Reduced constant-cost implementations of Clifford operations using global interactions

TL;DR

The paper addresses efficient, constant-cost Clifford synthesis using single-qubit gates plus programmable all-to-all multiqubit entangling gates, achieving a constant-cost circuit with at most six entangling gates for any Clifford. It presents an explicit algorithm that decomposes Clifford operations into a single-qubit layer and a CX layer realized with five MQ gates, with a final CZ that can merge with the next CZ layer, giving six MQ gates total for the Clifford. The construction uses the symplectic form representation of Pauli vectors, mapping Clifford operators to a symplectic matrix in GL(2n, F2) and deriving the CX decomposition via a factorization B = S2 S1 with S1,S2 symmetric. Drive-power analysis based on the nuclear-norm Ω_nuc shows the required power is comparable to Gaussian-elimination-based implementations, while depth and runtime are reduced; the method is compatible with block-circuit compilation and existing Clifford-synthesis frameworks.

Abstract

We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a constant-cost of no more than 6 application of such Clifford entangling multiqubit gates to realize any sequence of Clifford operations of any length, without ancillae. Furthermore, we show that any sequence of CNOT gates of any length, can be replaced with 5 applications of such Clifford entangling multiqubit gates, without ancillae. We investigate the required qubit drive power that is associated with these implementations. Our work introduces a practical and computationally efficient algorithm to realize these compilations.

Figures (1)

• Figure 1: Total nuclear norm of an implementation using a standard Gaussian elimination to $\sim n^2$ two-qubit gate followed by a merge of parallel operations (blue circles), compared to the total nuclear norm of the constant-cost implementation of this work (orange triangles), showing that the depth reduction is performed with comparable resources. We fit this data to a power law (solid), showing that the total nuclear norm scales approximately as $\sim n^{3/2}$ for both methods.