Classical simulations of noisy commuting quantum computations

Abstract

As research on building a scalable quantum computer is advancing, it is important to be able to check such a device’s correctness. One way to achieve verification is through classical simulations. Due to their exponential complexity, we can only perform smaller computations and then extrapolate results to the domain of quantum supremacy. In this project we extend the usual perfect simulations by also considering the architectural constraints and noise of a particular physical implementation. We aim to provide a general framework for constructing such experimentally realistic simulations. Two particular problems are described in order to exemplify how the more general methodology can be applied to specific scenarios. In our concrete examples we focus on fully commuting Instantaneous Quantum Polynomial-time (IQP) algorithms executed on the NQIT Q20:20 machine. The first example estimates the partition functions of random 2D complex-temperature Ising models in the circuit model of computation. The second example solves instances of IQP X-programs using measurement-based quantum computation (MBQC). We observe significantly different behaviour between the two in regards to their responses to noise.