Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications

TL;DR

This paper reviews the theoretical foundations, experimental progress, and diverse applications of GKP bosonic codes in quantum information processing, highlighting recent advances in superconducting circuits, multimode codes, and practical implementations.

Contribution

It provides a comprehensive overview of GKP codes, including recent experimental realizations, multimode extensions, and their applications in quantum computing, communication, and sensing.

Findings

GKP codes enable near-error-free quantum information encoding.

Recent superconducting circuit experiments have demonstrated GKP state stabilization.

Multimode GKP codes enhance quantum error correction capabilities.

Abstract

Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator -- including cat codes, binomial codes and Gottesman-Kitaev-Preskill (GKP) codes -- and are among the first to reach a break-even point for quantum error correction. Though GKP codes are widely recognized for their promise in quantum computation, they also facilitate near-optimal quantum communication rates in bosonic channels and offer the ability to safeguard arbitrary quantum states of oscillators. This review focuses on the basic working mechanism, performance characterization, and the many applications of GKP codes -- emphasizing recent experimental progress in superconducting circuit architectures and theoretical advancements in multimode GKP qubit codes and oscillators-to-oscillators (O2O) codes. We begin with a preliminary continuous-variable formalism needed for bosonic codes. We then proceed to the quantum engineering involved to physically realize GKP states. We take a deep dive into GKP stabilization and preparation in superconducting architectures and examine proposals for realizing GKP states in the optical domain (along with a concise review of GKP realization in trapped-ion platforms). Finally, we present multimode GKP qubits and GKP-O2O codes, examine code performance and discuss applications of GKP codes in quantum information processing tasks such as computing, communication, and sensing.