Methods for classically simulating noisy networked quantum architectures

As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification via this means fails. However, we can classically simulate small scale quantum computations and hence we are able to test that devices behave as expected in this domain. This constitutes the first step towards obtaining confidence in the anticipated quantum-advantage when we extend to scales that can no longer be simulated. Real devices have restrictions due to their architecture and limitations due to physical imperfections and noise. In this paper we extend the usual ideal simulations by considering those effects. We aim to provide a general methodology and framework for constructing simulations which emulate the physical system. These simulations should provide a benchmark for realistic devices and guide experimental research in the quest for quantum-advantage. To illustrate our methodology we give examples that involve networked architectures and the noise-model of the device developed by the Networked Quantum Information Technologies Hub (NQIT). For our simulations we use, with suitable modification, the classical simulator of Bravyi and Gosset while the specific problems considered belong to the Instantaneous Quantum Polynomial-time class. This class is believed to be hard for classical computational devices, and is regarded as a promising candidate for the first demonstration of quantum-advantage. We first consider a subclass of IQP, defined by Bermejo-Vega et al, involving two-dimensional dynamical quantum simulators, and then general instances of IQP, restricted to the architecture of NQIT.