Clifford synthesis via generalized S and CZ gates

TL;DR

This paper presents a method to implement any n-qubit Clifford unitary using at most 2n multi-qubit measurements, optimizing measurement sets for flexibility and fault-tolerance in quantum computing.

Contribution

It introduces a novel measurement-based implementation of Clifford unitaries with minimal measurement sets and discusses adaptations for fault-tolerant quantum hardware.

Findings

Any n-qubit Clifford can be implemented with ≤ 2n measurements.

Measurements can be organized into two commuting sets of size ≤ n.

The approach offers flexible space-time trade-offs for quantum circuit implementation.

Abstract

We show that any $n$-qubit Clifford unitary can be implemented using at most $2n$ multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of independent mutually-commuting measurements. Each of these sets is of size at most $n$. This enables very flexible space-time trade-offs when implementing Clifford unitaries. We also discuss a version of the result that relies on multi-target CNOTs and is more relevant for targeting fault-tolerant hardware based on Quantum LDPC codes.