Threshold Accuracy for Quantum Computation

TL;DR

This paper discusses a concatenation technique for fault-tolerant quantum and classical computation that achieves arbitrary accuracy under realistic error assumptions, including leakage errors, extending previous work on quantum memories.

Contribution

It introduces a new concatenation method applicable to classical and quantum networks that tolerates realistic operational errors and accounts for leakage errors.

Findings

The technique enables arbitrary accuracy in quantum and classical computations.

It works under more general error assumptions than previous stochastic models.

Methods to handle leakage errors are proposed, addressing a previously unrecognized problem.

Abstract

We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a similar concatenation technique which can be used with fault tolerant networks to achieve any desired accuracy when computing with classical initial states, provided a minimum gate accuracy can be achieved. The technique works under realistic assumptions on operational errors. These assumptions are more general than the stochastic error heuristic used in other work. Methods are proposed to account for leakage errors, a problem not previously recognized.