## Benchmarking, verifying and utilising near term quantum technology

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##### Date

30/11/2021##### Author

Mills, Daniel

Pappa, Anna

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##### Abstract

Quantum computers can, in theory, impressively reduce the time required to solve many pertinent problems. Such problems are found in applications as diverse as cryptography, machine learning and chemistry, to name a few. However, in practice the set of problems which can be solved depends on the amount and quality of the quantum resources available. With the addition of more qubits, improvements in noise levels, the development of quantum networks, and so on, comes more computing power. Motivated by the desire to measure the power of these devices as their capabilities change, this thesis explores the verification, characterisation and benchmarking techniques that are appropriate at each stage of development. We study the techniques that become available with each advance, and the ways that such techniques can be used to guide further development of quantum devices and their control software. Our focus is on advancements towards the first example of practical certifiable quantum computational supremacy; when a quantum computer demonstrably outperforms all classical computers at a task of practical concern. Doing so allows us to look a little beyond recent demonstrations of quantum computational supremacy for its own sake.
Systems consisting of only a few noisy qubits can be simulated by a classical computer. While this reduces the applicability of quantum technology of this size, we first provide a methodology for using classical simulations to guide progress towards demonstrations of quantum computational supremacy. Using measurements of the noise levels present in the NQIT Q20:20 device, an ion-trap based quantum computer, we use classical simulations to predict and prepare for the performance of larger devices with similar characteristics. We identify the noise sources that are the most impactful, and simulate the effectiveness of approaches to mitigating them.
As quantum technology advances, classically simulating it becomes increasingly resource intensive. However, simulations remain useful as a point of comparison against which to benchmark the performance of quantum devices. For so called ‘random quantum circuits’, such benchmarking techniques have been developed to support claims of demonstrations of quantum computational supremacy. To give better indications of the device’s performance in practice, instances of computations derived for practical applications have been used to benchmark devices. Our second contribution is to introduce a suite of circuits derived from structures that are common to many instances of computations derived for practical applications, contrasting with the aforementioned approach of using a collection of particular instances. This allows us to make broadly applicable predictions of performance, which are indicative of the device’s behaviour when investigating applications of concern. We use this suite to benchmark all layers of the quantum computing stack, exploring the interplay between the compilation strategy, device, and the computation itself. The circuit structures in the suite are sufficiently diverse to provide insights into the noise channels present in several real devices, and into the applications for which each quantum computing stack is best suited. We consider several figures of merit by which to assess performance when implementing these circuits, taking care to minimise the required number of uses of the quantum device.
As our third contribution, we consider benchmarking devices performing Instantaneous Quantum Polynomial time (IQP) computations; a subset of all the computations quantum computers are capable of performing in polynomial time. By using only a commuting gate set, IQP circuits do not require the development of a universal quantum computer, but are still thought impossible to simulate efficiently on a classical computer. Utilising a small quantum network, which allows for the transmission of single qubits, we introduce an approach to benchmarking the performance of devices capable of implementing IQP computations. As the resource consumption of our benchmarking technique grows reasonably as the size of the device grows, it enables us to benchmark IQP capable devices when they are of sufficient size to demonstrate quantum computational supremacy, and indeed to certify demonstrations of quantum computational supremacy. The approach we introduce is constructed by concealing some secret structure within an IQP computation. This structure can be taken advantage of by a quantum computer, but not by a classical one, in order to prove it is capable of accurately implementing IQP circuits. To achieve this we derive an implementation of IQP circuits which keeps the computation, and as a result the structure introduced, hidden from the device being tested. We prove this implementation to be information-theoretically and composably secure.
In the work described above we explore verification, characterisation and benchmarking of quantum technology both as it advances to demonstrations of quantum computational supremacy, and when it is applied to real world problems. Finally, we consider demonstrations of quantum computational supremacy with an instance of these real world problems. We consider quantum machine learning, and generative modelling in particular. Generative modelling is the task of producing new samples from a distribution, given a collection of samples from that distribution. We introduce and define ‘quantum learning supremacy’, which captures our intuitive notion of a demonstration of quantum computational supremacy in this setting, and allows us to speak formally about generative modelling tasks that can be completed by quantum, but not classical, computers. We introduce the Quantum Circuit Ising Born Machine (QCIBM), which consists of a parametrised quantum circuit and a classical optimisation loop to train the parameters, as a route to demonstrating quantum learning supremacy. We adapt results that exist for IQP circuits in order to argue that the QCIBM might indeed be used to demonstrate quantum learning supremacy. We discuss training procedures for the QCIBM, and Quantum Circuit Born Machines generally, and their implications on demonstrations of quantum learning supremacy.