The Fermi-Hubbard model, a cornerstone of condensed matter physics describing the behaviour of interacting electrons, presents a significant challenge for computational methods. Talal Ahmed Chowdhury from the University of Dhaka and University of Kansas, alongside Vladimir Korepin from Stony Brook University, Vincent R. Pascuzzi from IBM Quantum, and Kwangmin Yu, now demonstrate a practical quantum simulation of this model using over 100 qubits on IBM’s superconducting computers. Their work introduces and implements optimised computational techniques, allowing for the precise investigation of electron dynamics and entanglement, even at longer timescales. This achievement showcases the potential of superconducting quantum computers to surpass the limitations of classical methods in tackling complex problems in materials science and establishes a pathway towards understanding strongly correlated electron systems.
Quantum Simulation of Many-Body Systems and Entanglement
Research focuses on leveraging quantum computers to simulate physical systems beyond the reach of classical computers, encompassing many-body physics, high-energy physics, and quantum chemistry. Crucially, this work involves quantum error mitigation and correction to overcome limitations of current, noisy quantum computers. Scientists are developing and implementing quantum algorithms tailored for these simulations, assessing the performance of quantum hardware like IBM Quantum systems. Classical algorithms serve as benchmarks and inspiration for new quantum approaches. Key technologies include quantum computing platforms, variational quantum eigensolvers, and quantum phase estimation.
Quantum error mitigation employs techniques like zero noise extrapolation, dynamical decoupling, and randomized compiling, with pulse-level optimizations further minimizing errors and longer-term goals including full quantum error correction. Researchers are simulating the Hubbard model to understand strongly correlated electron systems and the SYK model, relevant to black hole physics and quantum gravity, by measuring entanglement dynamics. These simulations contribute to understanding quantum materials and exploring the black hole information paradox through the study of the Page curve. Fundamental concepts underpinning this research include entanglement entropy, the Page curve, and the behavior of strongly correlated electron systems.
The time-dependent variational principle guides the evolution of quantum states, while purification techniques reduce the effects of noise. Ongoing challenges include improving noise mitigation techniques, scaling up quantum simulations, developing new quantum algorithms, and enhancing quantum hardware. Verification and validation of simulation results are also critical, representing a vibrant field combining theoretical development, algorithmic innovation, and experimental validation to drive progress towards fault-tolerant quantum computation.
Simulating Fermi-Hubbard Model on Quantum Hardware
Scientists have pioneered a new approach to simulating the one-dimensional Fermi-Hubbard model using IBM’s superconducting quantum computers with over 100 qubits. This work harnesses quantum computation to explore the complex dynamics of strongly correlated electrons, a challenge for classical methods. Researchers mapped the model onto qubits, enabling the simulation of electron interactions and movements, and developed a first-order Trotterization scheme, subsequently optimized with a second-order version, tailored for current superconducting architectures. This innovative method decomposes the time evolution operator into a series of simpler quantum gates, allowing the simulation of the system’s dynamics over time.
The team ensured scalability by maintaining a constant circuit depth at each Trotter step, regardless of the number of qubits employed, crucial for investigating relaxation dynamics and measuring the expectation value of the Néel observable for time-evolved quantum states. Researchers focused on the time evolution of the Néel state to capture relaxation dynamics by tracking staggered magnetization during the simulation. To overcome limitations imposed by qubit coherence and noise, they implemented a combination of quantum error mitigation techniques, including Twirled Readout Error Extinction, dynamical decoupling, Pauli twirling, and zero-noise extrapolation. This significantly enhanced the precision of observable measurements in large-scale simulations, enabling the time evolution of staggered magnetization for systems involving over 100 qubits, exceeding the capabilities of classical exact methods.
Fermi-Hubbard Model Simulated on Superconducting Qubits
Scientists have achieved a significant breakthrough in quantum simulation by successfully modeling the one-dimensional Fermi-Hubbard model using IBM superconducting computers with over 100 qubits. The team implemented both first-order and optimized second-order Trotterization schemes, specifically designed to accommodate the limited qubit connectivity of current superconducting architectures, while maintaining a constant circuit depth regardless of the number of qubits used. Experiments focused on simulating the real-time dynamics of the Fermi-Hubbard model, measuring the expectation value of the Néel observable for time-evolved quantum states. Results demonstrate the ability to accurately track the relaxation dynamics of the system, providing insights into the behavior of strongly correlated electrons. The successful measurement of these expectation values in systems exceeding 100 qubits, particularly at longer time scales with increased entanglement, highlights the potential of superconducting platforms to surpass the limitations of conventional classical approximation methods. The team’s approach ensures scalability, maintaining a constant circuit depth even as the number of fermion sites, and therefore qubits, increases, and enabled the accurate time evolution of staggered magnetization for systems beyond the capabilities of classical exact methods.
Simulating Strong Correlations with Superconducting Qubits
This work demonstrates a successful simulation of the one-dimensional Fermi-Hubbard model using a superconducting quantum computer with over 100 qubits. Researchers developed and implemented both first and second-order Trotterization schemes, specifically optimized for the limited connectivity of current quantum hardware, enabling the measurement of the Néel observable, a key indicator of magnetic order, over extended timescales. The successful measurement of these expectation values, particularly at longer times and with increasing entanglement, highlights the potential of superconducting platforms to surpass the limitations of traditional classical approximation methods in studying strongly correlated electron systems. Future research will likely focus on extending these simulations to larger systems and exploring more sophisticated error correction strategies to further improve accuracy and unlock deeper insights into the behavior of complex materials.
👉 More information
🗞 Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
🧠 ArXiv: https://arxiv.org/abs/2509.14196