Quantum algorithms are coming to finance, slowly

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Something is happening on the fringes of financial services. Away from trading floors, in banks' Google-style 'moonshot research labs', PhD students are experimenting with the application of quantum computing and quantum algorithms to financial services. No one is saying that quantum algorithms have arrived, but in the next decade, this could change.

A new paper* from quantum computing specialist QC Ware and academics at the University of California, Berkeley, the University of California, Santa Barbara, and the University of Paris Diderot, explains what to expect: quantum algorithms could revolutionize Monte Carlo calculations for derivatives pricing and risk management; portfolio optimization, and machine learning. Some changes may be feasible soon; others will take time.

The problem with quantum computing is noise. As the paper's authors point out, 'current quantum devices cannot perform more than 102 − 103 simple operations before devolving into noise.' To mitigate this, it's either necessary to make noise-reducing alterations to the physical quantum systems, or to work around the noise. Noise-reducing alterations quickly become unviable for general use. Therefore, researchers are focusing on a regime known as “Noisy Intermediate-Scale Quantum” (NISQ), which allows for non-error-corrected quantum computations that work around the noise.

The near-term viability of quantum algorithms typically depends on their ability either to function on these kinds of NISQ devices, or to perform under reduced resource requirements. In many cases, the need to correct quantum errors slows down the physical clock speed of the device, so that use of the quantum algorithm only becomes quicker overall if the algorithm's speed itself can compensate. 

Quantum algorithms for Monte Carlo calculations 

In the long term, the researchers say quantum algorithms could revolutionize derivative pricing systems. Operating on, "fully scalable fault-tolerant quantum computers," quantum Monte Carlo algorithms have, "the potential to allow for close to real-time pricing of derivatives... potentially providing a strong competitive advantage for users of this technology."

For the moment, however, fully fault scalable quantum computers aren't available and the quadratic speedup for standard Monte Carlo methods requires very high quality qubits to achieve because of the so-called "circuit depth" of the Monte Carlo algorithm. "The algorithm requires running a large number of applications of the stochastic market model S and payoff function f in series, followed by a quantum Fourier transform," say the academics. "This necessitates very low error rates in the quantum hardware, which are currently unavailable."

In an effort to get around this, research is being focused on, "hybrid NISQier algorithms that will realize a smooth continuum between fully quantum and classical Monte Carlo algorithmically." If the Fourier transformation is eliminated, the algorithm is simplified, for example. There have been attempts to split the Monte Carlo algorithm into parallel sub-problems and to trade increased speed for a reduction in the depth of the quantum circuits. 

Quantum portfolio optimization 

Quantum algorithms can also be used to solve the perennial issue of allocating investments among multiple assets with differing but correlated returns while minimizing the risk of the portfolio and achieving a target rate of return given various other constraints.

Typically, however, the quantum linear algebra required for optimization problems has "medium to high hardware requirements" and is difficult to implement. The fundamental issue is that, "quantum algorithms for solving linear systems and other quantum linear algebra primitives all rely on quantum algorithms for Hamiltonian simulation," and that, "algorithms for Hamiltonian simulation are quite complex and difficult to implement on quantum hardware."

Attempts are being made to adapt portfolio optimization algorithms to NISQ machines, but there's still a long way to go. One possibility is mapping portfolio optimization problems to so-called "quantum annealing hardware," which encodes the solution to a portfolio optimization problem as the physical ground state (lowest energy state) of a quantum system.

Quantum machine learning

Lastly, quantum algorithms can enhance machine learning applications in finance, potentially significantly.

 "Quantum machine learning algorithms can in theory provide a speedup factor of more than a million, compared to both classical and quantum-inspired algorithms," note the researchers. In an industry where latency is critical, this would be huge. 

The researchers suggest various applications for quantum machine learning applications in finance, including analysis of data to identify different market regimes (eg. high/low volatility,rising/falling rates, rising/falling inflation).

Given the ongoing issues of quantum noise, however, the researchers caution against expecting any dramatic imminent breakthroughs.

Slowly, academics and industry specialists are adapting algorithms, either to handle noise or to function on NISQ platforms. Over time, the papers' authors say they're confident that quantum algorithms will, "be able to solve certain problems considerably faster than the best known classical algorithms." 

In the meantime, banks can't afford to ignore what's happening in the peripheries of quantum research. 

Photo by Tyler Lastovich on Unsplash

*Prospects and challenges of quantum finance

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