Machine Learning 1120\u20131128. https:\/\/proceedings.mlr.press\/v48\/arjovsky16.html<\/a> (PMLR, 2016).<\/p>\n<\/li>\n

  • \n

    Jing, L. et al. Tunable efficient unitary neural networks (EUNN) and their application to RNNs. In International Conference on Machine Learning 1733\u20131741. https:\/\/proceedings.mlr.press\/v70\/jing17a.html<\/a> (PMLR, 2017).<\/p>\n<\/li>\n

  • \n

    Bilkis, M., Cerezo, M., Verdon, G., Coles, P. J. & Cincio, L. A semi-agnostic ansatz with variable structure for variational quantum algorithms. Quant. Mach. Intell. 5<\/b>, 43 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Du, Y., Huang, T., You, S., Hsieh, M.-H. & Tao, D. Quantum circuit architecture search: error mitigation and trainability enhancement for variational quantum solvers. npj Quantum Inf. 8<\/b>, 62 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Grimsley, H. R., Economou, S. E., Barnes, E. & Mayhall, N. J. An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nat. Commun. 10<\/b>, 3007 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tang, H. L. et al. qubit-ADAPT-VQE: an adaptive algorithm for constructing hardware-efficient ans\u00e4tze on a quantum processor. PRX Quantum 2<\/b>, 020310 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sim, S., Romero, J., Gonthier, J. F. & Kunitsa, A. A. Adaptive pruning-based optimization of parameterized quantum circuits. Quantum Sci. Technol. 6<\/b>, 025019 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, Z.-J., Kyaw, T. H., Kottmann, J., Degroote, M. & Aspuru-Guzik, A. Mutual information-assisted adaptive variational quantum eigensolver. Quantum Sci. Technol. https:\/\/iopscience.iop.org\/article\/10.1088\/2058-9565\/abdca4<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Tkachenko, N. V. et al. Correlation-informed permutation of qubits for reducing ansatz depth in VQE. PRX Quantum 2<\/b>, 020337 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Claudino, D., Wright, J., McCaskey, A. J. & Humble, T. S. Benchmarking adaptive variational quantum eigensolvers. Front. Chem. 8<\/b>, 1152 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Rattew, A. G., Hu, S., Pistoia, M., Chen, R. & Wood, S. A domain-agnostic, noise-resistant, hardware-efficient evolutionary variational quantum eigensolver. Preprint at https:\/\/arxiv.org\/abs\/1910.09694<\/a> (2019).<\/p>\n<\/li>\n

  • \n

    Chivilikhin, D. et al. MoG-VQE: multiobjective genetic variational quantum eigensolver. Preprint at https:\/\/arxiv.org\/abs\/2007.04424<\/a> (2020).<\/p>\n<\/li>\n

  • \n

    Cincio, L., Suba\u015f\u0131, Y., Sornborger, A. T. & Coles, P. J. Learning the quantum algorithm for state overlap. N. J. Phys. 20<\/b>, 113022 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, S.-X., Hsieh, C.-Y., Zhang, S. & Yao, H. Differentiable quantum architecture search. Quantum Sci. Technol. 7<\/b>, 045023 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wada, K., Raymond, R., Sato, Y. & Watanabe, H. C. Sequential optimal selections of single-qubit gates in parameterized quantum circuits. Quantum Sci. Technol. 9<\/b>, 035030 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Grimsley, H. R., Mayhall, N. J., Barron, G. S., Barnes, E. & Economou, S. E. Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Inf. 9<\/b>, 19 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Anastasiou, P. G., Chen, Y., Mayhall, N. J., Barnes, E. & Economou, S. E. TETRIS-ADAPT-VQE: an adaptive algorithm that yields shallower, denser circuit ans\u00e4tze. Phys. Rev. Res. 6<\/b>, 013254 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Van Dyke, J. S. et al. Scaling adaptive quantum simulation algorithms via operator pool tiling. Phys. Rev. Res. 6<\/b>, L012030 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Romero, A., Engel, J., Tang, H. L. & Economou, S. E. Solving nuclear structure problems with the adaptive variational quantum algorithm. Phys. Rev. C 105<\/b>, 064317 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhu, L. et al. Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer. Phys. Rev. Res. 4<\/b>, 033029 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Grant, E., Wossnig, L., Ostaszewski, M. & Benedetti, M. An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3<\/b>, 214 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jain, N., Coyle, B., Kashefi, E. & Kumar, N. Graph neural network initialisation of quantum approximate optimisation. Quantum 6<\/b>, 861 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Skolik, A., McClean, J. R., Mohseni, M., van der Smagt, P. & Leib, M. Layerwise learning for quantum neural networks. Quant. Mach. Intell. 3<\/b>, 1\u201311 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kulshrestha, A. & Safro, I. BEINIT: avoiding barren plateaus in variational quantum algorithms. In 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 197\u2013203 https:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=9951195<\/a> (IEEE, 2022).<\/p>\n<\/li>\n

