The challenge you have posed is not breaking the current record for sailing solo around the world or winning the Trans-Sahara Rally. You are interested in classical optimization problems that arise in manufacturing and logistics. Nevertheless, the competition your students are now involved in does have some rather special features. What’s it all about?

Linnhoff-Popien: The task set by the Quantum Computing Optimization Challenge is to identify areas in logistics and production in which early implementations of quantum computing offer advantages over conventional computers. The range of possible applications for quantum computing is immense, but we are concentrating on optimization problems. We expect that a quantum advantage in this field can be demonstrated within five years. The term ‘quantum advantage’ is applied to tasks that that can be performed by quantum computers, but are either intractable for, or can only be carried out less efficiently or in less demanding contexts by conventional computers. We are already preparing our informatics students for the coming era of the quantum advantage. 
In the Challenge, we will ask four of the best quantum computers currently available to solve a set of realistic optimization problems supplied by our commercial partners BASF, BMW, SAP, Siemens and Trumpf. Our students, and the researchers in our QAR Lab who supervise them, will use IBM’s Q System One, the Rigetti Aspen-9, the D-Wave Advantage and the Fujitsu DAU for this purpose.

What sort of tasks are your students confronted with?

Linnhoff-Popien: The Challenge involves problems that are of practical relevance to our commercial partners. For example, what is the optimal route for the delivery of goods to a particular set of customers, or in what sequence should a robot remove test tubes from a rack, analyze their contents and replace them. In other cases, the problem relates to the optimal use of space, where any given object should be placed in relation to others. For example, in what sequence should a set of engine components be assembled so as to minimize the total number of tests required. In the factories of the future, in which assembly lines have been replaced by robots that deliver the components in a predetermined order, process scheduling is vital, so the optimal sequence of steps in the assembly process must be defined.

Can’t all this be done on conventional computers?

Linnhoff-Popien: Yes, but it can be done efficiently only for relatively small numbers of variables. Let’s take the problem of the combinatorial optimization of gate allocation at Munich’s Airport. For a terminal with 250 aircraft and 50 gates, a classical computer takes all night to optimize the allocation plan for the next day. It sounds like a simple problem. After all, a classical computer can evaluate every possible combination of allocations of aircraft to gates, and calculate the optimal one. But the space of possibilities rapidly explodes – and the high degree of complexity is pushing a classical computer to its limits.

You refer to generic quantum computers. But you have access to several different types.

Linnhoff-Popien: Yes, there are various technological implementations available. Let’s look first at quantum annealing. The typical representative of this ‘hybrid technology’ is the model developed by D-Wave Systems in Vancouver. This machine makes use of quantum superposition to solve optimization problems, but it must be cooled to cryogenic temperatures close to absolute zero. – That’s why the computer takes up as much space as a garage.

In contrast, the Japanese company Fujitsu uses a process called digital annealing. Strictly speaking, this is not really a quantum computer, but it doesn’t need cooling.

Linnhoff-Popien: What are called ‘gate-model’ computers, such as those that have been developed by Google, IBM, Rigetti and others, use what is regarded as a highly promising technology. However, it must be admitted that, at the moment, we are still at the stage of the NISQ-based computer, which depends on noisy, intermediate-scale quantum technology. These computers generate lots of noise, which must be filtered out in order to get the best result. What we need is a self-correcting quantum computer, but this will take time to develop. Since nobody can predict what kinds of developmental breakthroughs the future may hold, we are looking at the best available quantum computing technologies worldwide in parallel. As I mentioned, we currently have contracts for computers built by D-Wave, Fujitsu, Rigetti and IBM.

But even representatives of leading firms in the field admit that, in their present state, these computers have no industrial relevance.

Linnhoff-Popien: That’s true. Right now, we’re still doing things that a classical computer can do just as well.
But we are also showing that small-scale scenarios can also be handled by quantum computers. The level of performance of a quantum computer can be expressed in the number of qubits it can process. Qubits are two-state quantum systems. Each measurement causes these systems to take on a single, definite state. The more qubits that can be processed by quantum computer, the greater the size and complexity of the problems it can solve. The IBM Q System One in Ehningen (works with 27 qubits, the IBM model in the US – to which we also have access – can operate on up to 65 qubits. It’s exciting to experience for oneself what each model can already do, and what it can’t yet do. Based on the predicted rate of development, we expect to see the first commercially relevant results of quantum computing within the next five years or so.

