Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing

Anthony J. Brady; Jing Wu; Quntao Zhuang

doi:10.22331/q-2024-09-19-1478

Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing

Anthony J. Brady¹, Jing Wu², and Quntao Zhuang^1,3

¹Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
²James C. Wyant College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA
³Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA

Published:	2024-09-19, volume 8, page 1478
Eprint:	arXiv:2402.05888v2
Doi:	https://doi.org/10.22331/q-2024-09-19-1478
Citation:	Quantum 8, 1478 (2024).

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Abstract

Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond quantum computing to benefit quantum sensing by safeguarding squeezing — the essential resource in many quantum metrology protocols. However, the potential for quantum sensing to benefit quantum error correction has been less explored. In this work, we provide a unique example where techniques from quantum sensing can be applied to improve multi-mode GKP codes. Inspired by distributed quantum sensing, we propose the distributed two-mode squeezing (dtms) GKP codes that offer benefits in error correction with minimal active encoding operations. Indeed, the proposed codes rely on a $single$ (active) two-mode squeezing element and an array of beamsplitters that effectively distributes continuous-variable correlations to many GKP ancillae, similar to continuous-variable distributed quantum sensing. Despite this simple construction, the code distance achievable with dtms-GKP qubit codes is comparable to previous results obtained through brute-force numerical search [19]. Moreover, these codes enable analog noise suppression beyond that of the best-known two-mode codes [11] without requiring an additional squeezer. We also provide a simple two-stage decoder for the proposed codes, which appears near-optimal for the case of two modes and permits analytical evaluation.

Featured image: Combining ideas from analog and discrete quantum information. (a) Encoding oscillators or qudits into many oscillators. $k$ data oscillators (e.g., multi-partite entangled state) or $k$ data qudits (e.g., GKP square qubits, $d=2$) are encoded into a system of $N>k$ oscillators via $\hat{U}_{\rm enc}$. (b) Distributed quantum sensing. A multi-partite entangled state is prepared by generating and subsequently distributing a bright squeezed beam (i.e., a squeezed coherent state) to many modes. Inputs are separable probes, either vacuum or coherent states. This setup offers quantum enhanced sensing of global parameters, such as an average amplitude or phase. (c) Distributed two-mode squeezing (dtms) GKP codes introduced in this paper. Schematic of the dtms-GKP encoder for $k=1$, inspired by oscillator codes and distributed quantum sensing. The unitary Gaussian encoder $\hat{U}_{\rm dtms}$ comprises a single two-mode squeezer of gain $G$ and a staircase of beamsplitters with transmissivities $\eta_j$ and phases $\phi_j$. The block of $K=N-1$ oscillators consists of canonical ($d=1$) square GKP ancillae.

Popular summary

Quantum information processing promises to revolutionize computation, communication, and sensing, but faces significant challenges from decoherence (noise) due to the fragile nature of quantum information. To address this problem, quantum error-correcting (QEC) codes have been developed to safeguard precious quantum data, in both spin-based systems (e.g., qubits) and bosonic systems (e.g., oscillators, modes, fields). One approach in bosonic QEC utilizes Gottesman-Kitaev-Preskill (GKP) codes, which encode quantum information into a multi-dimensional lattice within the phase-space of the multi-mode bosonic system. The structure and infinite-dimensional nature of GKP codes offers great versatility, capable of protecting both qudits (discrete-variable data) and oscillators (continuous-variable, or analog, data).

In this study, we present a novel form of GKP codes that leverage distributed two-mode squeezing (dtms) to enhance QEC capabilities in the multi-mode setting. The strength of our method lies in its simplicity: The dtms codes require only a single (active) two-mode squeezing element that generates quantum correlations between two modes, which are then distributed across multiple modes via a network of beamsplitters—a concept inspired by the framework of distributed quantum sensing. We demonstrate that the dtms code design achieves QEC performance comparable to previously developed codes but with minimal resources and low complexity. The versatility of dtms codes permits suppression of both analog errors (e.g., additive white noise) when protecting continuous-variable data and digital errors (e.g., bit flips) when protecting DV data—making dtms codes a flexible and compelling option for applications in quantum repeaters and quantum sensor networks alike.

► BibTeX data

@article{Brady2024safeguarding,
  doi = {10.22331/q-2024-09-19-1478},
  url = {https://doi.org/10.22331/q-2024-09-19-1478},
  title = {Safeguarding {O}scillators and {Q}udits with {D}istributed {T}wo-{M}ode {S}queezing},
  author = {Brady, Anthony J. and Wu, Jing and Zhuang, Quntao},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1478},
  month = sep,
  year = {2024}
}

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