Bounding Fault-Tolerant Thresholds for Purification and Quantum Computation

TL;DR

This paper establishes a fundamental error threshold of 5.3% for noisy gate operations in quantum purification and fault-tolerant quantum computing, highlighting the limits of current error correction methods.

Contribution

It provides a new bound on the error rate for purification protocols and fault-tolerant quantum computation under adversarial noise, extending to error detection and post-selection methods.

Findings

Gate errors must be below 5.3% for purification to be possible

The bound applies to concatenated error correction codes with noisy gates

Trade-offs exist between gate errors and qubit loss errors

Abstract

In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to apply also to the case where error detection and post-selection, as proposed by Knill, is used to enhance the threshold. We demonstrate the trade-off between gate/environmentally induced faulty rotations and qubit loss errors.