Hello World Moment for the Quantum Actuary
Description of key concepts in Quantum Computing[1]
Every now and then we come across news describing latest milestone achieved in quantum computing, for example Google achieving quantum supremacy, making time crystals and so on. Even though the hardware challenges are extremely hard to date, these progresses shed hope that soon like within a decade we might have quantum computers as accessibly as we have classical computers right now. It is still up to each of us and our mindset how early we anticipate ‘Hello World’ moment for quantum computing to come (sooner or later? How soon? How later?).
It was Richard Feynman who proposed in the early 80s that if we want to simulate a quantum system, we will need a quantum system to do it with. “I’m not happy with all the analyses that go with just the classical theory, because nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical,” he concluded, in his inimitable way. Classical computers, as he deemed what everyone else just called computers, were insufficient to the task[1] . The next stage of realizing the vision of Alan Turing for a universal computing machine is a continuous progression from vacuum tubes to hand-built transistors to the densely packaged chips to now quantum computers in the foreseeable future.
In highlighting key concepts of quantum mechanics, definitions are usually already covered in any article that handles quantum computing topic, and so it is better to drink straight from the hose which is some excerpts from Chapter 37 ‘Quantum Behavior’ from my favorite book Feynman Lectures on Physics Volume I. This describes quantum mechanics as a whole as well as Heisenberg’s Uncertainty principle.?
As Feynman once wrote, quantum mechanics "describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So, I hope you can accept nature as She is-absurd."
The history of the strange world of quantum mechanics can be traced back to Young’s double-slit experiment demonstrating the wave nature of light in 1801[1] . During the 1920s, the Copenhagen interpretation of quantum mechanics was devised, largely by Bohr and Heisenberg, and remains the most common interpretation. According to this Copenhagen interpretation, microscopic quantum objects do not have definite properties prior to being measured, and quantum mechanics can only predict the probability distribution of a measurement’s possible results, such as its location. The wave function ψ is a mathematical representation of the quantum state of a quantum system and the probabilities for the possible results of measurements can be derived from it. The Schr?dinger equation determines how wave functions evolve over time. Upon measurement of the object, the wave function collapses into a single state[2] . Quantum theory is one of the significant concepts in modern physics, which was proposed by Max Planck in 1900. Many phenomena in nature and society also show the characteristics of "quantization", including the insurance market.
Probability is the cornerstone in the actuarial calculation while the quantum mechanics could give different perspectives on the probability[1] . Just like force, mass, acceleration, energy, and momentum in classical mechanics are continuous deterministic variables, actuarial variables, such as premium, claim, profit, expense, and distribution earning, are also considered to be continuous deterministic variables. In quantum theory, when several particles interact with each other, due to the properties of each particle having been integrated into a whole property, it is impossible to describe the properties of each particle alone, but only the properties of the whole system, which is called quantum entanglement. In the insurance field, there also exists the phenomenon of quantum entanglement. The reason why insurance can be priced and provide risk protection is not based on the individual risk probability, but the overall risk probability. In the face of a complex and changeable quantized insurance market, traditional actuarial theory may lack effective explanatory and predictive power. Each policy can be regarded as the smallest unit and cannot be separated continuously, so it can be said that each policy is similar as the quantum and have the quantum property.
Quantum computers utilize Qubit instead of bit in classical computer. Qubit have superimposition so that both 1 and 0 can occur simultaneously to speed up calculations. Parallel computing is given a huge boost due to entanglement as well. quantum entanglement is where pairs or groups of quantum particles are linked so that each particle cannot be described independently of the others, even when the particles are separated by a large distance; opposite ends of the universe for example which negates the general relativity point that nothing can travel faster than the speed of light. This is why Einstein called this “spooky action at a distance” and it’s the theoretical basis for quantum teleportation. The practical implication of this “spooky action”[1] is that, unlike conventional computers where bits and processing power are linearly related (doubling the number of bits results in double the processing power, simplistically), quantum computers grow exponentially more powerful with each qubit added—a one-qubit computer acts like two bits, a two-qubit computer acts like four qubits, four qubits act like 16, and so on.
