Global operations for protected quantum memories in atomic spin lattices

TL;DR

This paper explores methods for implementing global operations in atomic spin lattices for protected quantum memories, analyzing the effects of imperfections and decoherence, and proposing strategies to maintain high gate fidelity.

Contribution

It introduces two approaches for many-body gates using cavity interactions and analyzes how to mitigate decoherence effects in these systems.

Findings

High gate fidelities are achievable with current cavity-QED technology.

Monitoring cavity decay can help combat decoherence during quantum operations.

Strong coupling regimes improve robustness of quantum gates.

Abstract

Quantum information processed in strongly correlated states of matter can provide built in hardware protection against errors. We may encode information in highly non local degrees of freedom, such as using three dimensional spin lattices for subsystem codes or two dimensional spin lattices for topologically ordered surface codes and measurement based codes. Recently, in [L. Jiang et al., Nature Physics {\bf 4}, 482 (2008)] the authors showed how to manipulate these global degrees of freedom using optical lattices coupled to a bosonic degree of freedom via a cavity. We elaborate on these ideas and recapitulate two approaches to implement many body gates necessary for quantum information processing, both relying on controlled interactions of an ancillary cavity mode with the spin system and single ancilla particles. The main focus of the present paper is to analyze the effect of imperfections such a cavity decay and collective and individual spin decoherence. We present strategies to fight decoherence by monitoring cavity decay and show that high gate fidelities can be achieved in the strong coupling regime of cavity-QED with state of the art parameters.