  • \n

    Rad, A., Seif, A. & Linke, N. M. Surviving the barren plateau in variational quantum circuits with Bayesian learning initialization. Preprint at https:\/\/arxiv.org\/abs\/2203.02464<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Astrakhantsev, N., Mazzola, G., Tavernelli, I. & Carleo, G. Phenomenological theory of variational quantum ground-state preparation. Phys. Rev. Res. 5<\/b>, 033225 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Haug, T. & Kim, M. Optimal training of variational quantum algorithms without barren plateaus. Preprint at https:\/\/arxiv.org\/abs\/2104.14543<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Kashif, M., Rashid, M., Al-Kuwari, S. & Shafique, M. Alleviating barren plateaus in parameterized quantum machine learning circuits: investigating advanced parameter initialization strategies. In 2024 Design, Automation & Test in Europe Conference & Exhibition (DATE) https:\/\/ieeexplore.ieee.org\/document\/10546644<\/a> (IEEE 2024).<\/p>\n<\/li>\n

  • \n

    Shi, X. & Shang, Y. Avoiding barren plateaus via Gaussian mixture model. Preprint at https:\/\/arxiv.org\/abs\/2402.13501<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Friedrich, L. & Maziero, J. Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106<\/b>, 042433 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Rudolph, M. S. et al. Synergistic pretraining of parametrized quantum circuits via tensor networks. Nat. Commun. 14<\/b>, 8367 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Marin-Sanchez, G., Gonzalez-Conde, J. & Sanz, M. Quantum algorithms for approximate function loading. Phys. Rev. Res. 5<\/b>, 033114 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cervera-Lierta, A., Kottmann, J. S. & Aspuru-Guzik, A. The meta-variational quantum eigensolver (meta-VQE): learning energy profiles of parameterized Hamiltonians for quantum simulation. PRX Quantum 2<\/b>, 020329 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Goh, M. L., Larocca, M., Cincio, L., Cerezo, M. & Sauvage, F. Lie-algebraic classical simulations for variational quantum computing. Preprint at https:\/\/arxiv.org\/abs\/2308.01432<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Brandao, F. G., Broughton, M., Farhi, E., Gutmann, S. & Neven, H. For fixed control parameters the quantum approximate optimization algorithm\u2019s objective function value concentrates for typical instances. Preprint at https:\/\/arxiv.org\/abs\/1812.04170<\/a> (2018).<\/p>\n<\/li>\n

  • \n

    Zhou, L., Wang, S.-T., Choi, S., Pichler, H. & Lukin, M. D. Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices. Phys. Rev. X 10<\/b>, 021067 (2020).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wurtz, J. & Lykov, D. Fixed-angle conjectures for the quantum approximate optimization algorithm on regular maxcut graphs. Phys. Rev. A 104<\/b>, 052419 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Boulebnane, S. & Montanaro, A. Predicting parameters for the quantum approximate optimization algorithm for max-cut from the infinite-size limit. Preprint at https:\/\/arxiv.org\/abs\/2110.10685<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Galda, A., Liu, X., Lykov, D., Alexeev, Y. & Safro, I. Transferability of optimal QAOA parameters between random graphs. In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 171\u2013180 https:\/\/www.computer.org\/csdl\/proceedings-article\/qce\/2021\/169100a171\/1yEZ9MWWjSg<\/a> (IEEE, 2021).<\/p>\n<\/li>\n

