We live in a world of dramatic change. Companies and societies are trying to tackle increasingly complex issues, and they are turning their attention to quantum technologies. Although it is expected to take some time before we see full-fledged quantum computers that utilize quantum phenomena, Toshiba is already working on quantum-inspired optimization technologies. We are applying our own in-house combinatorial optimization technologies for producing optimal results from massive numbers of options, providing them in the form of the quantum-inspired “SQBM+” optimization solution. This solution uses existing computers to produce highly accurate approximate solutions in short amounts of time. In this running feature, we will explain quantum-inspired optimization technologies.

In Part 1, we explained two methods in quantum computers (the gate method and the Ising machine method) and the positioning and structure of the quantum-inspired optimization technologies for them. In Part 2, we explained bifurcation, an important element of these technologies, along with how processing is accelerated and improved. We also provided an overview of the technologies. In Part 3, we covered combinatorial optimization problems. In Part 4, the last part in this running feature, we will look at the application of quantum-inspired optimization technologies to fields such as drug discovery and finance.

Currently, studies are being performed on how quantum computers can be applied to various fields. Quantum computers have exceptional computing capabilities and show great potential for use in new applications beyond the reach of  conventional (classical) computers. However, the specific fields where quantum computers will excel remain uncertain, as do the challenges we will encounter during their practical deployment. That is why many companies and universities are implementing initiatives aimed at the application of quantum computers in the real world, sometimes developing new algorithms, while taking into account the characteristics of quantum computers that have become evident through past research.

Quantum computers have the potential to solve social problems in fields such as finance, drug discovery and chemistry, energy, and transportation. Contributions toward achieving carbon neutrality by combining these solutions are also expected. These issues are considered to require the computations of prodigious combinatorial optimization to be solved. There are also hopes for the ability of quantum computers to address industry-spanning needs such as the need for high-speed processing in machine learning, simulations, and optimization. At the same time, they are also said to pose a security threat because they could be used for decryption. The Cabinet Office’s vision for the quantum society of the future advances a concept of using quantum technology in a wide range of fields, including life services and safety & security (Fig. 1).

As the use of quantum computers in society advances, new applications that leverage these quantum computers will produce new industries. This will, in turn, create new social issues. In parallel with this, new issues will also arise related to carbon neutrality, circular economies, and the constantly evolving technology of AI. Quantum computers will be called on to solve problems that we have yet to see or even imagine. They will exert even greater strength in this era to come. To prepare for this era of high demand for quantum computers, it is important that we use our imaginations now to think about what kinds of fields and applications they could be used in.

In Part 1, we explained that quantum computers use either the gate method or the Ising machine method. The gate method is currently only used in small-scale hardware, and the number of algorithms that have been established for it are limited. Therefore, it is not yet at a practical level, and there is ongoing exploration for future applications, particularly in fields such as chemistry and finance.

On the other hand, Ising machines use quantum-inspired optimization technologies such as SQBM+ to deal with problems on a practical scale, and possible applications are being explored in various industries. For the time being, these efforts will primarily be focused on using Ising machines for optimization, but research is also being carried out on the use of Ising machines for machine learning and simulations, for example. This research aims to produce advances in the ability to select feature quantities that quantitatively represent the features and properties of data or objects to be analyzed, and improvements in the efficiency of physical simulations. Applying Ising machines to these fields is expected to have tremendous economic benefits, and there will likely be a great deal of future exploration of how Ising machines can be applied in areas other than optimization.

For SQBM+, Toshiba’s quantum-inspired optimization solution, we are working with various users and partners to explore use cases and gather examples for practical applications. In the use case explorations, the following three issues are investigated to evaluate the applicability of SQBM+.

(1) Is the problem itself a good fit for using SQBM+?

When searching for use cases, the first task is to determine if the problem at hand is one to which SQBM+ is applicable. In most cases, it is not immediately obvious whether or not SQBM+ can be used. It is only after thinking about a problem to some degree that one realizes whether or not the problem involves combinatorial optimization, and whether it is a candidate use case.

