Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code

TL;DR

This paper introduces a weak fault-tolerance approach using a quantum error-detecting code that improves small-scale quantum computations with less overhead than full fault-tolerant codes.

Contribution

It proposes a middle-ground quantum error-detecting scheme that detects single errors and enables universal computation with reduced overhead.

Findings

Significant improvement over no error correction at low physical error probabilities.

Requires much less overhead than full fault-tolerance codes.

Achieves universal quantum computation with weak fault tolerance.

Abstract

Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the $[[n,n-2,2]]$ quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.