# Towards Enhanced Verification of Near-Term Small-Scale Quantum Systems with Restricted Architectures

Lead Research Organisation:
University of Edinburgh

Department Name: Sch of Informatics

### Abstract

The focus of this project is to develop a quantum verification technique for restricted low-complexity quantum architectures, specifically analogue quantum simulators. It is widely accepted that quantum computers will be able to solve problems that are classically intractable. Quantum verification is the field of quantum computing that aims to answer the question: If a quantum computer solves a problem that can not be solved classically, how does one verify that the outcome is correct? This question is aimed at systems of high complexity. However, thinking of this question in terms of low-complexity quantum systems, we can redefine verification as a measure of the systems performance and a characterisation of the noise present in the system for specific instances.

Quantum simulators are engineered quantum systems that emulate another physical quantum device. Although most architectures for quantum computing and quantum simulation deal with discrete variables, quantum logic gates (digital), analogue quantum simulators involve something called a time-evolution operator and are therefore not compatible with current quantum verification techniques used for digital quantum computers/simulators. The goal of this project is to develop a quantum verification technique that can evaluate the performance of an analogue quantum simulator beyond the scope of current techniques that test for reliability in the simulators computation. Analogue quantum simulators are vital in terms of understanding dynamics of many-body quantum systems, quantum information, entanglement and specific properties of certain physical phenomena. Therefore, establishing confidence in an analogue quantum simulator as an emulation of a physical quantum system is incredibly important.

When analogue quantum simulators are engineered to create long-range interactions, current techniques fail at shorter time-scales and for a small amount of qubits. The aim of this project is to develop a technique independent of system size that can partially characterise the amount of noise present in the time-evolution of a long-range quantum simulator, and thereby have some measure of the systems performance. In this way, an analogue quantum simulator that seems to be performing correctly can act as a benchmark for other simulators and can establish confidence in your simulator.

Focus was put on randomized benchmarking, which is an experimental protocol used to measure the average strength of errors present in a quantum computer when running long randomly-chosen computations. It has only been applied to digital quantum systems, by adapting the theory to the analogue regime a protocol for analogue randomized benchmarking has been created, with the hope that it may be implemented experimentally in order to demonstrate that noise can be partially characterised for an analogue quantum simulator for long-range interactions and larger system sizes. This would be an important milestone in quantum simulation, many-body quantum physics and benchmarking as it combines techniques used for quantum computation with low-complexity quantum simulators.

So far, focus has been put on a one dimensional analogue quantum simulator that is a string of trapped calcium-ions, and classical simulations of analogue randomized benchmarking on this system are underway. Future directions include implementing analogue randomized benchmarking experimentally and applying analogue randomized benchmarking to Rydberg atoms. Eventually the goal is to combine the analogue randomized benchmarking protocol with current quantum verification ideas so that rather than obtaining a measure of the average strength of errors in the system, we can highlight where the biggest contributors to noise occur and for what type of computation performance is best.

Quantum simulators are engineered quantum systems that emulate another physical quantum device. Although most architectures for quantum computing and quantum simulation deal with discrete variables, quantum logic gates (digital), analogue quantum simulators involve something called a time-evolution operator and are therefore not compatible with current quantum verification techniques used for digital quantum computers/simulators. The goal of this project is to develop a quantum verification technique that can evaluate the performance of an analogue quantum simulator beyond the scope of current techniques that test for reliability in the simulators computation. Analogue quantum simulators are vital in terms of understanding dynamics of many-body quantum systems, quantum information, entanglement and specific properties of certain physical phenomena. Therefore, establishing confidence in an analogue quantum simulator as an emulation of a physical quantum system is incredibly important.

When analogue quantum simulators are engineered to create long-range interactions, current techniques fail at shorter time-scales and for a small amount of qubits. The aim of this project is to develop a technique independent of system size that can partially characterise the amount of noise present in the time-evolution of a long-range quantum simulator, and thereby have some measure of the systems performance. In this way, an analogue quantum simulator that seems to be performing correctly can act as a benchmark for other simulators and can establish confidence in your simulator.

Focus was put on randomized benchmarking, which is an experimental protocol used to measure the average strength of errors present in a quantum computer when running long randomly-chosen computations. It has only been applied to digital quantum systems, by adapting the theory to the analogue regime a protocol for analogue randomized benchmarking has been created, with the hope that it may be implemented experimentally in order to demonstrate that noise can be partially characterised for an analogue quantum simulator for long-range interactions and larger system sizes. This would be an important milestone in quantum simulation, many-body quantum physics and benchmarking as it combines techniques used for quantum computation with low-complexity quantum simulators.

So far, focus has been put on a one dimensional analogue quantum simulator that is a string of trapped calcium-ions, and classical simulations of analogue randomized benchmarking on this system are underway. Future directions include implementing analogue randomized benchmarking experimentally and applying analogue randomized benchmarking to Rydberg atoms. Eventually the goal is to combine the analogue randomized benchmarking protocol with current quantum verification ideas so that rather than obtaining a measure of the average strength of errors in the system, we can highlight where the biggest contributors to noise occur and for what type of computation performance is best.

### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/N509711/1 | 01/10/2016 | 30/09/2021 | |||

1951737 | Studentship | EP/N509711/1 | 01/10/2017 | 31/03/2021 | Ellen Elizabeth Derbyshire |

Description | By applying randomized benchmarking (RB), a technique usually reserved for digital quantum computers, to analog quantum simulators we found that the ARB protocol seems to be robust to several realistic noise ('unwanted perturbations' to the system that may cause the computation to deviate) models provided that the set of operations one tests is close enough to a uniformly random structure (an approximate t-design). Moreover, it seems that the simple noise assumptions that give a more straightforward result from RB, are more realistic in the analog setting. The development of this initial protocol have highlighted several new research areas, firstly finding a construction for analog operations that have this unique approximate t-design structure; this could lead to applications such as quantum cryptography, or demonstrating a quantum computational advantage, as well as benchmarking. Secondly, that the time-reversal aspect of the protocol will need to be modified in order to be physically implementable. |

Exploitation Route | This ARB protocol can be applied to physical quantum platforms, where experimentalists could adapt it to their devices knowing the outcomes if the necessary conditions are met. If we can find a way to generate these approximate t-designs in the analog setting then ARB would be more easily adaptable, particularly if we have a specific generic way to generate them (this is an ongoing project), and as mentioned approximate t-designs can be used to develop more applications for analog quantum simulators. |

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

URL | https://arxiv.org/pdf/1909.01295.pdf |

Description | Strathclyde Collaboration |

Organisation | University of Strathclyde |

Department | Department of Physics |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | To this collaboration our research team brought the expertise of computer science, quantum verification and randomized benchmarking. |

Collaborator Contribution | To this collaboration my partners brought the expertise in quantum physics, experimental physics and quantum simulation. |

Impact | This collaboration resulted in the development of the analogue randomized benchmarking protocol, shown to be robust to realistic noise provided the set of operations has the unique random structure of an approximate t-design. |

Start Year | 2018 |