# Randomness Resources for Quantum Technologies

Lead Research Organisation:
University of Bristol

Department Name: Physics

### Abstract

Quantum information science promises to fundamentally change the way we do things, not unlike how classical information science continues to change every aspect of our daily lives. Classical information science teaches us how difficult it is to break a cipher, or how long it will take a computer to do a calculation; quantum information science predicts fundamentally secure cryptography, and computers that solve certain problems faster than any conceivable classical machine.

At first glance, it is surprising to think that randomness can actually help perform information processing tasks, and yet it can: for example, a random cryptographic key is known to be the best way to hide messages; more surprisingly, there exist problems where, rather than execute a deterministic algorithm as classical computers normally do, it is better to guess -- that is, invoke randomness -- while computing a solution. Thus we say that randomness is a resource in classical information theory; having a coin at hand that one can flip is a tangible asset. This is especially true when one wants to test a complex device or process: send it random inputs, and investigate how the outputs behave.

We can also purposely introduce randomness into quantum information protocols and ask if this can make certain tasks easier. It turns out the answer is also yes, giving rise to the study, for example, of random quantum circuits, or random quantum error correcting codes. In the formalism of quantum mechanics these are expressed as random operators, rather than simple random numbers, but they can be thought of as resources for quantum information science in much the same way as in the classical case.

However, both classically and quantumly, generating truly random resources is very difficult; one can imagine trying to encrypt terabytes of information by flipping a coin billions of times. In practice we rely on so-called pseudorandom resources that, given a finite amount of time or computing power, can never be distinguished from truly random. If we think of increasingly complex tests one might do to check for randomness, a pseudorandom resource will pass these tests up to a certain level of complexity (and fail beyond that). Such resources are much easier to create than truly random ones, and pseudorandom number generators are a cornerstone of today's information technologies.

This research project aims to make pseudorandom resources available to quantum information technologies. In the quantum realm, the notion of pseudorandomness is captured by what are called quantum 't-designs'. These are resources -- ensembles of quantum operators -- that pass randomness tests up to some level of complexity (more precisely, t corresponds to the degree of a statistical moment). The project has two main components; the first will be a systematic study of the mathematical structure of t-designs, finding new ones along the way, and then optimising these resources for specific quantum technologies; at the University of Bristol a technology we focus on is integrated quantum photonics, and so the second part of this project will be to use our theoretical work to propose and perform quantum photonic experiments that demonstrate quantum pseudorandomness.

Quantum technology is in its infancy, and this research will be an important early step in understanding and solving the problem of efficiently producing the randomness that is crucial to information science. In the short term, the results will be used to tackle challenging problems such as finding the best way to characterise increasingly complex quantum devices, like the ones being developed by hundreds of partners in the UK Quantum Technology Network. In the longer term, it will enable customised, plug-in pseudorandom resources for any quantum platform, which will be used in a multitude of future quantum information applications.

At first glance, it is surprising to think that randomness can actually help perform information processing tasks, and yet it can: for example, a random cryptographic key is known to be the best way to hide messages; more surprisingly, there exist problems where, rather than execute a deterministic algorithm as classical computers normally do, it is better to guess -- that is, invoke randomness -- while computing a solution. Thus we say that randomness is a resource in classical information theory; having a coin at hand that one can flip is a tangible asset. This is especially true when one wants to test a complex device or process: send it random inputs, and investigate how the outputs behave.

We can also purposely introduce randomness into quantum information protocols and ask if this can make certain tasks easier. It turns out the answer is also yes, giving rise to the study, for example, of random quantum circuits, or random quantum error correcting codes. In the formalism of quantum mechanics these are expressed as random operators, rather than simple random numbers, but they can be thought of as resources for quantum information science in much the same way as in the classical case.

However, both classically and quantumly, generating truly random resources is very difficult; one can imagine trying to encrypt terabytes of information by flipping a coin billions of times. In practice we rely on so-called pseudorandom resources that, given a finite amount of time or computing power, can never be distinguished from truly random. If we think of increasingly complex tests one might do to check for randomness, a pseudorandom resource will pass these tests up to a certain level of complexity (and fail beyond that). Such resources are much easier to create than truly random ones, and pseudorandom number generators are a cornerstone of today's information technologies.

This research project aims to make pseudorandom resources available to quantum information technologies. In the quantum realm, the notion of pseudorandomness is captured by what are called quantum 't-designs'. These are resources -- ensembles of quantum operators -- that pass randomness tests up to some level of complexity (more precisely, t corresponds to the degree of a statistical moment). The project has two main components; the first will be a systematic study of the mathematical structure of t-designs, finding new ones along the way, and then optimising these resources for specific quantum technologies; at the University of Bristol a technology we focus on is integrated quantum photonics, and so the second part of this project will be to use our theoretical work to propose and perform quantum photonic experiments that demonstrate quantum pseudorandomness.

Quantum technology is in its infancy, and this research will be an important early step in understanding and solving the problem of efficiently producing the randomness that is crucial to information science. In the short term, the results will be used to tackle challenging problems such as finding the best way to characterise increasingly complex quantum devices, like the ones being developed by hundreds of partners in the UK Quantum Technology Network. In the longer term, it will enable customised, plug-in pseudorandom resources for any quantum platform, which will be used in a multitude of future quantum information applications.