Classical computers are built around transistors that, by holding or vacating a charge, signify either a 1 or a 0. By linking these transistors together into more complex formations they can represent data, or transform and combine it through logic gates like AND and NOR. With a complex language specific to digital computers that has evolved for decades, we can make them do all kinds of interesting things.
Quantum computers are actually quite similar in that they have a base unit that they perform logic on to perform various tasks. The difference is that the unit is more complex: a qubit, which represents a value in a higher mathematical space than simply “on” or “off.” Their state may be thought of as a location on a sphere, a point in 3D space. The logic is also more complicated, but still relatively basic (and helpfully still called gates): That point can be adjusted, flipped, and so on. Yet the qubit when observed is also digital, providing what amounts to either a 0 or 1 value. By virtue of representing a value in a richer mathematical space, these qubits and manipulations thereof can perform new and interesting tasks, including some which, as Google shows, we had no ability to do before.
there are, in fact, so many factors, and such mysterious ones, that Feynman made the call that at some point you wouldn’t be able to account for them all. And at that point you would have entered the realm where only a quantum computer can provide those results — the realm of “quantum supremacy.”[1]
The reason why quantum computing hasn’t yet become available in everyday life is due to hardware challenges. Qubits that are entangled are said to be in a state of “coherence,” and they can lose their coherence easily (called decoherence). Decoherence eliminates the scaling effects that make quantum computing so powerful and the computer’s results unusable. Decoherence is caused when the large outside world enters the small insulated world of the entangled qubits. Vibrations, temperature fluctuations, light and other environmental interference are all culprits, so quantum computers are kept in very cold and heavily managed environments to insulate them from these effects. Increasing the number of qubits and the length of time they are held in coherence is the key barrier to the growth of quantum computing technology.
Quantum modeling also requires a different breed of algorithms and this is where actuaries can face the steepest learning curves because while they are not responsible for working on the hardware side of quantum, they are responsible for modeling which requires algorithms. And quantum algorithms are very different from the type of models that we are used to. Controlling qubits requires new ways of designing computing algorithms as well. Traditional computing uses three basic “gate operations” (AND, OR and NOT) to replicate any function that turns multiple inputs into a single output (note that in practice, simplifications of the combination of these gates are used more efficiently than the three basic operators themselves). These gates are the physical building blocks of a computer—the electrical pathways on a central processing unit (CPU) are a series of billions of transistors that perform these gate operations.
Quantum computing involves a much richer set of basic gate operations—many more than three. Like classical computing, understanding the theoretical operation of the quantum gates is a math exercise. However, unlike classical computing, the practical operation of quantum gates is not as well understood, because the physical building blocks performing the gate operations are much more complex. Determining how to optimally combine quantum gate operations is an open area of research.
Applications of quantum computing
Given how fast technology is moving in the Fourth Industrial Revolution, from blockchain to AI to agritech/insuretech etc., It is easy to think that we have solved many of our problems using power of classical computers and that scope for quantum computing is there only for the big problems and not for every day life or for every day business/company. However, this is not so. We have only begun to scratch the surface of our problems, face overwhelming challenges and need herculean level of breakthroughs to arrive at the solutions that we desire. Reality is highly complex, has higher order nonlinear effects and the world is VUCA; volatile, uncertain, complex, ambiguous. Some instances are:
1.?????Full self-driving autonomy is an incredibly difficult task because every foreseeable topological data of the environment has to be mapped in instantly whether its night or day, winter or summer, rural or urban, developed or developing, etc.
2.?????The human brain is arguably the most complex unit in the universe and trying to augment that through BCIs has almost unfathomable engineering challenges.
3.?????Space has extremely hostile conditions and again engineering nightmares are commonly encountered by the people trying to make us humans a space faring species.
4.?????Also, as astrophysicists and theoretical physicists will testify, we have hardly scratched the surface of understanding the cosmos of which we are a part of. We don’t even have a “theory of everything” yet that combines general relativity of the macro structure to the quantum mechanics of the infinitesimally small micro-structure. Applying quantum mechanics to the universe (quantum cosmology leading to multiverses) or supersymmetry of Abdus Salam doesn’t have the theory of everything yet too.
