How quantum-inspired algorithms solve probably the most complex PDE and machine learning problems to attain real business advantage now.

By Michel Kurek, CEO, Multiverse Computing, France

The controversy about quantum hype rages on, with some within the industry claiming significant milestones already and a few criticizing claims of progress as an excessive amount of hype. Probably the most common query continues to be, “How long until quantum customers see real business advantage from quantum algorithms and hardware?”

Crédit Agricole CIB, Multiverse Computing and Pasqal recently announced results of two proof-of-concept projects that show progress is real. By utilizing clever algorithms from Multiverse and Pasqal’s neutral atom platform, CACIB has found business advantage with quantum computing. At the middle of those two projects are real business problems: predicting changes in credit worthiness and pricing derivatives.

These projects push the boundaries of what is feasible with quantum and quantum-inspired solutions. On this post, I’ll share extra information and takeaways from each projects.

Partial differential equations (PDE) and high-dimensional stochastic differential equations (SDE) are powerful tools used to model a variety of physical phenomena. There are also significant applications in finance. The solutions of some SDEs set the value of some derivatives in addition to their sensitivities to external parameters.

Although closed formulas exist for some derivatives, solving SDE for complex derivatives or in high-dimensional spaces will be extremely difficult, even with advanced analytical methods. Recent research focuses on neural networks (NN) to beat the restrictions of other traditional analytical methods. The concept is to search for a NN to represent a derivative’s price function which solves the underlying SDE. The advantage here is that when a NN is trained, the value computation becomes instantaneous.

Training neural networks can require massive amounts of time and compute resources. QC is a possible solution, but the present hardware is restricted in its capabilities. Nonetheless, we do have a complementary approach that mixes quantum calculations and classical computers and allows us to succeed in an actual business advantage.

We will do that by exploiting the facility of the mathematical and diagrammatical formalism of tensor networks (TN). Multiverse is the world’s leading expert on this field.

Tensor networks have their roots in physics. They’re powerful tools used for 25 years to simplify studies of huge numbers of interacting quantum particles using classical computers. Multiverse takes this tool out of the lab to use it to a wider class of business problems.

The resource requirement is reduced to the purpose that a computation that might not have been possible on a conventional computer is now possible. Complex optimization or machine learning problems can then be tackled.

Tensor networks come into play in this primary project with CACIB. By hybridizing TN and NN, we will solve increasingly complex SDE while saving lots of training time, reducing the variety of parameters without losing expressivity and getting the exact same price accuracy as state-of-the-art NN. We show that the added value of TN is more evident as the issue dimension increases.

CACIB is now convinced that the technique to quickly profit from quantum computing now could be through tensor networks.

Along with the derivative pricing test case, Multiverse and Pasqal worked with CACIB to use quantum computing to the “fallen angel” problem. When granting a loan, a bank’s credit analysts thoroughly review a client’s financials to substantiate the flexibility to repay. Nonetheless, the client’s creditworthiness may change unexpectedly throughout the loan’s term. A “fallen angel” (FA) refers to a client who was previously considered credit risk but has recently declined to a lower credit standing.

CACIB’s key challenge is predicting with reasonable accuracy the creditworthiness of clients over time: how likely is a specific customer to falter financially throughout the next 6 to fifteen months?

This financial use case is fundamentally a binary classification problem: To be or to not be a fallen angel.

This figure illustrates a binary classification problem coping with two
classes (squares and triangles). The classifier is trained on the labeled training data and tasked to categorise the instances, i.e. to seek out a call boundary (black line) separating the test data. Considering that the test data comprising two features k and l, the model either predicts accurately the category of an instance, thus increasing Tp/n (green squares/blue triangles) or incorrectly, thus increasing Fp/n (green triangles/blue squares). This figure is from the research paper, “Financial Risk Management on a Neutral Atom Quantum Processor.”

To deal with this problem, the cutting-edge solution uses machine learning. Such a machine learning model must learn patterns which might be typical to fallen angels, based on a set of historical data containing client information, market conditions, macroeconomic trends, and other relevant aspects. Along with the variety of features, the proven fact that data is very imbalanced (only a couple of clients go bankrupt) could make the usual approaches suboptimal.

CACIB uses a model that has been trained on a dataset that features information from 2,300 corporations in 10 industrial fields and 70 countries. The dataset includes 91,000 instances and every fallen angel is labelled as such.

Traditional ML methods can require considerable training time and IT resources. As a pioneer and leader in the applying of quantum and quantum-inspired algorithms to finance use cases, Multiverse was compelled to take up this challenge. Quantum and quantum-inspired algorithms based on tensor networks (TN) can solve the issue as they intrinsically allow a more efficient exploration of a wider space of possible solutions.

The goal of this project was to construct a quantum/quantum-inspired machine learning (QML) model and integrate it in an end-to-end process where Pasqal’s cold atom-based simulator was used for a selected optimization task at the tip of the workflow.

Taken alone, Multiverse’s quantum-inspired ML model using a proprietary TN optimizer was in a position to catch the identical variety of downgrades with a bit more precision than the prevailing model, as shown within the charts above and immediately below. As well as, we managed to scale back the variety of required submodels (individual classifiers) from 1,200 to 90, which makes our solution more interpretable. These figures come from our research paper published on arXiv in December 2022: Financial Risk Management on a Neutral Atom Quantum Processor conjointly written with Pasqal’s team.

The outcomes achieved by utilizing the Pasqal QPU for optimization are also highly encouraging. Despite the present limitations imposed by the 50–60 qubits available for the project, we were very near the present CACIB KPI. Once we extrapolate that with the 300 or so qubits which might be on Pasqal’s short-term roadmap, we should always exceed this limit.