### Planned Impact

This project represents an important milestone in applying advanced theory to answer practical questions arising in quantum information technology. The impact of this research will have benefits extending the life of this project, including:

People - In addition to the PI, the project directly supports a postdoctoral researcher who will receive the benefit of the experience gained by working at the interface of state of the art quantum information theory and experiment, amounting to training that is difficult if not impossible to obtain anywhere else. The project also involves engaging with Bristol's EPSRC Centre for Doctoral Training in Quantum Engineering (QE-CDT) by submitting short research projects that can be taken on by QE-CDT PhD students, who will then benefit similarly being trained at the cutting edge of quantum research. This will also be true of any project partners' students, in the UK and internationally, involved. The Quantum in the Cloud outreach project (see Pathways to Impact) will provide a learning tool available via internet to anyone who is inclined to play with this exciting technology, helping inspire a new generation of quantum scientists and engineers.

Industry - The national UK Quantum Technology (QT) Network recently received £270M of funding in order to sow the seeds of a new industry. There are several major challenges that this enterprise faces; one important one is the characterisation and verification of increasingly complex quantum devices, a problem that we know will be too difficult to solve by existing means. Pseudorandom ensembles of quantum operations are one way to address the problem, in the form of 'test patterns' that can be used to probe such devices. As such, this research will have major impact across the UK QT Network towards overcoming this challenge. Furthermore, in order to convince government and industry that quantum technology is viable, the QT Network keenly needs examples of new devices that are novel, despite being in an early stage of development. The quantum randomness resources that this project will produce represent a realistic short term demonstrator of an enabling quantum technology, something that could play an important role in moving the QT Network beyond its current five year term by showing commerical feasibility. Precedent does exist for similar implementations being commericialisable, as quantum random number generators have already been marketed by companies such as IDQuantique. Any promising results of this First Grant along these lines will be brought to the University Research and Enterprise Development office's commercialisation team for consideration.

Society - In the long term, the potential for quantum technology's impact on society is difficult to overstate; a quantum computer's ability to simulate materials alone could revolutionise society (e.g. the search for a high temperature superconductor), not to mention pharmaceutical drug design. Any tool that radically improves our technical abilities will always eventually have important societal impact. This project will contribute to realising the viability of such future quantum technologies by providing randomness resources and all their scientific and technological benefits. The UK is currently a world leader in the nascent Quantum Technology sector, and this project will also help to reinforce that position by making these resources widely available. Finally, through interaction with the QE-CDT the project will see people trained in new techniques in quantum information science, supplying young scientist and engineers ready to be the leaders society will need in this field.

People - In addition to the PI, the project directly supports a postdoctoral researcher who will receive the benefit of the experience gained by working at the interface of state of the art quantum information theory and experiment, amounting to training that is difficult if not impossible to obtain anywhere else. The project also involves engaging with Bristol's EPSRC Centre for Doctoral Training in Quantum Engineering (QE-CDT) by submitting short research projects that can be taken on by QE-CDT PhD students, who will then benefit similarly being trained at the cutting edge of quantum research. This will also be true of any project partners' students, in the UK and internationally, involved. The Quantum in the Cloud outreach project (see Pathways to Impact) will provide a learning tool available via internet to anyone who is inclined to play with this exciting technology, helping inspire a new generation of quantum scientists and engineers.

Industry - The national UK Quantum Technology (QT) Network recently received £270M of funding in order to sow the seeds of a new industry. There are several major challenges that this enterprise faces; one important one is the characterisation and verification of increasingly complex quantum devices, a problem that we know will be too difficult to solve by existing means. Pseudorandom ensembles of quantum operations are one way to address the problem, in the form of 'test patterns' that can be used to probe such devices. As such, this research will have major impact across the UK QT Network towards overcoming this challenge. Furthermore, in order to convince government and industry that quantum technology is viable, the QT Network keenly needs examples of new devices that are novel, despite being in an early stage of development. The quantum randomness resources that this project will produce represent a realistic short term demonstrator of an enabling quantum technology, something that could play an important role in moving the QT Network beyond its current five year term by showing commerical feasibility. Precedent does exist for similar implementations being commericialisable, as quantum random number generators have already been marketed by companies such as IDQuantique. Any promising results of this First Grant along these lines will be brought to the University Research and Enterprise Development office's commercialisation team for consideration.

Society - In the long term, the potential for quantum technology's impact on society is difficult to overstate; a quantum computer's ability to simulate materials alone could revolutionise society (e.g. the search for a high temperature superconductor), not to mention pharmaceutical drug design. Any tool that radically improves our technical abilities will always eventually have important societal impact. This project will contribute to realising the viability of such future quantum technologies by providing randomness resources and all their scientific and technological benefits. The UK is currently a world leader in the nascent Quantum Technology sector, and this project will also help to reinforce that position by making these resources widely available. Finally, through interaction with the QE-CDT the project will see people trained in new techniques in quantum information science, supplying young scientist and engineers ready to be the leaders society will need in this field.

## People |
## ORCID iD |

Peter Turner (Principal Investigator) |

### Publications

Turner PS
(2016)

*Derandomizing Quantum Circuits with Measurement-Based Unitary Designs.*in Physical review letters
Stanisic S
(2018)

*Discriminating distinguishability*in Physical Review A
Stanisic S
(2017)

*Generating entanglement with linear optics*in Physical Review A
Moylett A
(2018)

*Quantum simulation of partially distinguishable boson sampling*in Physical Review A
Alexander R
(2016)

*Randomized benchmarking in measurement-based quantum computing*in Physical Review ADescription | We have discovered a new kind of randomness resource, related specifically to a novel model of quantum computing (QC) called the measurement based (MB) model. We have already used these resources -- measurement based t-designs -- to design a benchmarking protocol for future MBQC devices. |

Exploitation Route | Although inspired by the measurement based model of quantum computation, as a pseudorandom ensemble of quantum operations our results can be used in the circuit model as well, and thus can have applications in any quantum technology where, e.g., randomized benchmarking is used. |

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