5.?????Genetic engineering, longevity research, geo-engineering building quantum computers, nuclear fusion all have to contend with similar confounding perplexities.
6.?????We have to face human-made challenges like climate change, wars, poverty, our collective irrationalities, etc.
7.?????Unintended consequences of exponential technologies that have potential for catastrophic consequences.
8.?????We haven’t mapped most of world’s oceans. Depths are unknown to us 95% of ocean is not mapped.
9.?????We talk of conquering death in longevity tech but we can’t even find cure for a virus like COVID19 yet
10.??The earth’s core is about 2,900 Km below surface. Compared to that, our deepest hole is just 12 Km Kola Superdeep Borehole in Russia?
In face of these challenges and our desired solutions to these (we want to solve traffic issues, cure a lot of diseases, have settlements in Moon and Mars, explore all of seas etc.), the more solutions we can have the better whether through improvement in social connections, business models or in tech such as quantum computing. We need all the bandwidth that we can arrange.?
When writing on the applications of quantum computing, it is usually emphasized that this will open doors unknown so far. But it’s important to understand a nuance here, our problems have been always extremely huge in scope and we have always relied on practical patchwork/shortcuts to arrive at solutions. So the scope of problem will remain the same but it is our ability of arriving at solutions that will change. For example, since 1700s we have tried to quantify mortality risk so that we can load it for expenses and profits and charge that as premium for providing life protection insurance. At that time, we had no calculators so date of deaths was painstakingly taken from graveyards to arrive at a mortality table. That lead us to know the average mortality probability of a given life. In 1950s we hear that there were clunky heavy machines that would set the life reserves. Then came calculators and spreadsheets and our computation capacity increased enormously at a faction of the given time. However, we still rely on limited number of rows and columns and factors to calculate mortality risk given our computer’s limitations. Once quantum computer becomes a reality and merges with other tech components such as big data and machine learning, we can get almost unlimited amount of different types of data and use that to determine mortality risk in more surgical way and in more permutations and combinations than possible currently. The original scope was and still remains the same over the centuries which is quantifying mortality risk but it is the scope of our solution formulation that keeps improving.
Given this, every application will benefit from quantum computing. All problems are huge in scope from asset management to insurance to biology to whatnot, and there is modeling for so many problems in these areas, modeling will face a paradigm shift to determine better solutions. Hence, it is difficult to say that any area will not benefit from quantum computing.
Within insurance, our ability to dimensionalize risk will shoot to the moon. ?The preferred method for creating simulations today to analyze impact of risk and uncertainty in financial models is Monte Carlo simulation but that will be replaced by quantum simulation and even in present time, IBM published research recently that used quantum algorithms to outcompete conventional Monte Carlo simulations for assessing financial risk[1] :
Monte Carlo simulations are routinely employed to compute frequently-used risk measures like the Value at Risk (VaR) or the Conditional Value at Risk (CVaR, also called Expected Shortfall or TVaR Tail Value at Risk). The Monte Carlo method’s convergence rate (i.e.: the rate at which the desired accuracy is approached) scales as the inverse of the square root of the number of samples (one sample corresponds to one set of parameter values). In contrast, the researchers’ quantum algorithm converges at a rate proportional to the inverse of the number of samples which represents a quadratic speed-up with respect to the Monte Carlo method.
Using Monte Carlo simulations, the risk assessment computation for large portfolios is often an overnight task. In the worst case, the computing time can even extend over days. The quadratic speedup provided by quantum computing may reduce calculation time from overnight to near-real time or from days to hours, respectively. Although it might take a few years until the hardware to realize this speed-up becomes available at the required scale, the potential impact would be enormous.
The researchers went on to show how our algorithm can be applied to the task of pricing an asset using real quantum hardware. We chose the simple model of a treasury bill whose value depends only on the interest rate. This simple experiment on 5 qubits confirmed the theoretical convergence rate of the algorithm and underlines its potential advantage compared to classical Monte Carlo methods.
