# Hybrid Quantum Energy Landscape Computing

Lead Research Organisation:
Durham University

Department Name: Physics

### Abstract

At its most fundamental level, computation relies on being able to use physical components to represent and manipulate abstract information. Representation of information can be accomplished in two ways:

(1) Digital computing, in which all information is represented in a discrete way, ones and zeros.

(2) Analog computing, in which some of the information is represented as continuous variables.

Classical computing is currently dominated by digital technology, e.g. desktops, laptops, and smart phones are all governed by digital technology. Within living memory, hybrid computation has dominated, calculations where performed by analog slide rules, supplemented by digital-like pen and paper calculations. Algorithms based on emulating natural (analog) processes are powerful computational tools. An example would be simulated annealing, where solutions to optimization problems are found by simulating a cooling process. A more sophisticated algorithm such as parallel tempering, which involves 'swapping' systems at different temperatures, is even more powerful than simulated annealing and has made it obsolete.

Quantum computing:

(1) Uses the quantum nature of the world we live in to produce more powerful computation.

(2) Has proven to be better at solving some problems than any non-quantum approach.

(3) Quantum computing devices are just getting to the stage of being useful. Therefore, the design of algorithms which can get the most performance out of small and imperfect devices is imperative.

Quantum annealing:

(1) Is a quantum analogue of simulated annealing, which uses quantum mechanics to aid calculations.

(2) Quantum annealing already has experimental implementations, which are commercially available, e.g. devices produced by D-Wave systems Inc. have been purchased for use by Google, NASA, and Lockheed Martin.

(3) Quantum annealers are especially suited to optimisation and machine learning problems, such as the travelling salesperson problem.

My project:

(1) I will develop protocols, which are hybrids between analog (like continuous-time quantum computation which harness fundamental laws of physics) and classical digital computation, to make computations more powerful.

(2) The algorithms that I will develop will run on hybrid part-classical, part-quantum hardware.

(3) I will also develop algorithms based on continuous-time quantum computing methods such as quantum random walks.

(4) Additionally, I will develop algorithms based on simulations of analog quantum systems. They can be run either on digital quantum computers, based on discrete 'gates', or on classical machines. I will develop techniques, which work on many quantum computing platforms and will be useful regardless of relative rates of development.

The project will take a three-pronged approach:

(1) I will construct more sophisticated hybrid algorithms, for instance, analogues of parallel tempering rather than simulated annealing.

(2) Then, I will provide proof-of-principle that these algorithms have an advantage over current methods.

(3) Finally, I will develop implementations on real devices and case studies for real-world industrial problems.

(1) Digital computing, in which all information is represented in a discrete way, ones and zeros.

(2) Analog computing, in which some of the information is represented as continuous variables.

Classical computing is currently dominated by digital technology, e.g. desktops, laptops, and smart phones are all governed by digital technology. Within living memory, hybrid computation has dominated, calculations where performed by analog slide rules, supplemented by digital-like pen and paper calculations. Algorithms based on emulating natural (analog) processes are powerful computational tools. An example would be simulated annealing, where solutions to optimization problems are found by simulating a cooling process. A more sophisticated algorithm such as parallel tempering, which involves 'swapping' systems at different temperatures, is even more powerful than simulated annealing and has made it obsolete.

Quantum computing:

(1) Uses the quantum nature of the world we live in to produce more powerful computation.

(2) Has proven to be better at solving some problems than any non-quantum approach.

(3) Quantum computing devices are just getting to the stage of being useful. Therefore, the design of algorithms which can get the most performance out of small and imperfect devices is imperative.

Quantum annealing:

(1) Is a quantum analogue of simulated annealing, which uses quantum mechanics to aid calculations.

(2) Quantum annealing already has experimental implementations, which are commercially available, e.g. devices produced by D-Wave systems Inc. have been purchased for use by Google, NASA, and Lockheed Martin.

(3) Quantum annealers are especially suited to optimisation and machine learning problems, such as the travelling salesperson problem.

My project:

(1) I will develop protocols, which are hybrids between analog (like continuous-time quantum computation which harness fundamental laws of physics) and classical digital computation, to make computations more powerful.

(2) The algorithms that I will develop will run on hybrid part-classical, part-quantum hardware.

