Composite Toffoli gate with two-round error detection

TL;DR

This paper presents a fault-tolerant method to implement a composite Toffoli gate with significantly reduced resource requirements using error detection and Clifford operations, enhancing quantum computer efficiency.

Contribution

Introduces a novel fault-tolerant construction for composite Toffoli gates utilizing Clifford operations and multiple T-gates, reducing resource overheads by over an order of magnitude.

Findings

Resource overhead reduced by more than tenfold.

Error detection lowers failure probability significantly.

Postselected failure rate scales as 3072p^4 for dominant T-gate errors.

Abstract

We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for quantum computers by more than an order of magnitude. The procedure uses Clifford operations and 64 copies of the non-Clifford gate $T = \exp[i \pi (I - \sigma^z) /8]$. Quantum codes detect errors in the circuit. When the dominant source of error is $T$-gate failure with probability $p$, then the composite Toffoli circuit has postselected failure rate of $3072p^4$ to lowest order.