**Ed Hill**

Quantum technologies, once the stuff of science fiction, are advancing rapidly. Individual quantum computers are finding a variety of applications, driven primarily by the immense speeds they offer compared to regular computers. And soon, the nascent quantum Internet should connect those isolated computers. 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 could they take advantage of? And where could the differences with classic markets lie?

**What is quantum computing?**

At the beginning of the 20th century, physicists (those in Oppenheimer’s film) were faced with a new discipline, quantum physics, which describes the strange behavior 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 in the world we are used to and it is the difference between quantum and normal, “classical” computers that I will focus on here.

Like those physicists, we can use a thought experiment to understand superposition: Imagine that 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 “faces,” it’s because it landed on “faces” and stayed 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 look and “collapse the superposition” into “heads.”

Now we will imagine throwing a larger number of coins (Figure 1). Start with two. Until we look, they are in a quantum superposition of four (2×2=2^{2}) possible combined states: heads-heads, heads-tails, tails-heads and tails-tails. (In a classical world they are not in superposition, but simply in a combined state once they land, heads or 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 = 2^{10} = 1,024, and with 100 there are 2 left^{100} which is approximately 1 million billion billion.

**Figure 1: Launch of classical and quantum coins**

Notes: When landed, classic coins remain in a single state waiting to be observed; Quantum coins are in a superposition of all possible states that only resolves to a single state when we look at them later. Quantum computers use this superposition for their calculations.

A century later, quantum computers have made this thought experiment a reality. Coins are replaced by ‘qubits’ (quantum information bits like 0s and 1s in classical computers) implemented using cold ions, superconducting circuits or photons of light. A quantum computer then attaches a calculation to each of those superimposed states, so that with 100 qubits it can perform 1 million trillion trillion calculations at a time (a classical computer does the calculations a few at a time, which obviously takes much longer). Or, thinking about it another way, you can consider all the possible outcomes of 100 coin tosses at the same time and choose those that have certain characteristics: 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.

However, current quantum computers have problems. Parts of the computer and the surrounding environment accidentally “look” at the overlay before we want to see it properly, disrupting it and corrupting the response to the calculation. And its number of qubits is very limited. Together, these problems lead to current quantum computers being called “noisy intermediate-scale quantum” (NISQ). They are also very expensive to purchase and operate, so they are overwhelmingly accessed remotely via the cloud, with each computer shared among many users. Together, these factors limit its advantage relative to cheap, error-free, large-scale classical computers.

Despite these problems, quantum computers are currently used for a variety of problems for which 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 for when and if post-NISQ (sufficiently quiet, fault-tolerant, and large-scale) quantum computers can be created.

There are also nascent quantum networks and they are key to the quantum markets that I will discuss below. The Internet enabled entirely new ways of using the very limited (by today’s standards) computers of the 1980s. Analogously, quantum networks will connect current NISQ computers and enable use cases in directions other than those requiring post-computing. Commercially viable NISQ.

Quantum computing can also be used for private communications and computing. 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 (as taking a look at the quantum state being sends interrupts it, allowing spies to be detected). Additionally, Blind Quantum Computing and similar ideas allow the user to detect any eavesdropping or miscalculations when using a remote computer, such as when using the Cloud. By allowing physically remote counterparts to use nearby computers, this reliable quantum cloud would significantly reduce the technical barriers to the formation of quantum networks.

**Two examples of quantum markets**

I will now give two examples of possible parts of a near-term quantum market: They derive 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 all states of the world. More complete markets should be more efficient. Indeed, the development of options and other financial derivatives was aimed at making markets more complete, and there is a continued appetite for more exotic instruments, even with the associated costs and frictions.

The internal models of financial companies are becoming more advanced and “complete”, capable of considering and valuing more states of the world and more possible combinations of events. But they are still used to inform positions on the relatively small number of tradable things in today’s “less complete” market. The enormous information flows enabled by quantum networks would allow companies to communicate their views on any complex combination of events they are considering.

Furthermore, internal models of companies are short-term targets for the use of 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 through a quantum network would allow other companies to value overlays that encode companies’ opinions on any possible combination of events as “quantum options” in an even more complete and necessarily fully quantum market.

**Enable efficient and innovative payment systems**

Recent work has shown that NISQ computers can solve complex, existing scheduling problems in high-value payment systems (that settle transactions between large financial institutions) better than classical algorithms under real-world constraints.

However, quantum networks would enable a fundamental change in what a payment means, allowing counterparties to communicate sophisticated and conditional strategies to the payments system. Let’s imagine that instead of simply saying “buy”, a party can say “buy, if…” certain conditions are met in other simultaneous payments or events, like chains when buying and selling houses, but much more complex and interrelated. A quantum computer would then allow us to solve the problem of what combination of instructions should proceed.

Smart contracts, flash loans in crypto/DeFi, and debates over conditional payments in digital currencies show the growing demand for these facilities, while quantum game theory highlights the novel behaviors that arise when quantum strategies are combined in this way. way, even in simpler environments. UPS.

**Discussion**

These examples, which build on existing applications that 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 generate value, initially by optimizing interactions through a classical market.

However, the introduction of quantum networks between these computers would allow a “quantum market” and would provide an outlet for their enormous computational power. Instead of being locked in, they could interact directly with each other through a quantum market infrastructure that would enable the types of complex and conditional strategies discussed above.

In the short term, the adoption of quantum technologies could well be driven by the benefits to individual institutions of this more “complete” market, including the ability to efficiently underwrite risk and exploit information. Inherently secure quantum communications and trusted cloud computing can lower barriers to entry by enabling commercial use of shared hardware and enabling a surrounding Fintech ecosystem.

As quantum markets develop, there will be scope for high-level changes to market functioning. Initially, these could draw directly on the new financial market infrastructure (with its privacy and verifiability enabling decentralized quantum markets for both retail and institutions) and the ability of participants 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 that new markets produce.

Overall, this begins to paint a very different picture than a classical market: enormous amounts of information and computing flow in fully quantum systems, integrated into a new commercial landscape of hardware and service providers. This picture, 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 at the Bank’s Fintech Hub.**

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