Towards reliable quantum computation: mitigation and certification from NISQ to early fault-tolerance

Abstract

The recent pace of experimental progress in quantum technologies suggests we may soon reach a time when quantum devices can be applied to solve problems of practical interest.

Despite this, we are still far from being able to abstract away the effects of noise on quantum computation. The reliable execution of computations on current devices remains a significant challenge. This holds true both for computation with noisy physical qubits and for computation using the limited forms of error correction available on early fault-tolerant quantum devices. In this thesis, I propose methods for improving the reliability of quantum devices, as the field transitions from the regime of noisy intermediate-scale quantum (NISQ) devices to that of early fault-tolerance. These span the topics of quantum error mitigation, quantum error correction and quantum certification. In the first instance, I propose methods for improving the performance of quantum devices affected by limited amounts of noise. Specifically, I present a method for mitigating the effects of time-dependent noise. This adapts a computational certification protocol called accreditation into a method for postselecting on weaker time-dependent noise behaviours. The method is analytically shown to lead to a provable reduction in errors for the case of depolarising noise, and demonstrated in experiments on superconducting hardware. I also present a method for mitigating the effects of photon loss in photonic quantum devices. Through a combination of analytical and numerical analysis, it is shown that there are wide regimes of photon loss for which this method outperforms postselection, the standard method of handling loss in photonic devices. Additionally, evidence is provided that the method enhances the performance of a quantum machine learning model known as a Quantum Circuit Born Machine in the presence of photon loss. Next, I introduce a framework for certifying the correctness of computations run on encoded logical qubits. This is sensitive to considerably more general forms of noise than is usually considered in quantum error correction. It can be applied to efficiently certify the correctness of quantum computations for large system sizes, beyond the capabilities of methods relying on classical simulation. In numerical experiments, the framework was applied to certify the accuracy of instantaneous quantum polynomial (IQP) circuit sampling and Trotterised Hamiltonian simulation. It can be used to efficiently assess whether quantum error mitigation may be usefully applied to a computation, to upper-bound the infidelity of the encoded logical state, and to extend the method of entropy density benchmarking to logical computation. The methods presented in this thesis contribute to the wider effort of building towards reliable quantum computation: both in the sense of reducing the effects of noise on computational output, and in the sense of certifying the correctness of computation beyond the capabilities of classical simulators. Only with reliable quantum computation can the full potential of this technology be realised.