(3) I will also develop algorithms based on continuous-time quantum computing methods such as quantum random walks.

(4) Additionally, I will develop algorithms based on simulations of analog quantum systems. They can be run either on digital quantum computers, based on discrete 'gates', or on classical machines. I will develop techniques, which work on many quantum computing platforms and will be useful regardless of relative rates of development.

The project will take a three-pronged approach:

(1) I will construct more sophisticated hybrid algorithms, for instance, analogues of parallel tempering rather than simulated annealing.

(2) Then, I will provide proof-of-principle that these algorithms have an advantage over current methods.

(3) Finally, I will develop implementations on real devices and case studies for real-world industrial problems.

### Planned Impact

This project will improve solution methods for a wide range of optimisation and machine learning problems through smarter algorithms.

Published work (see references in case for support) has already been done to show that the quantum optimization and machine learning methods I will develop are relevant to finance, microbiology, computer science, aerospace, communications, schedule optimisation, neural networks, and many other fields.

Impact on end users and technology developers:

1) Companies, researchers, and also government can benefit from better optimisation. For example, more efficient transport routes will guarantee energy savings, while more efficiently scheduling might optimise the use of valuable equipment.

2) By developing more efficient algorithms, this project can bridge the gap between quantum computing as an academic research topic and it becoming a commercially viable industrial tool. With the algorithms produced in this project, developers of hardware will thus be able to commercialise their hardware sooner.

3) This project will influence technology development as it makes the controls more compatible with algorithm design. D-Wave Systems Inc. have begun to incorporate some of the ideas on which this project is based. They are adding controls to their quantum annealing devices which are very similar to ones I proposed in a single authored paper [P.2, my publications]. This is a concrete demonstration of my ability to influence technology development.

Robustness of impact:

1) The project will have a positive impact regardless of the rate of advance in different quantum computing technologies, because my algorithms will run on both gate-based and continuous time platforms ranging from highly dissipative to fully coherent.

2) Classical quantum-inspired algorithms which I will develop are still useful even if experimental quantum computing fails to significantly outperform classical methods.

National impact:

1) This project allows the UK to play a leading role in quantum optimisation and machine learning through software and application development. This project is much less expensive than developing an experimental platform, thus providing excellent value-for-money.

2) UK industry and government will benefit from the results of improved quantum computing methods, and an excellent algorithmic research program will attract more applied quantum computing research to the UK.

3) I will train a PDRA (who is already an expert in operational research) in quantum optimization algorithms. This PDRA will act as an ambassador between technology developers and industry in the UK.

Published work (see references in case for support) has already been done to show that the quantum optimization and machine learning methods I will develop are relevant to finance, microbiology, computer science, aerospace, communications, schedule optimisation, neural networks, and many other fields.

Impact on end users and technology developers:

1) Companies, researchers, and also government can benefit from better optimisation. For example, more efficient transport routes will guarantee energy savings, while more efficiently scheduling might optimise the use of valuable equipment.

2) By developing more efficient algorithms, this project can bridge the gap between quantum computing as an academic research topic and it becoming a commercially viable industrial tool. With the algorithms produced in this project, developers of hardware will thus be able to commercialise their hardware sooner.

3) This project will influence technology development as it makes the controls more compatible with algorithm design. D-Wave Systems Inc. have begun to incorporate some of the ideas on which this project is based. They are adding controls to their quantum annealing devices which are very similar to ones I proposed in a single authored paper [P.2, my publications]. This is a concrete demonstration of my ability to influence technology development.

Robustness of impact:

1) The project will have a positive impact regardless of the rate of advance in different quantum computing technologies, because my algorithms will run on both gate-based and continuous time platforms ranging from highly dissipative to fully coherent.

2) Classical quantum-inspired algorithms which I will develop are still useful even if experimental quantum computing fails to significantly outperform classical methods.

National impact:

1) This project allows the UK to play a leading role in quantum optimisation and machine learning through software and application development. This project is much less expensive than developing an experimental platform, thus providing excellent value-for-money.

2) UK industry and government will benefit from the results of improved quantum computing methods, and an excellent algorithmic research program will attract more applied quantum computing research to the UK.

3) I will train a PDRA (who is already an expert in operational research) in quantum optimization algorithms. This PDRA will act as an ambassador between technology developers and industry in the UK.