Quantum computing isn’t just for theoretical physicists or software engineers – it opens up an entirely new horizon for actuaries. Picture a policyholder caught in a Schrödinger’s cat-like paradox: simultaneously alive and dead until an event is observed. Or imagine pricing an annuity across a tapestry of parallel universes. Much like theoretical physicist Richard Feynman’s ideas about simulating natural phenomena with quantum mechanics, actuaries, too, can ‘quantise’ their work.

Here, we’ll take a brief look at how quantum computing can be applied to actuarial work – flipping ‘quantum coins’ that leverage superposition and entanglement (the physics terms), running a joint survival calculation on real quantum hardware, and even valuing an annuity using quantum logic.

Schrödinger’s policyholder

In 1935, physicist Erwin Schrödinger challenged the Copenhagen interpretation of quantum mechanics via a thought experiment. Under it, a system exists in a superposition of all possible states until it is measured. Schrödinger’s cat, enclosed in a box with a radioactive atom, a Geiger counter, a hammer and poison, finds itself both alive and dead simultaneously – until someone looks inside the box. In mathematical terms, the state of Schrödinger’s cat can be written in bra-ket notation as

|Cat> = √(1-p) |Alive> + √p |Dead>

where p is the probability of radioactive decay. If we replace the cat with Alice, a 50-year-old term assurance policyholder, we get

|Alice> = √(1-q50) |Alive> + √q50 |Dead>

where q50 is the one-year mortality probability at age 50. 

Beneath the quantum veneer lies a familiar binomial distribution. Schrödinger’s box is ultimately a reflection of standard actuarial risk, in quantum guise.

Schrödinger’s box is ultimately a reflection of standard actuarial risk, in quantum guise

Actuaries’ quantum coin

We often take random number generators (such as Excel’s ‘RAND()’ function) for granted as a source of randomness, but they are pseudo-random mechanisms that cycle through fixed seeds. While the storage of one probability value in double precision requires 64 bits, the Mersenne Twister algorithm used for RAND()maintains an internal state array of nearly 20,000 bits. 

Unlike classical simulation, which relies on pseudo-random number generation, quantum computing naturally embeds probabilities (such as mortality rates) into qubits (the quantum equivalent of the data unit ‘bit’, short for binary digit, in classical computing), where randomness is a fundamental part of physics.

To see how we can encode probabilities into qubits, consider Alice’s state:

|Alice> = √(1-q50) |Alive> + √q50 |Dead>

which generalises to: 

|Ψ> = cos(θ/2) |0> + e^(i*φ) sin(θ/2) |1>

Bloch spheres (Figure 1) provide a geometric representation of a qubit’s quantum state. Any quantum state can be represented as a point on the surface, and can be located with two angles, θ and φ – like specifying longitude and latitude for geolocation. By adjusting these angles (using sin(θ/2) = √p), we can encode probabilities (for example q50) directly into quantum states. This goes beyond a ‘coin toss’ analogy, leveraging the full sphere of possibilities rather than two binary extremes. We can easily implement this in Python using the Qiskit framework (Figure 2).