## Financial institutions (FIs) are required to solve a range of computational problems in their day-to-day operations. Examples include portfolio optimization, risk evaluation, and the pricing of financial derivatives. The ability to solve such problems with greater speed and accuracy is key to remaining competitive, and, unsurprisingly, a number of FIs have turned towards quantum computing and are investigating how this revolutionary technology could be exploited.

Most of the computational problems encountered by FIs can be formulated as optimisation problems (optimisation problems are problems that require finding the best solution out of all feasible solutions – portfolio optimization, risk evaluation, and pricing fall into this category). In classical computing, Monte Carlo (MC) simulations are the method of choice for solving optimisation problems. MC simulations are computationally intensive because they require a large number of runs to obtain accurate results (MC simulations typically require several days to compute). Quantum computers, however, enable different and potentially faster quantum algorithms to be used. In general, the advantage of quantum algorithms arises because quantum computers use qubits to encode information, instead of classical bits. While a classical bit is either in a state of 1 or 0, a qubit can be in a superposition of states |0> and |1>. By formulating a problem using qubits, which are in a superposition of states (rather than just being 0 or 1), several states can be accessed simultaneously and, thus, a solution may be arrived at after fewer runs.

For example, estimating risk using a classical computer by MC methods results in an output having a confidence interval width that scales as the inverse of the square root of M (1/√M), where M represents the different realizations of the model input parameters [3]. Put simply, M represents the complexity of the problem, and the larger the value of M, the more complex the problem, and the longer it would take find a solution (the more slowly the MC method converges). For example, with a 10-fold increase in M, a 100-fold increase in the computational effort is required to obtain an output with the same degree of confidence.

## Using a quantum computer, quantum algorithms such as an Amplitude estimation (AE) may be used instead of MC methods.

The AE converges, at least theoretically, at a rate of 1/M (this means that for a 10-fold increase in problem complexity M, a 10-fold increase in the number of computations is required to achieve a comparable result). In fact, at least in principle, a number of computational problems in the field of finance and beyond can be solved more quickly by using quantum algorithms instead of classical algorithms.

A few early demonstrations of computations using actual quantum computers based on IBM’s superconducting qubit quantum computer have been reported. For example, the estimation of risk using a 5-qubit computer or the pricing of options using a 3-qubit system has been demonstrated. Although most practical problems will require far more advanced quantum computers than the 3 or 5 qubit systems, these results do demonstrate that the predicted computational advantage (in terms of the rates of convergence) can be obtained in practice.

Experts generally agree that significant improvements in the capabilities of quantum computers (e.g. in terms number of qubits and suppression of errors) will be required in order to enable practical applications. In fact, increasing the number of qubits while suppressing errors is critical to enable real-world applications since the advantage of quantum algorithms over their classical counterparts lies in their favourable scaling as the problem being solved becomes more complex, and, since, in general, large qubit numbers are required to tackle complex problems.

The technical challenges ahead are significant, and, even by optimistic standards, quantum computers are between 5 to 10 years away from being able to perform practical computations. Nevertheless, given the potential of being able to reduce the time to perform complex calculations from hours or even days to near real-time, several FIs have thrown their hats in the ring by partnering with quantum technology companies.

## For the time being, a number of different core technologies are being explored in parallel.

For example, JP Morgan is collaborating with Honeywell to use trapped-ion quantum computers, Standard Chartered is working with D-wave’s superconducting quantum annealing hardware, and Scotiabank is collaborating with Xanadu to investigate photonic quantum computing technology- suggesting that it is not yet clear which technical approach leads the race.

As with any technical innovation, securing IP rights for developments in quantum technology confers commercial advantages. In particular, innovators that are able to patent their technology will gain exclusive rights to exploit products or methods covered by their granted patents. Whilst patents covering the hardware inventions underpinning quantum computers should be relatively straightforward to obtain (subject to being novel and inventive over the prior art), the situation with regards to inventions relating to quantum algorithms for finance is more nuanced.

In Europe, in particular, obtaining patents covering methods for financial applications is considered to be notoriously difficult, and this is due to the fact that European patent law explicitly excludes the patenting of mathematical methods, computer programs and methods of doing business when claimed as such. However, in general, such inventions can be patented at the European Patent Office (EPO) when the invention is “technical” (e.g. when the claimed program/method provides a non-obvious technical solution to a technical problem). In particular, computer programs may be considered technical when they are based on specific technical considerations of the internal functioning of the computer (e.g. when they are adapted to the specific architecture of the computer). Therefore, at least for aspects of quantum algorithms that are intimately linked to the hardware on which they are executed, innovators developing quantum algorithms for finance should not forgo patent protection.