In order to further demonstrate the capabilities of our algorithm, the researchers used classical simulations of quantum hardware to show that it can also be applied to speed up the computation of risk measures of a simple two-asset portfolio. Nevertheless, they also noticed that to achieve quantum advantage in a real-world scenario, the quality of current quantum hardware needs to be improved. Errors arising from the limited coherence time and cross-talk when measuring the states of qubits need to be substantially suppressed. Furthermore, the number of qubits must be increased.
Optimization problems are all around us and we have to keep them to manageable levels through various shortcuts otherwise the complexity would quickly explode and our classical computers would shut down. With quantum computing methods such as quantum annealing, we can increase the scope of depth considered in optimization problems without worrying of it blowing up in our face. Quantum annealing is well suited for solving optimization problems. In other words, the approach can quickly find the most efficient configuration among many possible combinations of variables. D-Wave offers a commercially available quantum annealer that uses the properties of qubits to find the lowest energy state of a system, which corresponds to the optimal solution for a specific problem that has been mapped against this system. For example, D-Wave says that Volkswagen used its quantum annealer to make its paint shops more efficient by figuring out how to reduce color switching on its production line by more than a factor of 5. Meanwhile, Canadian grocer Save-On-Foods claims that D-Wave’s system helped it reduce the time taken to complete a recurring business analytics task from 25 hours per week to just 2 minutes.
Financial services have a history of successfully applying physics to help solve its thorniest problems. The Black Scholes-Merton model, for example, uses the concept of Brownian motion to price financial instruments – like European call options – over time. Econophysics is a whole field dedicated to combining physics with economics. Thermodynamics energy modeling, law of conservation and so much more can be applied to modeling in economics, finance and insurance. This is my hope that we are able to merge my two passions over my lifetime; not just quantum but overall physics as well with actuarial science modeling. Insurance modeling both on the assets and liabilities side is ripe for disruption by quantum modeling.?
Already big tech has quantum hardware in a centralized location and few qubits are available online for free on the cloud to carry out quantum simulations and optimization. Fuzzy logic also has similarities with quantum computing and can be used for modeling as simulations. In fuzzy set theory, an object can partially belong to a fuzzy set. A statement can be both partially true and false. So, superimposition Schrodinger’s cat is alive and dead at the same time and is similar to fuzzy logic (but not exactly the same; differences exist). In simple terms, without an observer, the item has probability of existing in multiple states but that collapses to a single state when observer observes it[1] .
Which Quantum cat is your favorite? Schrodinger’s cat or Cheshire cat[1] ? Neither, the winner is our photogenic Moezza (our in-house furball Persian kitten in author’s real life)!
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Quantum mechanics was developed when it was realized that energy comes in discrete amounts, called quanta, instead of continuously. The same is true for money—it comes in discrete packets, such as a paycheck or premium for an insurance policy.
Some more ways to connect quantum mechanics to finance/economics/insurance concepts are[1] :
·???????Money Vs Value: In classical economics, money is used as a simple tool to represent value and is seen as an easy way to broker trade. In quantum economics, money and value are two different concepts. Value is a fuzzy concept represented by the state of the qubit. Before a transaction, value is in a superposition of trade and no trade. It is only at the time of transaction that money is used as the measurement device to determine the actual observed worth of an item. This is especially true for illiquid instruments. What is the value of an illiquid asset, a reinsurance treaty or a block of variable annuities? The instruments have a deterministic evolution through their contracts, which allows a probability to be put on their value. The money required to purchase the instrument is indeterministic until a transaction is completed.
