In the world of financial services, a lot of computation goes into the pricing of derivatives, and those derivatives themselves are becoming more complex. It’s a process that could—and perhaps one day will—be improved using a quantum computer, according to executives at Goldman Sachs and IBM.

Last year, executives from the Wall Street titan and the technology giant partnered to see how this process could be improved, publishing their results in mid-December. The paper serves as the first detailed estimate of the quantum computing resources needed to achieve quantum advantage for derivatives pricing.

There are two ways that computation comes into pricing one derivative. First, trading firms have large portfolios that they need to price, and they need to understand those portfolios’ risk. Today, portfolio managers traditionally use Monte Carlo simulations and other risk models to simulate how a derivative’s price will change over time relative to market conditions. William Zeng, head of quantum research at Goldman Sachs, says that these are often “large, overnight calculations,” making it a problem of scale and time. There’s also the challenge of “real-time compute,” which occurs when a client asks the manager to let them know what a particular derivative’s price should be.

In the first case, the more accurately a firm can gauge the value and risk in a portfolio, the more efficiently it can allocate capital. In the second case, if a firm can accurately quote a price for a client, it can lead to a competitive advantage and increased market share. While there are several areas of finance that could potentially benefit from quantum advantage, Zeng believes that this sort of process is an achievable first step for quantum research.

“Most of the time when people talk about quantum advantage, it’s usually to allow you to compute something that you never could compute before,” Zeng tells WatersTechnology. “Here, actually, if we do it just a little bit better, because the problem is so big, it could matter a lot. So that makes it appealing as a place to start.”

Classical computers—or the computers commonly used today to run these calculations—have computational limits, as the number of samples in a Monte Carlo simulation, for example, would need to be increased by a factor of 100 in order to improve an estimate’s precision by an order of magnitude. A quantum computer, on the other hand, could reach the same improvement by increasing the samples by a factor of only 10, which is known as a quantum speedup, according to the researchers at IBM and Goldman.

Stefan Woerner, quantum applications lead at IBM Quantum, says that they decided to start with options pricing because it was a process that could conceptually achieve quantum advantage. The problem, however, was that there were never any numbers put to the concept, which this joint benchmark achieves.

“This is the first time that we have concrete numbers,” Woerner tells WatersTechnology. “We knew conceptually that we could do this, but now for the first time we have a complete blueprint to map an option that is relevant in practice to a quantum circuit that, if we would have such a hardware available, could be executed. We are not there yet—it will take years before the hardware reaches that point—but it’s the first time that we have a full picture.”

Specific to those concrete numbers, the resource estimates that it would need 7,500 logical qubits (or physical qubits in a quantum error-correcting code, which are used to protect information from errors) of sufficient distance to support the required number of operations to achieve a quantum advantage. It also estimates that 46 million gates (the operations a qubit can perform before there’s a loss of information) are needed. Additionally, the researchers posit that in this scenario, quantum advantage would need quantum circuits to run at 10 megahertz or faster, assuming a target of one second for pricing certain types of derivatives.

Woerner says that this is an initial milestone, and they expect these numbers will improve “quite a bit over the coming years.”

Miles to Go

As both Zeng and Woerner note, these are important first steps to document, but it doesn’t mean that commercial quantum computers are going to be available anytime soon. Quantum computing, which was born out of the realm of theoretical physics, is complex and stuffed with specialized definitions and terms.

The research field—especially as it pertains to finance—is nascent. And because the researchers still have a long way to go before true quantum advantage takes hold, quantum fatigue is setting in at some banks.

Back in October, Jezri Mohideen, global chief digital officer at Nomura’s wholesale business, told WatersTechnology sibling publication Risk.net that the bank may wait before becoming an adopter. “Two years ago, I was a lot more bullish, and I felt the evolution would come through a lot faster,” he said. “Practical quantum computers can’t be used for a lot of tasks that we typically face in 98% of financial domain applications.” And the head of digital at one investment bank said that “it always feels like we’re two years away from a real quantum use-case. The order of magnitude of the efficacy of the processing just wasn’t where everybody thought it would be.”

While speaking on the Waters Wavelength Podcast in October, Bill Murphy, former CTO at Blackstone, had this to say: “Most of the problems that we’re solving with technology today are not what quantum is good at. [Capital markets firms are worried about] connecting workflows and processes, and making things more efficient—those types of things. So I think that quantum computing can be revolutionary in the right circumstances, [but] sometimes the marketing is like, it’s going to change everything tomorrow, and that’s not really true. It could potentially change a few things a huge amount, and we should pay attention to that and take advantage of it, but it’s not the silver bullet to solve every technology problem.”

Zeng says he has faced similar questions as to how long it will take to reap rewards in this field, but he stresses that this early work is a critical foundation for answering those questions. To take quantum computing out of the abstract, they need specific numbers that can be worked and improved.

“Right now it’s, how do we make this really concrete? Let’s get concrete applications, roadmaps, and estimates, and then once we start to think about production—which comes after that—I’ll be excited to see us get there, but we’re not there yet,” he says.

Going forward, Zeng says there are three broad categories that suit quantum exploration in finance.

First, there’s the field of simulation, which is where derivatives pricing falls, but there are also many risk calculations where the bank would like to better understand probabilistic behavior and how calculations can be modeled more accurately. “That’s a big category and there’s a lot that falls in there,” Zeng says.

The second category is optimization, such as portfolio optimization. And in the third group there’s quantum machine learning. “The first two, we have a pretty clear handle in theoretical quantum computer science, at least on the first advantages, and we also have pretty concrete classical applications,” he says. “Machine learning is of interest, but it’s a little more nascent. … There has been some interesting heuristic work and motivating intuition, but quantum machine learning is a much younger field than optimization and simulation.”

In addition to building out its own hardware and developing more stability around qubits, IBM has partnered with other financial institutions, including JP Morgan, Barclays, and Wells Fargo. Woerner says that his team is looking at understanding algorithms used for optimization—trying to come up with a theory that shows when to expect a quantum advantage there—and understanding what approximations a quantum computer could achieve.

He also notes that growth in the field of quantum computing has been rapid, but more importantly, the research is now crossing disciplines, which could help accelerate advancement.

“People from mathematical optimization are now starting to look more and more at quantum computing as one tool to solve that problem,” Woerner says. “It’s growing out of theoretical physics, where it originated, into all these different application fields. This can give the whole field a boost by having not only more brain power, but also way more diverse brain power with completely different points of view and angles to approach a problem. I think it will be really exciting seeing that continue.”