Fault-tolerant quantum computation with non-deterministic entangling gates

TL;DR

This paper investigates fault-tolerant quantum computation using topological cluster states with probabilistic entangling gates, proposing methods to handle missing bonds due to gate failures and analyzing their thresholds.

Contribution

It introduces two strategies for managing missing bonds in topological cluster states caused by non-deterministic entangling gates, enhancing fault-tolerance.

Findings

Fault-tolerance threshold at 6.5% bond-loss with non-adaptive scheme.

Threshold increases to 14.5% bond-loss with adaptive scheme.

Adaptive approach significantly improves robustness against gate failures.

Abstract

Performing entangling gates between physical qubits is necessary for building a large-scale universal quantum computer, but in some physical implementations - for example, those that are based on linear optics or networks of ion traps - entangling gates can only be implemented probabilistically. In this work, we study the fault-tolerant performance of a topological cluster state scheme with local non-deterministic entanglement generation, where failed entangling gates (which correspond to bonds on the lattice representation of the cluster state) lead to a defective three-dimensional lattice with missing bonds. We present two approaches for dealing with missing bonds; the first is a non-adaptive scheme that requires no additional quantum processing, and the second is an adaptive scheme in which qubits can be measured in an alternative basis to effectively remove them from the lattice, hence eliminating their damaging effect and leading to better threshold performance. We find that a fault-tolerance threshold can still be observed with a bond-loss rate of 6.5% for the non-adaptive scheme, and a bond-loss rate as high as 14.5% for the adaptive scheme.