Quantum computing isn\u2019t just for theoretical physicists or software engineers \u2013 it opens up an entirely new horizon for actuaries. Picture a policyholder caught in a Schr\u00f6dinger\u2019s 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\u2019s ideas about simulating natural phenomena with quantum mechanics, actuaries, too, can \u2018quantise\u2019 their work.<\/p>\n
Here, we\u2019ll take a brief look at how quantum computing can be applied to actuarial work \u2013 flipping \u2018quantum coins\u2019 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.<\/p>\n
Schr\u00f6dinger\u2019s policyholder<\/strong><\/p>\n In 1935, physicist Erwin Schr\u00f6dinger 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. Schr\u00f6dinger\u2019s cat, enclosed in a box with a radioactive atom, a Geiger counter, a hammer and poison, finds itself both alive and dead simultaneously \u2013 until someone looks inside the box. In mathematical terms, the state of Schr\u00f6dinger\u2019s cat can be written in bra-ket notation as<\/p>\n |Cat> = \u221a(1-p) |Alive> + \u221ap |Dead><\/p>\n where p is the probability of radioactive decay. If we replace the cat with Alice, a 50-year-old term assurance policyholder, we get<\/p>\n |Alice> = \u221a(1-q50) |Alive> + \u221aq50 |Dead><\/p>\n where q50 is the one-year mortality probability at age 50.\u00a0<\/p>\n Beneath the quantum veneer lies a familiar binomial distribution. Schr\u00f6dinger\u2019s box is ultimately a reflection of standard actuarial risk, in quantum guise.<\/p>\n Schr\u00f6dinger\u2019s box is ultimately a reflection of standard actuarial risk, in quantum guise<\/p>\n<\/blockquote>\n Actuaries\u2019 quantum coin<\/strong><\/p>\n We often take random number generators (such as Excel\u2019s \u2018RAND()\u2019 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.\u00a0<\/p>\n 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 \u2018bit\u2019, short for binary digit, in classical computing), where randomness is a fundamental part of physics.<\/p>\n To see how we can encode probabilities into qubits, consider Alice\u2019s state:<\/p>\n |Alice> = \u221a(1-q50) |Alive> + \u221aq50 |Dead><\/p>\n which generalises to:\u00a0<\/p>\n |\u03a8> = cos(\u03b8\/2) |0> + e^(i*\u03c6) sin(\u03b8\/2) |1><\/p>\n Bloch spheres (Figure 1) provide a geometric representation of a qubit\u2019s quantum state. Any quantum state can be represented as a point on the surface, and can be located with two angles, \u03b8 and \u03c6 \u2013 like specifying longitude and latitude for geolocation. By adjusting these angles (using sin(\u03b8\/2) = \u221ap), we can encode probabilities (for example q50) directly into quantum states. This goes beyond a \u2018coin toss\u2019 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).<\/p>\n","protected":false},"excerpt":{"rendered":"Quantum computing isn\u2019t just for theoretical physicists or software engineers \u2013 it opens up an entirely new horizon…\n","protected":false},"author":2,"featured_media":88500,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3164],"tags":[3284,42153,42154,53,16,15],"class_list":{"0":"post-88499","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-computing","8":"tag-computing","9":"tag-general-features","10":"tag-life-insurance","11":"tag-technology","12":"tag-uk","13":"tag-united-kingdom"},"share_on_mastodon":{"url":"","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/88499","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=88499"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/88499\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/88500"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=88499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=88499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=88499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n