Measurement-Assisted Clifford Synthesis

TL;DR

This paper presents a measurement-assisted method for synthesizing n-qubit Clifford unitaries from their inverse's stabilizer tableau, optimizing gate count and depth using ancilla qubits and measurements.

Contribution

It introduces a novel normal form for Clifford synthesis that minimizes two-qubit gates and linearizes circuit depth based on the stabilizer tableau weight.

Findings

Gate count equals the stabilizer tableau weight.

Circuit depth is linear in the number of qubits.

Method uses ancilla states and measurements for synthesis.

Abstract

In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C\dag$, using ancilla qubits and measurements. The procedure uses ancillary $|+\rangle$ states, controlled-Paulis, $X$-basis measurements and single-qubit Pauli corrections on the data qubits (based on the measurement results). This introduces a new normal form for Clifford synthesis, with the number of two-qubit gates required exactly equal to the weight of the stabilizer tableau, and a depth linear in $n$.