·???????Financial Entanglement: In quantum finance, the relationship between money and credit is a form of social entanglement, explicitly encoded using contracts. This entanglement, when aggregated, can affect the entire financial system. It is analogous to entangled spin of two electrons. Consider a loan contract between a debtor and creditor with each party represented as a qubit. If we look at the state of each party, then they are both in a superposition of default and no default. If the debtor changes state and defaults, then this action will have an immediate impact on the state of the creditor even though the creditor was not directly manipulated or notified of the default. The debt/credit relationships throughout the economy create an intricate web of entanglement, which was on full display during the 2008 housing crisis
·???????Quantum Reinsurance: Reinsurance can be viewed anecdotally to the debt and credit of the banking system, where the creditor is the reinsurance organization and the debtor is the ceding company. The ceding company during the life of the treaty can be in a superposition of solvency and insolvency. This creates the intricate web of entanglement between the reinsurer and the ceding company. Even with information about both companies, the more entangled the companies, the less information there is about the individual independent entities.
·???????Quantum Insurance: Representing insurance through entanglement can be taken a step further. What if the risks of the ceding company were modeled as individual qubits in superposition? For example, mortality is in a superposition of dead and alive, just like Schrodinger’s cat. Morbidity, lapse, assets, reinvestment and disintermediation are in a superpositions of sick and not sick, pay and not pay, default and not default, above rate of return and below rate of return, and surrender and not surrender, respectively. This means an insurance organization is an entangled system of risks. It is exceedingly difficult to segregate risks into independent buckets because they are so intertwined. Using a quantum approach to risk management may make the exercise easier and more intuitive because risks appear to be fuzzy instead of mutually exclusive.
Now that we can increase the variety of data, algorithms and computing power due to quantum computing, we can answer more questions in the same given time and open up avenues to which we were shy to wander before. This opens up unexplored avenues as well as better insights into the same existing problems that we have been tackling with historically.
There are many such examples. Cyber insurance is an area that does not respect boundaries like climate change and pandemics and is a collective risk entangled with our inter-connected modern world and its manufactured risks. For such risks, assuming simplifying assumptions like ‘ceteris paribus’, ‘future will be similar to history’ and assume only 4 variable in our model doesn’t make much sense. Web3.0 and metaverse is another example which requires fast intensive computing in real time and is too vast to be modeled using our traditional modeling tools. 3D printing and material sciences requires testing of almost infinite permutations and combinations but if quantum computers can open these, it can mean personalized materials can be made by individuals that are not seen in nature and can change the way we make our tools and buildings. Genomic testing can be done to reveal hidden secrets inside DNA and drugs and vaccines can be developed fairly quickly and cheaply (especially the latest drugs like biologic drugs making Brain Computer Interfaces etc.; in-fact there is even a field quantum biology).
A lot of real-world phenomenon such as weather forecast or traffic management or autonomous vehicles driving software have small starting points that become very huge very quickly (this is known as butterfly effect) and suffer from skewed imbalanced data but if quantum computing can increase the data that we can model, the variables and type of datasets, our predictive analytics can churn out more realistic forecasts as well.
Page 90 of 353 from Michio Kaku ‘Physics of the Impossible’ also discusses quantum computers and sheds further light on this. “Quantum computers may one day replace the familiar digital computer sitting on our desks. In fact, the future of the world's economy may one day depend on such computers, so there is enormous commercial interest in these technologies. One day Silicon Valley could become a Rust Belt, replaced by new technologies emerging from quantum computing”.
“Quantum teleportation and quantum computers both share the same fatal weakness: maintaining coherence for large collections of atoms. If this problem can be solved, it would be an enormous breakthrough in both fields”.
“If we can solve the problem of coherence, not only might we be able to solve the challenge of teleportation; we might also have the ability to advance technology of all kinds in untold ways via quantum computers”.
Conclusion
While broad commercial applications may remain several years away, quantum computing is expected to produce breakthrough products and services likely to successfully solve very specific business problems within three-to-five years[1] .
There is no reason to wait for quantum computers to be invented and wait for their ‘Hello World’ moment. We need to start training as actuaries now to enter the quantum realm so that we can take advantage of it when it comes available. When it comes and if we haven’t done our homework at that time, catching up then might prove to be very difficult. Within few years we might have to modify this iconic statement of Frank Redington “An actuary who is only an actuary is not an actuary at all” to “An actuary who does not recognize the quantum realm in his practitioner’s toolkit is not an actuary at all”.
