Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code

Abstract

Photon loss is the dominant source of noise in optical quantum systems. The Gottesman-Kitaev-Preskill (GKP) bosonic code provides significant protection; however, even low levels of loss can generate uncorrectable errors that another concatenated code must handle. In this work, we characterize these errors by deriving analytic expressions for the logical channel that arises from pure loss acting on approximate GKP qubits. Unlike random displacement noise, we find that the loss-induced logical channel is not a stochastic Pauli channel. We also provide analytic expressions for the logical channel for "heralded loss," when the light scattered out of the signal mode is measured either by photon number counting -- i.e., photon subtraction -- or heterodyne detection. These offer a pathway to intentionally inducing non-Pauli channels for, e.g., magic-state production.

(v3) New results subsection for average channel fidelity, 20 pages, 7 figures; (v2) typos corrected, explained odd-numbered heralding result; (v1) 19 pages, 6 figures

References in corpus (19)

• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Towards Scalable Bosonic Quantum Error Correction
• Analog quantum error correction with encoding a qubit into an oscillator
• Continuous-variable gate teleportation and bosonic-code error correction
• All-Optical Long-Distance Quantum Communication with Gottesman-Kitaev-Preskill qubits
• Fault-tolerant quantum computation with static linear optics
• Robust and Deterministic Preparation of Bosonic Logical States in a Trapped Ion
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
• Subsystem analysis of continuous-variable resource states
• Streamlined quantum computing with macronode cluster states
• The Near-optimal Performance of Quantum Error Correction Codes
• The Zak transform: a framework for quantum computation with the Gottesman-Kitaev-Preskill code
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code
• Linear-optical quantum computation with arbitrary error-correcting codes
• Equivalent noise properties of scalable continuous-variable cluster states

Cited by in corpus (2)

• Logical channels in approximate Gottesman-Kitaev-Preskill error correction
• Extensible universal photonic quantum computing with nonlinearity