Project »AnQuC-3«: Application-Oriented Quantum Computing

In the project »AnQuC-3«, the focus is increasingly on the topics »Quantum Fourier Transformation«, »Quantum Machine Learning«, and variational algorithms. Our team at Fraunhofer ITWM concentrates in particular on the first two areas. 

Since a few years, the first commercial quantum computers are available. Although we are still in a quantum era, in which a lot of noise and media hype is made about the new techniques, it is important to remain realistic: The opportunity to use quantum computers to accelerate currently intractable problems seems tantalizing. We ask ourselves: is quantum computing a game changer for the future? If so, for which applications and processes exactly? This is what we want to find out with our research. We develop, implement and test algorithms that are relevant for industrial applications on hardware backends. We are a partner of IBM, which gives us access to the Fraunhofer IBMQ system in Ehningen.

Three Phases Drive Project Development of Quantum Computing

The first project, AnQuC, focused on applications on the IBM quantum computer System One, always with a view to a broad exploitation of quantum computing. Runtime measurements were used to study hybrid algorithms that have both classical and quantum components, and to investigate the effects of characteristic quantities such as the coherence time and error rate of 2-qubit circuits on specific algorithms.

Key research questions include: Which application scenarios are suitable for computation with a quantum computer? How can algorithms for it be developed and translated into applications?

»You have made good use of the start-up funding,« emphasized Science Minister Hoch at the award ceremony. In the next funding phase, the researchers will deepen the work packages. This will include identifying further applications – a strategy also endorsed by the Industrial Advisory Board. It consists of representatives from BASF, Debeka, Deutsche Bahn and Schaeffler. 

High Performance Computing

Our division »High Performance Computing« (HPC) focuses on the interplay between HPC and quantum computing. In the context of AnQuC, we consider on the one hand the benchmarking of quantum computers and on the other hand quantum chemistry simulations. 

Benchmarking of quantum computers is important to compare different systems and finally to quantify the path to quantum advantage. Various metrics can be considered. In particular, we focus on the running time of quantum circuits. In addition to the concrete measurements in AnQuC, we are collaborating on DIN SPEC 91480 »Benchmarking of Quantum Computers« to identify suitable metrics and methods.  

Among the most promising applications in quantum computing are quantum simulations of chemical systems using variational eigensolver (VQE) methods. The interplay between the quantum processing unit (QPU) and classical processing resources is the fundamental idea behind VQE – where the QPU is only used for the difficult part of the computations that allows meaningful results to be obtained from nonerror-corrected quantum computations.

Our research shows that quantum computing calculations are qualitatively good, but when compared to classical results, they are still far from accurate and reliable. Further research will reveal whether there are algorithmic solutions that affect the accuracy and reliability of the results and/or whether there are severe hardware limitations that prohibit obtaining quantitatively good results without further changes to software and hardware resources.

Image Processing 

In the field of machine learning (ML) with quantum computers, we have used the quantum counterpart of the classical artificial neuron, i.e., the basic element of neural networks, to detect edges in images using quantum computers. The algorithm we developed provides very robust results [1].

This succeeds not only on a quantum simulator, but also on the currently still error-prone superconducting quantum computers. Thus, it is probably the first quantum edge detection algorithm for real data and real quantum computers that is also applicable for larger image sizes. Compared to existing methods, the method we developed requires only a few measurements of the quantum states to reliably detect the edges.

Flow and Material Simulation

Numerical simulation is an important tool for the characterization of composite materials. We focus on the potential of quantum computers to resolve complex material models quickly and efficiently. For this purpose, we consider both methods that promise long-term benefits – such as the quantum Fourier transform (QFT) – and heuristic methods that would be applicable in the short to medium term – such as variational hybrid methods.

The QFT allows the classical Fourier transform to be exponentially accelerated. The latter is the bottleneck in creating surrogate models for multiscale simulations of composites. We have succeeded in performing small material simulations on IBM quantum computers. However, there are still open issues that prevent scaling up to realistic resolutions, such as data transfer to the quantum computer [see 1, 2].

Since hybrid methods use quantum algorithms with lower complexity, they can be used to solve larger problems. For this, we tested a simple model on IBM quantum computers [see 3]. Despite the progress, we have found that hybrid methods also struggle to perform simulations at realistic resolutions. This is because classical methods and data structures are poorly suited to quantum computations.

Inspired by our findings, we are currently investigating novel approaches to quantum material simulation, such as quantum AI methods for predicting effective material properties.

Financial Mathematics

Our activities in AnQuC include:

• identifying use cases in financial mathematics
• transfer classical financial mathematics methods to quantum computing (QC) applications
• further development of QC algorithms

We focus primarily on the ability of QCs to solve complex financial mathematics problems faster and more accurately than classical computers. We investigate the automated finding of QC circuits to facilitate the implementation of financial mathematical problems on a quantum computer. Artificial Intelligence methods are used to enable the most efficient computation of a wide variety of simulation problems. We rely on existing, so-called variational QC algorithms and adapt them according to our use cases.

Options are one of the most traded financial derivatives on the market and their risk-neutral valuation is essential for many financial institutions. A classically very costly method to simulate the underlying asset are valuation trees. We have studied and shown that the computation of certain financial derivatives on trees can be significantly accelerated by QC [1]. To make this possible, we have developed a new type of payoff function for QC [2].

Risk measures are important metrics used by financial institutions to adequately assess their future risks. In many cases, the computation of such risk measures is done using time-consuming Monte Carlo methods. In our research, we investigated how these time-consuming calculations can be accelerated using quantum computing methods. For example, by applying Amplitude Estimation, a QC algorithm for estimating an unknown amplitude, a quadratic reduction in computation time can be achieved [3].

Optimization

For the application fields of the division »Optimization«, we see the potential of quantum computers mainly in specialized optimization algorithms and for quantum-enhanced Machine Learning (ML) methods. We pursue various research questions  to evaluate these approaches on currently available quantum computing hardware.

Hybrid quantum algorithms are methods that combine conventional digital computers with quantum computers. Such methods can be used, for example, to solve combinatorial optimization problems. For this purpose, classical optimization methods control free parameters of quantum circuits such that the measurement result corresponds to the optimal solution. As an alternative approach, we investigate evolutionary algorithms that also modify the circuit structure in addition to the parameters [see 1]

Randomness of measurement results is an intrinsic property of quantum systems. Random numbers are also an essential part of numerous Machine Learning methods, especially in the field of Deep Learning (DL). Therefore, it seems natural to combine these two topics to investigate whether quantum random number generators can provide a benefit for Machine Learning methods. To this end, we have performed an empirical study in which we present a detailed analysis of random initializations of artificial neural networks using quantum computers [see 2]. Our results refute previous results in which a clear quantum advantage was predicted.

Mathematics for Vehicle Engineering

In our division »Mathematics for Vehicle Engineering«, we are looking at various possibilities for using quantum computers for traffic control.

In this context, we are studying whether the use of hybrid quantum algorithms, such as the »Quantum Approximate Optimization Algorithm« (QAOA) or »Quantum Annealing«, can already achieve performance gains compared to classical optimization methods.