  • \n

    Mele, A. A., Mbeng, G. B., Santoro, G. E., Collura, M. & Torta, P. Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz. Phys. Rev. A 106<\/b>, L060401 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, H.-Y., Sun, T.-P., Wu, Y.-C., Han, Y.-J. & Guo, G.-P. Mitigating barren plateaus with transfer-learning-inspired parameter initializations. N. J. Phys. 25<\/b>, 013039 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, Z.-J., Sun, J., Yuan, X. & Yung, M.-H. Low-depth Hamiltonian simulation by an adaptive product formula. Phys. Rev. Lett. 130<\/b>, 040601 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gacon, J., Nys, J., Rossi, R., Woerner, S. & Carleo, G. Variational quantum time evolution without the quantum geometric tensor. Phys. Rev. Res. 6<\/b>, 013143 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Campos, E., Rabinovich, D., Akshay, V. & Biamonte, J. Training saturation in layerwise quantum approximate optimization. Phys. Rev. A 104<\/b>, L030401 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Campos, E., Nasrallah, A. & Biamonte, J. Abrupt transitions in variational quantum circuit training. Phys. Rev. A 103<\/b>, 032607 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fitzek, D., Jonsson, R. S., Dobrautz, W. & Sch\u00e4fer, C. Optimizing variational quantum algorithms with qBang: efficiently interweaving metric and momentum to navigate flat energy landscapes. Quantum 8<\/b>, 1313 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Acampora, G., Chiatto, A. & Vitiello, A. A comparison of evolutionary algorithms for training variational quantum classifiers. In 2023 IEEE Congress on Evolutionary Computation (CEC) 1\u20138 https:\/\/ieeexplore.ieee.org\/abstract\/document\/10254076<\/a> (IEEE, 2023).<\/p>\n<\/li>\n

