Multi-ion entangling gates mediated by spectrally unresolved modes

TL;DR

This paper presents a nonperturbative scheme for entangling trapped-ion qubits using all axial motional modes via a time-dependent magnetic-field gradient, enabling faster, multi-qubit, and pairwise gates without spectral addressing.

Contribution

It introduces a novel nonperturbative method utilizing all motional modes for entangling trapped-ion qubits with a magnetic-field gradient, improving speed and scalability.

Findings

Enables simultaneous gates on multiple ion pairs.

Demonstrates advantages over existing magnetic-gradient schemes.

Allows non-spectral addressing of motional modes.

Abstract

Entangling interactions between distant qubits can be mediated via an additional degree of freedom. In conventional trapped-ion schemes, realizing a well-defined, coherent gate typically requires spectrally addressing a specific bus mode. As the ion number increases, the coupling to each individual motional mode becomes weaker, so gates on large ion strings mediated by a single mode are necessarily slow. Moreover, addressing a large number of modes demands complex driving schemes, and the fundamentally perturbative character of these approaches imposes constraints on achievable gate speed and fidelity. Here, we introduce a scheme for entangling trapped-ion qubits using a time-dependent magnetic-field gradient, in which all axial motional modes participate in mediating the interaction and the gate construction is nonperturbative. The framework can be used to implement both multi-qubit gates and two-qubit gates between arbitrary pairs in a linear ion string. Through several explicit examples, we highlight the advantages over existing magnetic-gradient schemes and show how gates on multiple ion pairs can be carried out simultaneously.