Optimal constant-cost implementations of Clifford operations using global interactions

TL;DR

This paper presents a method to implement any Clifford operation with a constant number of global entangling gates, optimizing quantum circuit efficiency on platforms like trapped-ion systems.

Contribution

It introduces a constant-cost, ancilla-free implementation of all Clifford operations using global interactions, achieving theoretical optimality and practical efficiency.

Findings

Constant cost of four global gates for any Clifford sequence

Implementation reduces qubit drive power compared to standard methods

Provides a practical algorithm for Clifford compilation

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 four applications of such Clifford entangling multiqubit gates to realize any sequence of Clifford operations of any length, without ancillae, which is the theoretically optimal gate count cost. We do this by implementing any sequence of CNOT gates of any length with four applications of such gates, without ancillae, and show that the extension to general Clifford operations incurs no additional cost. We investigate the required qubit drive power that is associated with our implementation and show that it is lower than that of a standard approach. Our work introduces a practical and computationally efficient algorithm to realize these compilations.