But only for very specific problems.

Linnhoff-Popien: Not necessarily. Optimization problems are a fundamental component of logistics and Industry 4.0, the manufacturing plant of the future.
In addition, the financial industry faces the challenge of portfolio optimization. In medicine and the pharmaceutical industry there are problems of combinatorial optimization, such as determining which vaccine formulations provide the best protection against diverse mutant versions of viruses. Energy utilities need to optimize the operation of their power grids, and many optimization issues also arise in AI. All aspects of our lives and livelihoods are confronted with innumerable optimization problems.

If, as you say, the range of possible applications is broad, how realistic is the hope that quantum computer will someday replace conventional electronic computers?

Linnhoff-Popien: We proceed on the assumption that quantum computers will always be employed as co-processors, as adjuncts to conventional computer systems.

Some years ago, you set up a special laboratory to explore quantum computing from the standpoint of informatics – from the user’s perspective – and to advise companies on possible applications. What was the thinking behind this strategy?

Linnhoff-Popien: We started the QAR Lab in 2016. QAR stands for Quantum Applications and Research. At that point, a DAX-listed concern asked us whether we were in a position to program a particular problem on a quantum annealer. At that time, there were very few groups working on the topic, we were among the first in the world. But after an initial period of skepticism, I became fascinated with the field.
In the context of the PlanQK project, which was initiated by the German Government in 2019 in order to stimulate research on quantum computing, we received a substantial amount of funding to extend our research, and we are now a partner in the new Munich Quantum Valley (MQV) collaboration.
In the meantime, the business world has discovered quantum computing, and alliances like the recently founded Quantum Technology and Application Consortium QUTAC – most of whose members are DAX-listed firms – will undoubtedly explore the commercial opportunities offered by quantum computing in the future.

Are SMEs also interested?

Linnhoff-Popien: For commercial firms, quantum computing represents an investment opportunity – it currently yields no returns. That’s why the companies now involved are the larger ones willing and able to take on the risks. But SMEs are beginning to take note of the chances it offers for them.

What can you offer clients at the moment?

Linnhoff-Popien: We help companies to find the quickest possible route to a quantum advantage for their businesses. We begin by assessing where the firm now stands, on the basis of a six-level scheme defined by the QAR Lab.
On levels 0 and 1, we first evaluate the company’s expertise in a range of favorable fields of application. On level 2, we compile a long-list of ‘use cases’ for quantum computing. Level 3 then analyzes and ranks these use cases, and identifies the most promising application. On level 4, we assist the firm in implementing the selected application on several quantum computers, and on level 5 we estimate the number of qubits required to achieve a quantum advantage for that particular problem.
Perhaps the most exciting component of the whole procedure for us is writing the programs for the different quantum computers, executing them and finding out what is actually feasible with each machine.

You were a member of the panel of experts of Quantum Computing set up to advise the Federal Government on the issue, and contributed to the Road-Map for Quantum Computing in Germany. What sort of strategy do you favor?

Linnhoff-Popien: Initially, the Federal Government provided 2 billion euros for the construction of one or more quantum computers. We have excellent research programs and some modules in Germany. But, as far as I know, there is no computer anywhere in Europe at present that can compete with existing machines elsewhere – which can handle, let’s say 50 qubits, in a gate model. As an information scientist on the expert panel, I argued strongly that these funds should not only be used to build quantum computers, but also to develop and test algorithms, software and applications on the quantum computers that are currently available. This is the best way of optimally preparing German businesses for the era of quantum computing, which has already begun.

Prof. Dr. Claudia Linnhoff-Popien holds the Chair of Mobile and Distributed Systems in the Institute of Informatics at LMU. She initiated the development of the QAR Lab, which focuses on the challenges of quantum computing from the point of view of information science.