  • \n

    Stokes, J., Izaac, J., Killoran, N. & Carleo, G. Quantum natural gradient. Quantum 4<\/b>, 269 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Koczor, B. & Benjamin, S. C. Quantum natural gradient generalized to noisy and nonunitary circuits. Phys. Rev. A 106<\/b>, 062416 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Arrasmith, A., Cerezo, M., Czarnik, P., Cincio, L. & Coles, P. J. Effect of barren plateaus on gradient-free optimization. Quantum 5<\/b>, 558 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Temme, K., Bravyi, S. & Gambetta, J. M. Error mitigation for short-depth quantum circuits. Phys. Rev. Lett. 119<\/b>, 180509 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Li, Y. & Benjamin, S. C. Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X 7<\/b>, 021050 (2017).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Cai, Z. et al. Quantum error mitigation. Rev. Mod. Phys. 95<\/b>, 045005 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, K., Chen, Y.-A. & Wang, X. Mitigating quantum errors via truncated Neumann series. Sci. China Inf. Sci. 66<\/b>, 180508 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Takagi, R., Endo, S., Minagawa, S. & Gu, M. Fundamental limits of quantum error mitigation. npj Quantum Inf. 8<\/b>, 114 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Takagi, R., Tajima, H. & Gu, M. Universal sampling lower bounds for quantum error mitigation. Phys. Rev. Lett. 131<\/b>, 210602 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Quek, Y., Fran\u00e7a, D. S., Khatri, S., Meyer, J. J. & Eisert, J. Exponentially tighter bounds on limitations of quantum error mitigation. Nat. Phys. 20<\/b>, 1648\u20131658 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Perdomo-Ortiz, A., Benedetti, M., Realpe-G\u00f3mez, J. & Biswas, R. Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers. Quantum Sci. Technol. 3<\/b>, 030502 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gao, X., Anschuetz, E. R., Wang, S.-T., Cirac, J. I. & Lukin, M. D. Enhancing generative models via quantum correlations. Phys. Rev. X 12<\/b>, 021037 (2022).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Benedetti, M. et al. A generative modeling approach for benchmarking and training shallow quantum circuits. npj Quantum Inf. 5<\/b>, 45 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, J.-G. & Wang, L. Differentiable learning of quantum circuit born machines. Phys. Rev. A 98<\/b>, 062324 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Coyle, B., Mills, D., Danos, V. & Kashefi, E. The Born supremacy: quantum advantage and training of an Ising Born Machine. npj Quantum Inf. 6<\/b>, 60 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Rudolph, M. S. et al. Trainability barriers and opportunities in quantum generative modeling. npj Quantum Inf. 10<\/b>, 116 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zoufal, C. Generative quantum machine learning. Preprint at https:\/\/arxiv.org\/abs\/2111.12738<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Lloyd, S. & Weedbrook, C. Quantum generative adversarial learning. Phys. Rev. Lett. 121<\/b>, 040502 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B. & Melko, R. Quantum Boltzmann machine. Phys. Rev. X 8<\/b>, 021050 (2018).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Coopmans, L. & Benedetti, M. On the sample complexity of quantum Boltzmann machine learning. Commun. Phys. 7<\/b>, 274 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chang, S. Y., Thanasilp, S., Saux, B. L., Vallecorsa, S. & Grossi, M. Latent style-based quantum GAN for high-quality image generation. Preprint at https:\/\/arxiv.org\/abs\/2406.02668<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Kieferova, M., Carlos, O. M. & Wiebe, N. Quantum generative training using R\u00e9nyi divergences. Preprint at https:\/\/arxiv.org\/abs\/2106.09567<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Huang, H.-Y. et al. Power of data in quantum machine learning. Nat. Commun. 12<\/b>, 2631 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Thanasilp, S., Wang, S., Cerezo, M. & Holmes, Z. Exponential concentration in quantum kernel methods. Nat. Commun. 15<\/b>, 5200 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    K\u00fcbler, J., Buchholz, S. & Sch\u00f6lkopf, B. The inductive bias of quantum kernels. Adv. Neural Inf. Process. Syst. 34<\/b>, 12661\u201312673 (2021).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Canatar, A., Peters, E., Pehlevan, C., Wild, S. M. & Shaydulin, R. Bandwidth enables generalization in quantum kernel models. Trans. Mach. Learn. Res. https:\/\/openreview.net\/forum?id=A1N2qp4yAq<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Suzuki, Y. & Li, M. Effect of alternating layered ansatzes on trainability of projected quantum kernel. Phys. Rev. A 110<\/b>, 012409 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Suzuki, Y., Kawaguchi, H. & Yamamoto, N. Quantum Fisher kernel for mitigating the vanishing similarity issue. Quantum Sci. Technol. 9<\/b>, 035050 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Xiong, W. et al. On fundamental aspects of quantum extreme learning machines. Quant. Mach. Intell. 7<\/b>, 20 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yu, L.-W. et al. Expressibility-induced concentration of quantum neural tangent kernels. Rep. Prog. Phys. 87<\/b>, 110501 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schuld, M. & Petruccione, F. Supervised Learning with Quantum Computers Vol. 17 (Springer, 2018).<\/p>\n<\/li>\n

  • \n

    Havl\u00ed\u010dek, V. et al. Supervised learning with quantum-enhanced feature spaces. Nature 567<\/b>, 209\u2013212 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schuld, M. Supervised quantum machine learning models are kernel methods. Preprint at https:\/\/arxiv.org\/abs\/2101.11020<\/a> (2021).<\/p>\n<\/li>\n

