# Property Testing for Quantum Engineering (ProTeQE)

Lead Research Organisation:
University of Warwick

Department Name: Physics

### Abstract

Our senses incessantly inundate us with information on a multitude of issues in multifarious forms. Yet, when it comes to deciding any given topic, it is seldom feasible to use all of this information. Rather, we decide by deliberating on a selected, typically small, part of the whole.

This self-evident realisation raises some fundamental questions. For instance, given a topic, is it even possible to make a meaningful decision by considering a small part of all the available information? Even if it were, how should this small part be selected?

Theoretical computer science seeks to formalise these questions, and then answer them for specific mathematical problems. This forms the subject of property testing, which is concerned with the design of ultra-fast algorithms for approximate decision making. In this context, an approximate decision means choosing between objects that have a predetermined property and those that are 'far' from having that property. Applications range from checking the correctness of extremely large and complex software programmes to detecting pathologies based on interactions between proteins in the human body. For instance, deciding the correctness of a software by checking every line of code (which for a modern car can exceed 100 million lines) would be prohibitively expensive, time-consuming, and itself error prone. The ultra-fast property testing algorithms inspect only relatively small and random portions of these huge objects.

ProTeQE will apply property testing to quantum engineering.

Quantum computers are believed to be capable of solving several problems exponentially more efficiently than classical computers. Unsurprisingly, this comes at an exponential cost. Describing a quantum computer operating of n quantum bits (qubits) typically requires 4^n numbers. Once such a system is engineered, how can we decide if it can be used to build a reliable quantum computer?

A reliable quantum computer - technically called a fault-tolerant quantum computer (FTQC) is only possible if the engineered quantum system obeys a specific set of mathematical properties. ProTeQE has the objective of answering the question: Given an object, in this case an engineered quantum system, does it have the properties necessary for FTQC, or is it far from having them?

An ultra-fast algorithm to answer this question will remove a severe bottleneck in the development of quantum engineering and quantum technologies - that of testing quantum devices. The present testing regimen of measuring and processing exponentially many numbers to make a decision is prohibitively expensive, time-consuming, and itself error prone. ProTeQE will thus enable a faster turnaround in the designing and prototyping of engineered quantum systems. This should accelerate the development of reliable real-world quantum computers, and facilitate greater advances in quantum engineering and technologies more generally.

ProTeQE should also nourish our basic curiosity. Quantum mechanics, which is presently our fundamental theory of Nature, is inherently probabilistic and non-local. When these concepts interface with those of property testing and approximate decision-making, the outcome could impact the foundations of our understanding of the laws of Nature. In particular, ProTeQE may eventually shed light on an abiding question: Are all fundamental laws of Nature (such as quantum mechanics) efficiently testable?

This self-evident realisation raises some fundamental questions. For instance, given a topic, is it even possible to make a meaningful decision by considering a small part of all the available information? Even if it were, how should this small part be selected?

Theoretical computer science seeks to formalise these questions, and then answer them for specific mathematical problems. This forms the subject of property testing, which is concerned with the design of ultra-fast algorithms for approximate decision making. In this context, an approximate decision means choosing between objects that have a predetermined property and those that are 'far' from having that property. Applications range from checking the correctness of extremely large and complex software programmes to detecting pathologies based on interactions between proteins in the human body. For instance, deciding the correctness of a software by checking every line of code (which for a modern car can exceed 100 million lines) would be prohibitively expensive, time-consuming, and itself error prone. The ultra-fast property testing algorithms inspect only relatively small and random portions of these huge objects.

ProTeQE will apply property testing to quantum engineering.

Quantum computers are believed to be capable of solving several problems exponentially more efficiently than classical computers. Unsurprisingly, this comes at an exponential cost. Describing a quantum computer operating of n quantum bits (qubits) typically requires 4^n numbers. Once such a system is engineered, how can we decide if it can be used to build a reliable quantum computer?

A reliable quantum computer - technically called a fault-tolerant quantum computer (FTQC) is only possible if the engineered quantum system obeys a specific set of mathematical properties. ProTeQE has the objective of answering the question: Given an object, in this case an engineered quantum system, does it have the properties necessary for FTQC, or is it far from having them?

An ultra-fast algorithm to answer this question will remove a severe bottleneck in the development of quantum engineering and quantum technologies - that of testing quantum devices. The present testing regimen of measuring and processing exponentially many numbers to make a decision is prohibitively expensive, time-consuming, and itself error prone. ProTeQE will thus enable a faster turnaround in the designing and prototyping of engineered quantum systems. This should accelerate the development of reliable real-world quantum computers, and facilitate greater advances in quantum engineering and technologies more generally.

ProTeQE should also nourish our basic curiosity. Quantum mechanics, which is presently our fundamental theory of Nature, is inherently probabilistic and non-local. When these concepts interface with those of property testing and approximate decision-making, the outcome could impact the foundations of our understanding of the laws of Nature. In particular, ProTeQE may eventually shed light on an abiding question: Are all fundamental laws of Nature (such as quantum mechanics) efficiently testable?