# 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.

### Publications

Dodds Ben
(2018)

*Practical designs for permutation symmetric problem Hamiltonians on hypercubes*in arXiv e-prints
Dattani Nike
(2019)

*Pegasus: The second connectivity graph for large-scale quantum annealing hardware*in arXiv e-prints
Chancellor N
(2019)

*Domain wall encoding of discrete variables for quantum annealing and QAOA*in Quantum Science and Technology
Dodds A
(2019)

*Practical designs for permutation-symmetric problem Hamiltonians on hypercubes*in Physical Review A
Dattani Nike
(2019)

*Embedding quadratization gadgets on Chimera and Pegasus graphs*in arXiv e-prints
Callison A
(2019)

*Finding spin glass ground states using quantum walks*in New Journal of Physics
Roffe J
(2020)

*Quantum Codes From Classical Graphical Models*in IEEE Transactions on Information TheoryDescription | Approximately 1 and a half years into the award, I can now report that there is substantial progress on understanding how continuous time quantum computing solves problems, and we have published results in this area (see previous), I would consider this goal to now have been met. Even though I would consider the basic goal to have been met, I am continuing to advance this strand of research and suspect another breakthrough is imminent. I am also advancing some of the other goals of the award which have not been fully completed. I am constructing case studies for the use of quantum computing in ambulance dispatch and in network problems, and have already written a methodology for constructing case studies. Additionally, I am planning the workshop associates with the fellowship which should allow me to seek new use cases |

Exploitation Route | An improved understanding of the underlying mechanisms of quantum optimization could greatly improve the development of algorithms for quantum computing. Additionally the case studies will help inform which problems are most appropriate for early quantum machines, and more importantly how this decision can be made by others. |

Sectors | Digital/Communication/Information Technologies (including Software),Other |

Description | I have built on the ideas of reverse annealing which has now been included as a protocol in the quantum annealing systems produced by D-Wave Systems Inc. (which sell for about 10 million US dollars) and were first published in a a single author paper by me which was written before my current grant was awarded. Since the project has started, I have done some proof-of-principle experiments to show that these techniques work, these findings were presented at AQC 2018 where I was an invited speaker, and were seen by representatives of D-Wave Systems Inc. my work on reverse annealing continues to influence quantum annealing protocols. |

First Year Of Impact | 2015 |

Sector | Digital/Communication/Information Technologies (including Software) |

Description | First encounters with quantum computing: can games teach quantum reasoning? |

Amount | £19,836 (GBP) |

Funding ID | BB/T018666/1 |

Organisation | Biotechnology and Biological Sciences Research Council (BBSRC) |

Sector | Public |

Country | United Kingdom |

Start | 01/2020 |

End | 03/2020 |