  • \n

    Gan, B. Y., Leykam, D. & Thanasilp, S. A unified framework for trace-induced quantum kernels. Preprint at https:\/\/arxiv.org\/abs\/2311.13552<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Magann, A. B. et al. From pulses to circuits and back again: a quantum optimal control perspective on variational quantum algorithms. PRX Quantum 2<\/b>, 010101 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ge, X., Wu, R.-B. & Rabitz, H. The optimization landscape of hybrid quantum\u2013classical algorithms: from quantum control to NISQ applications. Annu. Rev. Control https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1367578822000840<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Broers, L. & Mathey, L. Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols. Phys. Rev. Res. 6<\/b>, 013076 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tao, H.-X., Hu, J. & Wu, R.-B. Unleashing the expressive power of pulse-based quantum neural networks. Preprint at https:\/\/arxiv.org\/abs\/2402.02880<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    de Keijzer, R., Tse, O. & Kokkelmans, S. Pulse based variational quantum optimal control for hybrid quantum computing. Quantum 7<\/b>, 908 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Pecci, G., Wang, R., Torta, P., Mbeng, G. B. & Santoro, G. Beyond quantum annealing: optimal control solutions to maxcut problems. Quantum Sci. Technol. 9<\/b>, 045013 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mart\u00edn, E. C., Plekhanov, K. & Lubasch, M. Barren plateaus in quantum tensor network optimization. Quantum 7<\/b>, 974 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Feldman, V. Statistical Query Learning, 2090\u20132095. https:\/\/doi.org\/10.1007\/978-1-4939-2864-4_401<\/a> (Springer New York, 2016).<\/p>\n<\/li>\n

  • \n

    Arunachalam, S., Grilo, A. B. & Yuen, H. Quantum statistical query learning. Preprint at https:\/\/arxiv.org\/abs\/2002.08240<\/a> (2020).<\/p>\n<\/li>\n

  • \n

    Anshu, A. & Arunachalam, S. A survey on the complexity of learning quantum states. Nat. Rev. Phys. 6<\/b>, 59\u201369 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Angrisani, A. Learning unitaries with quantum statistical queries. Preprint at https:\/\/arxiv.org\/abs\/2310.02254<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Wadhwa, C. & Doosti, M. Learning quantum processes with quantum statistical queries. Preprint at https:\/\/arxiv.org\/abs\/2310.02075<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Nietner, A. Unifying (quantum) statistical and parametrized (quantum) algorithms. Preprint at https:\/\/arxiv.org\/abs\/2310.17716<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Nietner, A. et al. On the average-case complexity of learning output distributions of quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2305.05765<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Anschuetz, E. R. & Kiani, B. T. Quantum variational algorithms are swamped with traps. Nat. Commun. 13<\/b>, 7760 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    You, X. & Wu, X. Exponentially many local minima in quantum neural networks. In International Conference on Machine Learning 12144\u201312155. https:\/\/proceedings.mlr.press\/v139\/you21c.html<\/a> (PMLR, 2021).<\/p>\n<\/li>\n

  • \n

    Huang, H.-Y. et al. Learning shallow quantum circuits. In Proc. 56th Annual ACM Symposium on Theory of Computing 1343\u20131351. https:\/\/dl.acm.org\/doi\/10.1145\/3618260.3649722<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Nemkov, N. A., Kiktenko, E. O. & Fedorov, A. K. Barren plateaus are swamped with traps. Phys. Rev. A 111<\/b>, 012441 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Anschuetz, E. R. A unified theory of quantum neural network loss landscapes. Preprint at https:\/\/arxiv.org\/abs\/2408.11901<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Tikku, A. & Kim, I. H. Circuit depth versus energy in topologically ordered systems. Preprint at https:\/\/arxiv.org\/abs\/2210.06796<\/a> (2022).<\/p>\n<\/li>\n

  • \n

    Basheer, A., Feng, Y., Ferrie, C. & Li, S. Alternating layered variational quantum circuits can be classically optimized efficiently using classical shadows. Proceedings of the AAAI Conference on Artificial Intelligence 37<\/b>, 6 (AAAI, 2023).<\/p>\n<\/li>\n

