Measurement-Assisted Clifford Synthesis

TL;DR

This work addresses the problem of Clifford synthesis by introducing a measurement-assisted method that derives an $n$-qubit Clifford unitary $C$ from the inverse stabilizer tableau using $2n$ ancillas. The circuit employs layers of controlled-Pauli gates, $X$-basis measurements, and single-qubit corrections, forming a new normal form with a two-qubit-gate count equal to the tableau weight and a depth of $n+2$. The authors prove correctness via a quantum-filter argument in the $2$-qubit case and outline how the inverse tableau can be obtained and generalized to $n$ qubits. This approach offers a depth-efficient, ancilla-driven alternative for Clifford synthesis, with practical appeal for architectures like trapped ions that support all-to-all inter-register connectivity.

Abstract

In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C†$, 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 $n$.

Figures (3)

• Figure 1: Measurement-Assisted Clifford Synthesis
• Figure 2: (a) Synthesis circuit for a 2-qubit Clifford. (b) Equivalent circuit.
• Figure 3: Single-qubit quantum filter