Ed Hill
Once the stuff of science fiction, quantum technologies are advancing fast. Individual quantum computers are finding a range of applications, primarily driven by the immense speed-ups they offer over normal computers. And soon the nascent quantum internet should connect those isolated computers together. This blog post starts to think about what this new interconnected quantum world means for the financial system. What could the first ‘quantum markets’ look like? What algorithms and infrastructure might they leverage? And where might the differences from classical markets lie?
What is quantum computing?
In the early 20th century, physicists (the ones in the Oppenheimer film) grappled with a new discipline, quantum physics, which describes the strange behaviour of atoms and electrons and the world of the very small. Superposition – that a quantum system can be in many states at the same time – is a key difference to the world we are used to and is the difference between quantum and normal, ‘classical’, computers I’ll focus on here.
Like those physicists, we can use a thought experiment to understand superposition: imagine you toss a coin and don’t look at it when it lands. We’re used to thinking that if you then look and see ‘heads’, it is because it landed on ‘heads’ and was sat there as ‘heads’ until you looked at it. In the quantum world if we look and see ‘heads’, we instead say that it was in a superposition of ‘heads’ and ‘tails’ at the same time, until we looked and ‘collapsed the superposition’ to ‘heads’.
We will now imagine tossing larger numbers of coins (Figure 1). Start with two. Until we look, they are in a quantum superposition of four (2×2=22) possible combined states: heads-heads, heads-tails, tails-heads and tails-tails. (In a classical world they are not in superposition, but just in one combined state once they land, heads-tails for example, waiting for us to look.) Adding each new coin doubles the number of quantum states, so with 10 coins there are 2x2x2x2x2x2x2x2x2x2 = 210 = 1,024, and with 100 there are 2100 which is about 1 million trillion trillion.
Figure 1: Tossing classical and quantum coins
Notes: When they land, classical coins sit in a single state waiting to be observed; quantum coins are in a superposition of all possible states which only resolves to a single state when we observe them later. Quantum computers use this superposition for their calculations.
A century later, quantum computers have made this thought experiment a reality. The coins are replaced by ‘qubits’ (quantum bits of information like the 0s and 1s in classical computers) implemented using cold ions, superconducting circuits, or photons of light. A quantum computer then attaches a computation to each of those superposed states, so with 100 qubits it can perform 1 million trillion trillion computations at once (a classical computer does the computations a few at a time, which obviously takes far longer). Or, thinking about it another way, it can consider all possible outcomes of 100 coin tosses at the same time and can pick the ones which have certain features – a certain series of heads and tails, or those with more tails in the last 50 tosses if they had more heads in the first 50, for example.
Current quantum computers have problems, however. Parts of the computer and the surrounding environment accidentally ‘peek’ at the superposition before we want to look properly, disrupting it, and corrupting the answer to the calculation. And they are very limited in their number of qubits. Together these problems lead to current quantum computers being called ‘noisy intermediate-scale quantum’ (NISQ). They are also very expensive to buy and to run and so are overwhelmingly accessed remotely via the Cloud, each computer being shared between many users. Together, these factors limit their advantage relative to cheap, error-free, and very large-scale classical computers.
Despite these problems, quantum computers are used, now, for a variety of problems where NISQ is sufficient (some specific examples in finance are referenced below). They are continually improving, driven by these use cases. And there are impressive theoretical possibilities when, and if, post-NISQ (sufficiently noiseless or fault-tolerant, and large-scale) quantum computers can be realised.
Nascent quantum networks also exist and are key to the quantum markets I will discuss below. The internet allowed completely new ways of using the very limited (by today’s standards) computers of the 1980s. Analogously, quantum networks will connect today’s NISQ computers and enable use cases in different directions to those which require commercially viable post-NISQ computing.