  • \n

    Jerbi, S. et al. The power and limitations of learning quantum dynamics incoherently. Preprint at https:\/\/arxiv.org\/abs\/2303.12834<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Somma, R., Barnum, H., Ortiz, G. & Knill, E. Efficient solvability of Hamiltonians and limits on the power of some quantum computational models. Phys. Rev. Lett. 97<\/b>, 190501 (2006).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Galitski, V. Quantum-to-classical correspondence and Hubbard\u2013Stratonovich dynamical systems: a Lie-algebraic approach. Phys. Rev. A 84<\/b>, 012118 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Anschuetz, E. R., Bauer, A., Kiani, B. T. & Lloyd, S. Efficient classical algorithms for simulating symmetric quantum systems. Quantum 7<\/b>, 1189 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Angrisani, A. et al. Classically estimating observables of noiseless quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2409.01706<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Rudolph, M. S., Fontana, E., Holmes, Z. & Cincio, L. Classical surrogate simulation of quantum systems with lowesa. Preprint at https:\/\/arxiv.org\/abs\/2308.09109<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Fontana, E., Rudolph, M. S., Duncan, R., Rungger, I. & C\u00eerstoiu, C. Classical simulations of noisy variational quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2306.05400<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Lerch, S. et al. Efficient quantum-enhanced classical simulation for patches of quantum landscapes. Preprint at https:\/\/arxiv.org\/abs\/2411.19896<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Bharti, K. & Haug, T. Iterative quantum-assisted eigensolver. Phys. Rev. A 104<\/b>, L050401 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bharti, K. & Haug, T. Quantum-assisted simulator. Phys. Rev. A 104<\/b>, 042418 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gil-Fuster, E., Gyurik, C., P\u00e9rez-Salinas, A. & Dunjko, V. On the relation between trainability and dequantization of variational quantum learning models. Preprint at https:\/\/arxiv.org\/abs\/2406.07072<\/a> (2024).<\/p>\n<\/li>\n

  • \n

    Parrish, R. M., Hohenstein, E. G., McMahon, P. L. & Mart\u00ednez, T. J. Quantum computation of electronic transitions using a variational quantum eigensolver. Phys. Rev. Lett. 122<\/b>, 230401 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jerbi, S., Gyurik, C., Marshall, S. C., Molteni, R. & Dunjko, V. Shadows of quantum machine learning. Nat. Commun. 15<\/b>, 5676 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gyurik, C., Molteni, R. & Dunjko, V. Limitations of measure-first protocols in quantum machine learning. Preprint at https:\/\/arxiv.org\/abs\/2311.12618<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Elben, A. et al. The randomized measurement toolbox. Nat. Rev. Phys. 5<\/b>, 1 (2023).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69<\/b>, 2863 (1992).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lee, S. et al. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nat. Commun. 14<\/b>, 1952 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355<\/b>, 602\u2013606 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sharir, O., Levine, Y., Wies, N., Carleo, G. & Shashua, A. Deep autoregressive models for the efficient variational simulation of many-body quantum systems. Phys. Rev. Lett. 124<\/b>, 020503 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Carrasquilla, J. & Melko, R. G. Machine learning phases of matter. Nat. Phys. 13<\/b>, 431 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Torlai, G. et al. Neural-network quantum state tomography. Nat. Phys. 14<\/b>, 447\u2013450 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proc. Thirteenth International Conference on Artificial Intelligence and Statistics 249\u2013256. https:\/\/proceedings.mlr.press\/v9\/glorot10a<\/a> (JMLR Workshop and Conference Proceedings, 2010).<\/p>\n<\/li>\n

  • \n

    Ioffe, S. & Szegedy, C. Batch normalization: accelerating deep network training by reducing internal covariate shift. In International Conference on Machine Learning 448\u2013456. https:\/\/proceedings.mlr.press\/v37\/ioffe15.html<\/a> (PMLR, 2015).<\/p>\n<\/li>\n

  • \n

    Ba, J. L., Kiros, J. R. & Hinton, G. E. Layer normalization. Preprint at https:\/\/arxiv.org\/abs\/1607.06450<\/a> (2016).<\/p>\n<\/li>\n

