Extensions to randomized benchmarking for digital and analogue near-term quantum devices

Abstract

The distant promise of a full-scale fault-tolerant universal quantum computer offers a speed-up in run-time for certain problems compared to the best classical algorithms. Inevitably, attention has fallen on the quantum devices that exist today, commonly referred to as noisy intermediate-scale quantum (NISQ) devices, and their role in the quantum revolution. Before the realisation of applications for any NISQ devices, the noisy part of the acronym needs to be addressed; practical, scalable noise characterisation, certification and benchmarking techniques are essential. In this thesis we address noise in both digital and analogue NISQ devices, focusing on a partial noise characterisation technique called randomized benchmarking (RB) that provides a measure of the average performance of a set of quantum gates on a chosen quantum device. We first introduce RB, the theory behind it and the latest results in the field. Next, in the first part of this thesis, we look at RB for digital NISQ devices. We address the notion of trust. Trust in RB has not been questioned before, but we determine a malicious noise scenario that could affect the output of performing a Clifford RB protocol. We introduce a new protocol Randomized Benchmarking with Stabilizer Verification (RBSV), in two forms, that captures this malicious noise scenario or confirms that the device is doing what it is intended to do. We present numerical results supporting our conjectures and end with a discussion of future work, particularly with regards to making the proposal more practical. In the second part of this thesis we explore RB in the analogue setting. In place of exact unitary 2-designs we derive bounds on the RB output data in the case that we have an ϵ-approximate unitary 2-design, which we conjecture is a worst-case bound. We present the first proposal for RB in the analogue quantum setting which, for convenience, we refer to as analogue randomized benchmarking (ARB). Our proposal is not dependent on the model that describes the system, and the gate-set is a family of unitaries created from evolving a set of disordered Hamiltonians for the same fixed time. We stipulate conditions on the disorder terms added to the system Hamiltonian for generating -approximate unitary 2-designs on the Hilbert space of the system. We simulate ARB for different noise models, including spontaneous emission and general stray magnetic field fluctuations, and show heuristically that ARB gives reasonable estimates for the average error rate of our unitaries in different contexts. We debate the meaning of the RB parameter in this setting and discuss future work, particularly with regards to formalising our conjectures.