Quantum computing can also be used for private communication and computation. While the use of post-NISQ quantum computers to break existing encryption schemes is cited as a key risk around quantum computing, quantum communications themselves are very secure (since peeking at the quantum state being sent disrupts it, allowing eavesdroppers to be detected). Also, Blind Quantum Computation and similar ideas allow a user to detect any snooping or mis-performed calculations when using a remote computer, such as when using the Cloud. By allowing physically remote counterparties to use computers close together, this trustable quantum Cloud would significantly lower the technical barriers to forming quantum networks.
Two examples of quantum markets
I will now give two examples of possible parts of a near-term quantum market – they draw building blocks and commercial motivation from existing processes and problems, but would not work at scale without an interconnected quantum system.
Quantum options for more complete markets
A complete market is a market where assets can be priced and risks insured in every state of the world. More complete markets should be more efficient. Indeed, the development of options and other financial derivatives was intended to make markets more complete, and there is continuing appetite for more exotic instruments, even with their associated costs and frictions.
Financial firms’ internal models are becoming more advanced and ‘complete’, able to consider and value more states of the world and more possible combinations of events. But they are still used to inform positions on the relatively tiny number of things tradable in the current ‘less complete’ market. The huge flows of information quantum networking enables would allow firms to communicate their views on any complex combination of the events they are considering.
Additionally, the firms’ internal models are near-term targets for using quantum computers since they can consider all possible combinations of some events (the superposition of all possible series of coin tosses) much faster than classical ones. Connecting these new, quantum, models over a quantum network would allow superpositions encoding firms’ views on any possible combinations of the events to be priced by other firms as ‘quantum options’ in an even more complete, and necessarily wholly quantum, market.
Enabling efficient and novel payments systems
Recent work has shown that NISQ computers can solve existing, complex, scheduling problems in high-value payments systems (which settle transactions between large financial institutions) better than classical algorithms under real-world constraints.
However, quantum networks would allow a fundamental change to what a payment means, allowing counterparties to communicate sophisticated, conditional, strategies to the payments system. Imagine that instead of simply saying ‘buy’, a party can say ‘buy, if…’ certain conditions on other simultaneous payments or events are fulfilled – like chains when houses are bought and sold, but much more complex and interrelated. A quantum computer would then allow the problem of which combination of instructions should proceed to be solved.
Smart contracts, flash loans in crypto/DeFi, and discussions around conditional payments in digital currencies show the burgeoning demand for these facilities, while quantum game theory highlights the novel behaviours which emerge when quantum strategies are combined in this way, even in simpler set-ups.
Discussion
These examples, building on existing applications which involve considering and valuing complex combinations of events, are natural areas for early adoption of quantum computing. Perfection is not required and even NISQ computers can drive value, initially by optimising interactions through a classical market.
However, introducing quantum networks between those computers would enable a ‘quantum market’ and give an outlet for their huge computational power. Rather than being boxed in they could then interact directly with each other through a quantum market infrastructure enabling the kinds of complex and conditional strategies discussed above.
In the short term, the adoption of quantum technologies could well be driven by the benefits for individual institutions of this more ‘complete’ market, including the ability to efficiently insure risk and exploit information. Inherently secure quantum communications and trustable Cloud computation can lower barriers to entry by allowing the commercial use of shared hardware and enabling a surrounding Fintech ecosystem.
As quantum markets develop, there would be scope for high-level changes to how the market functions. Initially, these might draw directly on the new financial market infrastructure (with its privacy and verifiability allowing decentralised quantum markets on both the retail side and for institutions) and participants’ ability to simply express and value complex financial instruments. Second-round effects could involve the use of quantum machine learning and artificial intelligence (ML and AI) on the quantum data the new markets produce.
Overall, this begins to paint a very different picture to a classical market: huge amounts of information and computation flow in wholly-quantum systems, embedded in a new commercial landscape of hardware and service providers. This image, and its trajectory, will become clearer as quantum computers, networks and other technologies continue their journey from science fiction to reality.
Ed Hill works in the Bank’s Advanced Analytics Division. The author would like to thank Mohammed Gharbawi who works in the Bank’s Fintech Hub.
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