Let’s look at this through the transport field example that we discussed in Part 3: optimizing a vehicle’s driving route. In this example, our goal is to reduce road congestion. We could use various measures to accomplish this, such as widening roads, building grade-separated intersections, or billing for road usage at certain times. We pick one of potential solutions: controlling the driving routes of individual vehicles. After considering possible ways to implement this and trying to formulate it to some extent, we discover that this problem is a strong candidate for solving as a combinatorial optimization problem. In other words, when given the initial requirements of reducing traffic congestion, it is not clear whether this could be an SQBM+ use case. It is only after some deliberation and problem design that this could be an SQBM+ use case.

(2) Would it be appropriate to apply SQBM+?

Simply knowing that a problem can be solved as a combinatorial optimization problem -- that is, that the problem can be solved using SQBM+ -- is not enough. We need to consider whether SQBM+ is the most suitable choice for how to solve the problem.

For example, in the case of a small problem, we could simply solve the problem using conventional methods without having to apply SQBM+. In the case of the vehicle driving route example, if the number of vehicles to be controlled is low, optimization could be performed without using SQBM+.

Effective algorithms have also been found for other problems which have been researched for years, such as linear programming problems and travelling salesman problems. Using one of these effective algorithms could produce faster and more accurate results. SQBM+ is fast at solving general Quadratic Unconstrained Binary Optimization (QUBO) problems. However, experience has shown that when defining a problem, before putting it in QUBO form, there are sometimes special conditions for which specific techniques are effective. Methods that make use of these conditions are often more effective than using SQBM+.

Even if SQBM+ is a good fit for a problem, there may be cases where other faster methods can be applied by making small changes to the problem’s conditions. When making changes to these conditions would have an insignificant impact on the solving of the problem, we can determine, by considering the problem holistically, that there is no need to apply SQBM+ to the problem, and other effective methods may be selected.

SQBM+ excels at rapidly discovering solutions that are near-optimal solutions (suboptimal solutions). SQBM+ is extremely effective when suboptimal solutions are sufficient and when candidate solutions need to be discovered quickly, or when you wish to obtain a large number of suboptimal solutions. On the other hand, when you need an accurate optimal solution, conventional optimization solvers may be suitable for the task.

(3) Would SQBM+ function for the system?

After considering the advisability and appropriateness of applying SQBM+ to the problem, it is necessary to consider whether the application of SQBM+ would make sense for the system and whether it would function appropriately as a system.

In many cases, SQBM+ alone is not enough to solve a problem. Use cases are made up of multiple steps, one of which is combinatorial optimization using SQBM+. Therefore, it is vital that we confirm that the processing, including steps other than SQBM+ steps, is meaningful for the system as a whole. If the SQBM+ portion is a bottleneck for the system as a whole, then the high speeds of SQBM+ can prove beneficial. However, if there are other slow areas, then even if the SQBM+ portion is sped up, it will not have an impact on the overall problem. Furthermore, we will need to smoothly connect SQBM+ to the steps that precede and follow it, we will need to refine the techniques used to call it, and we will need to perform design work to ensure that the system functions correctly.

One of the fields in which SQBM+ use cases are being explored is drug discovery.

A great deal of active R&D is being performed in the drug discovery field, and hopes are high for the benefits IT will provide. With respect to quantum computers, expectations are particularly high for the combined use of high performance computing (HPC) and AI to dramatically improve the efficiency of processes and develop revolutionary new drugs. We are currently working with Revorf Co., Ltd., a drug discovery start-up company, to apply SQBM+ to allosteric drug discovery.

Drugs produce their effects by acting on the specific proteins, of the many proteins in the human body, that cause illnesses. Until now, new drugs have been discovered by finding compounds (reactants) that act on disease-causing proteins by directly binding to their active sites. This means that in areas where reactants can be easily found, drug developers have made progress with discovering drugs. However, where finding reactants is a challenge, they have had difficulty in discovering new drugs.

There are hopes that this problem can be solved by employing drug discovery methods that use allosteric regulation* to regulate protein functions (allosteric drug discovery). Allosteric drug discovery takes a whole new approach. It searches for reactants that bind to the allosteric regulatory sites on the protein, which are sites that regulate the function of the disease-causing sites (active sites) (Fig. 2).

* Allosteric regulation: Protein functions are controlled by when needed by regulators, a mechanism called allosteric regulation. Targeting sites that regulators bind to (allosteric regulatory sites) provides many benefits, including producing more drug targets, formulating highly specific drugs, and potentially reducing side effects. Technology that identifies allosteric regulatory sites is seen as the key to increasing the success rate of new drug development.