If there is a technology that allows to us solve the same problems in a fraction of the time it takes and with a fraction of the resources, shouldn't we be exploring that technology to the fullest of its possibilities? The quantum industry pace is accelerating. Some people say it’s three years away, others argue it is five or seven. Every week there is a major milestone in the field (either from basic research, engineering or company launches) so it appears that within a few years our industry will be fully disrupted[2] . So even if quantum computers are years away, we need to prepare for it from today because by the time the technology will be invented, at that time it will be too late to play catch-up. We need not be fooled by the linearity of progress as the nature is such that there will be no likely progress but suddenly a huge paradigm shifting changing everything. Change is coming quickly. Once key achievements in quantum computing are unlocked, the gap between early adopters and laggards will widen quickly.
“It looks like nothing is happening, nothing is happening, and then whoops, suddenly you’re in a different world.” — HARTMUT NEVEN, DIRECTOR, GOOGLE QUANTUM ARTIFICIAL INTELLIGENCE LAB.
“We believe we’re right on the cusp of providing capabilities you can’t get with classical computing. In almost every discipline you’ll see these types of computers make this kind of impact.” – VERN BROWNELL, FORMER CEO, D-WAVE SYSTEMS.
[1] Flother, Frederik, Dario Gil; Lynn Kesterson-Townes, Jesus Mantas, Chris Schnabel, Bob Sutor. “Coming soon to your business – Quantum Computing.” IBM Institute for Business Value. November 2018. https://www.ibm.com/thought-leadership/institute-business-value/report/quantumstrategy; Lacan, Francis, Stefan Woerner, Elena Yndurain. “Getting your financial institution ready for the quantum computing revolution.” IBM Institute for Business Value. April 2019. https://www.ibm.com/downloads/cas/MBZYGRKY
[1] https://www.nat ure.com/articles/nindia.2020.104#:~:text=In%20quantum%20physics%20parlance%2C%20separating,will%20leaving%20its%20weak%20grin ; image source: https://www.shutterstock.com/search/cheshire-cat
[1] But then are we the object of observation? Or are we the observers? Chung Tzu Butterfly dream describes the point perfectly. The master has a dream that he is a butterfly with no individual human consciousness and is just fluttering around and it felt so real. After waking up from the dream, the master ponders that was he having the dream as human that he was a butterfly? Or was the butterfly having a dream now that it is a human? For further reference on what we can learn from the universe as social insights as well as meditation as an individual please refer to Astonishing Astrophysics: How Our Universe is Stranger than Fiction- Part 2 and Astonishing Astrophysics: How Our Universe is Stranger than Fiction- Part 3 .
[1] For further details on double slit experiment, delayed choice experiment and quantum entanglement please refer to: https://medium.com/@SyedDanishAli/astonishing-astrophysics-how-our-universe-is-stranger-than-fiction-3d080e3a137f#.shs7z3nmv ?
[2] https://www.actuaries.org.uk/system/files/field/document/assetliability-modelling-in-the-quantum-era.%20to%20use.pdf
Actuarial Professional, Data Scientist, Futurist
1 年Despite continuing development in the field of classical computers, we are approaching a technological barrier The technological barrier and difficulties in handling complex problems in conventional computers encourages us to focus on quantum computing and emerging technologies.?Microsoft's Quantum Developers Kit (QDK) can be used by actuaries to develop quantum-based financial models, potentially leading to improved accuracy and efficiency when predicting risks associated with various types of insurance policies.?Quantum entanglement can be incredibly useful for actuaries when it comes to modeling risk. In essence, it allows for particles to become interconnected through their interactions with each other, even when separated by large distances. This means that non-linear relationships between different variables can be taken into account in the model. This is especially important when dealing with complex systems like insurance where multiple factors interact and influence the outcome of a decision or situation. Actuaries are able to build more accurate models which take into account these hidden relationships and ultimately lead to better decision making within the industry.
Assistant Vice President Product Development
1 年You should check out David Orrell book "Quantum Economics and Finance" and his other paperback book Economyths on the relationship between Quantum mechanics and the money supply. Given the subject matter, they are relatively easy reads.