Proof of finite surface code threshold for matching

TL;DR

This paper proves that reliable quantum computation is feasible with the surface code using only realistic two-qubit gates and measurements, establishing a practical error threshold that many current experiments meet.

Contribution

It provides the first formal proof of a finite error threshold for the surface code under realistic assumptions, confirming experimental feasibility.

Findings

Error threshold p<7.4x10^-4 established

Surface code can be implemented with only nearest neighbor two-qubit gates

Reliable quantum computation is possible under practical error rates

Abstract

The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising quantum error correction code, requiring only a physically reasonable 2-D lattice of qubits with nearest neighbor interactions. However, existing proofs that reliable quantum computation is possible using this code assume the ability to measure four-body operators and, despite making this difficult to realize assumption, require that the error rate of these operator measurements is less than 10^-9, an unphysically low target. High error rates have been proved tolerable only when assuming tunable interactions of strength and error rate independent of distance, which is also unphysical. In this work, given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and single-qubit measurement, initialization, and unitary gates, all of which have error rate p, we prove that arbitrarily reliable quantum computation is possible provided p<7.4x10^-4, a target that many experiments have already achieved. This closes a long-standing open problem, formally proving the experimental feasibility of quantum computation under physically reasonable assumptions.