Generalised state spaces and non-locality in fault tolerant quantum computing schemes

TL;DR

This paper explores how restricted measurements in quantum computing alter entanglement and non-locality, leading to new classical simulation methods and insights into fault tolerance thresholds.

Contribution

It introduces a framework linking restricted measurement-based entanglement to classical simulability and non-local correlations in fault-tolerant quantum schemes.

Findings

Restricted measurements change entanglement properties.

Some noisy quantum computers can be classically simulated.

New regimes of quantum evolution are identified that do not improve fault tolerance bounds.

Abstract

We develop connections between generalised notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli directions. By considering restricted measurements one can (by considering the dual positive operators) construct single particle state spaces that are different to the usual quantum state space. This leads to a modified notion of entanglement that can be very different to the quantum version (for example, Bell states can become separable). We use this approach to develop alternative methods of classical simulation that have strong connections to the study of non-local correlations: we construct noisy quantum computers that admit operations outside the Clifford set and can generate some forms of multiparty quantum entanglement, but are otherwise classical in that they can be efficiently simulated classically and cannot generate non-local statistics. Although the approach provides new regimes of noisy quantum evolution that can be efficiently simulated classically, it does not appear to lead to significant reductions of existing upper bounds to fault tolerance thresholds for common noise models.