  • \n

    Nair, V. & Hinton, G. E. Rectified linear units improve restricted Boltzmann machines. In Proc. 27th International Conference on Machine Learning (ICML-10) 807\u2013814. https:\/\/www.cs.toronto.edu\/~hinton\/absps\/reluICML.pdf<\/a> (2010).<\/p>\n<\/li>\n

  • \n

    Hochreiter, S. The vanishing gradient problem during learning recurrent neural nets and problem solutions. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 6<\/b>, 107\u2013116 (1998).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9<\/b>, 1735\u20131780 (1997).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Narkhede, M. V., Bartakke, P. P. & Sutaone, M. S. A review on weight initialization strategies for neural networks. Artif. Intell. Rev. 55<\/b>, 291\u2013322 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, M., Pennington, J. & Schoenholz, S. Dynamical isometry and a mean field theory of RNNs: gating enables signal propagation in recurrent neural networks. In Proc. 35th International Conference on Machine Learning (eds Dy, J. & Krause, A.) Vol. 80 of Proceedings of Machine Learning Research 873\u2013882. https:\/\/proceedings.mlr.press\/v80\/chen18i.html<\/a> (PMLR, 2018).<\/p>\n<\/li>\n

  • \n

    Xiao, L., Bahri, Y., Sohl-Dickstein, J., Schoenholz, S. & Pennington, J. Dynamical isometry and a mean field theory of CNNs: how to train 10,000-layer vanilla convolutional neural networks. In Proc. 35th International Conference on Machine Learning (eds Dy, J. & Krause, A.) Vol. 80 of Proceedings of Machine Learning Research 5393\u20135402. https:\/\/proceedings.mlr.press\/v80\/xiao18a.html<\/a> (PMLR, 2018).<\/p>\n<\/li>\n

  • \n

    Saxe, A. M., McClelland, J. L. & Ganguli, S. Exact solutions to the nonlinear dynamics of learning in deep linear neural networks. Preprint at https:\/\/doi.org\/10.48550\/arXiv.1312.6120<\/a> (2013).<\/p>\n<\/li>\n

  • \n

    Baird, L. & Moore, A. Gradient descent for general reinforcement learning. Adv. Neural Inform. Process. Syst. 11<\/b> https:\/\/proceedings.neurips.cc\/paper\/1998\/hash\/af5afd7f7c807171981d443ad4f4f648-Abstract.html<\/a> (1998).<\/p>\n<\/li>\n

  • \n

    Salimans, T., Ho, J., Chen, X., Sidor, S. & Sutskever, I. Evolution strategies as a scalable alternative to reinforcement learning. Preprint at https:\/\/arxiv.org\/abs\/1703.03864<\/a> (2017).<\/p>\n<\/li>\n

  • \n

    Standard Deviation. https:\/\/en.wikipedia.org\/wiki\/Standard_deviation#Sample_standard_deviation<\/a>.<\/p>\n<\/li>\n

  • \n

    Zeier, R. & Schulte-Herbr\u00fcggen, T. Symmetry principles in quantum systems theory. J. Math. Phys. 52<\/b>, 113510 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wierichs, D., East, R. D., Larocca, M., Cerezo, M. & Killoran, N. Symmetric derivatives of parametrized quantum circuits. Preprint at https:\/\/arxiv.org\/abs\/2312.06752<\/a> (2023).<\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3, 625\u2013644 (2021). Review on variational quantum algorithms…\n","protected":false},"author":2,"featured_media":186412,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3164],"tags":[3284,3968,15108,74,7030,53,16,15],"class_list":{"0":"post-186411","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-computing","8":"tag-computing","9":"tag-general","10":"tag-information-theory-and-computation","11":"tag-physics","12":"tag-quantum-information","13":"tag-technology","14":"tag-uk","15":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114687561905141018","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/186411","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=186411"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/186411\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/186412"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=186411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=186411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=186411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}