Robust gate design for large ion crystals through excitation of local phonon modes

TL;DR

This paper introduces a scalable, robust entangling gate design for large ion crystals that operates beyond the Lamb-Dicke limit, is insensitive to phase variations, and reduces infidelity below fault-tolerance thresholds.

Contribution

It presents a novel gate scheme based on local phonon mode excitation, extending quantum gate applicability to larger ion systems beyond previous collective mode approaches.

Findings

Gate fidelity can be reduced below fault-tolerance thresholds.

The scheme works outside the Lamb-Dicke regime.

The gate is insensitive to slow laser phase variations.

Abstract

We propose a scalable design of entangling quantum gates for large ion crystals with the following desirable features: 1) The gate design is universal and applicable for large ion crystals of arbitrary sizes; 2) The gate has no speed limitation and can work outside of the Lamb-Dicke region; 3) The gate operates by driving from either continuous-wave or pulsed laser beams; 4) The gate is insensitive to slow variation of the laser optical phase and works under a thermal state for the ions' motion; 5) The intrinsic gate infidelity can be reduced to a level well below the threshold for fault-tolerant quantum computation under realistic experimental parameters. Different from the previous gate schemes, here we propose a gate design based on driving of the local oscillation mode of the ions instead of the collective normal modes and develop a formalism based on the Heisenberg equations to deal with the many-body quantum dynamics outside of the Lamb-Dicke region.