This approach requires the identification of the allosteric regulatory site on the protein that acts on the site that is the cause of the disease (active site). Using SQBM+ to perform combinatorial optimization and search for these allosteric regulatory sites dramatically improves the efficiency of the process of searching for allosteric regulatory sites compared to past experimental approaches. Furthermore, progress is also being made with discovering unknown allosteric regulatory sites that went unfound with conventional methods.

SQBM+-based allosteric regulatory site prediction is performed using the following procedure (Fig. 3).

(1) Mathematical modeling: The target protein is modeled as a graph.

(2) Formulation: The conditions that apply to the allosteric regulatory sites that correspond to the disease cause sites (active sites) in the graph are assigned, and then an objective function is defined based on these conditions.

(3) Minimization/maximization: The vertex set that minimizes the objective function is determined, and this vertex set is used to predict allosteric regulatory site locations.

Currently, we are in the process of verifying if the sites identified using this procedure are actual allosteric regulatory sites. Going forward, we would like to advance with their research to ultimately discover substances that could be used as candidate drugs that target the allosteric regulatory sites found using this process.

Let’s look at another use case for SQBM+: High-speed trading in the financial industry. The financial industry generates profit through systems, and it uses state-of-the-art IT such as advanced financial product designs, algorithmic trading, and high speed trading. Eyes are turning to quantum computers for their ultra-high speed computation technologies, which could generate new revenue.

In financial markets, large amounts of revenue are generated by discovering advantageous trading conditions and using them to make trades before other market participants. When combinatorial optimization is effective for discovering advantageous trading conditions, SQBM+ can be applied (Fig. 4).

However, for a high speed trading system to be effective, another key issue is if the entire system (not just the combinatorial optimization portion that uses SQBM+) can operate at high speeds.

For example, if the high-speed trading system’s processing is connected to the cloud, then transmissions between the system and the cloud can produce delays that take away from the edge the system has in trading. Therefore, systems need to perform a series of processes on-premises. This includes transmitting data to and from the market, computing trading strategies using combinatorial optimization, and actually executing trades. It is beneficial for systems to be located in collocation areas that are physically close to the market, because this minimizes any delays when transmitting essential information to and from the market.

Given these conditions, let’s think about how a quantum computer could be used in a high-speed trading system. Current quantum computers require massive cooling facilities, so installing one of these quantum computers would require a dedicated data center. Therefore, it would not be feasible to place the entire high-speed trading system, including the quantum computer, within the collocation area. Placing part of the system in the collocation area and part in a dedicated data center would result in transmission delays within the system, causing the system to lose its competitive edge.

In the future, massive cooling devices may no longer be necessary, and it might become possible to place an entire system within a collocation area. However, until a quantum communication system is developed, the system would still require the use of classical computers to perform data transmission. This would require processing to convert between the quantum computer processing and the processing performed on the classical computer. With quantum-inspired optimization technology like SQBM+, on the other hand, all processing, including data transmission, is performed on classical computers, so there is no need for conversion between quantum and classical processing. This is why we believe that applications that require the minimization of processing time, such as high-speed trading, are a use case for SQBM+ that will continue to be viable in the future.

Currently, various ideas are being tested, such as identifying pairs of stocks whose movements are highly correlated and performing trading when the price of one shifts, based on the assumption that the other stock will also be affected. These ideas will undergo mathematical modeling and formulation as combinatorial optimization problems, and the results will be used to include simulated bifurcation algorithms in Field Programmable Gate Arrays (FPGAs). An on-premise proof-of-concept (PoC) system with these FPGAs has already been confirmed as usable for actual trading on the Tokyo Stock Exchange*. We are currently at the stage where system verification has been achieved,  and we plan to develop strategies with even better risk-return characteristics as it works towards practical deployment.

* https://www.global.toshiba/ww/technology/corporate/rdc/rd/topics/23/2312-03.html

In this, the last part of this four-part running feature, we have looked at the concepts involved in SQBM+ practical deployment and examples of its application. We believe SQBM+ is a high-potential technology that can help pave the way to the future quantum age, and we will continue to strive to develop helpful applications for a wide range of fields. 

• Quantum-Inspired Optimization Solutions “SQBM+”