Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
arXiv:2504.13497 · doi:10.1103/rmlm-vbfd
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.
arXiv comment(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 (43)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Encoding a qubit in an oscillator
- Quantum Computing with Very Noisy Devices
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- New class of quantum error-correcting codes for a bosonic mode
- Encoding a qubit in a trapped-ion mechanical oscillator
- Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
- Active stabilisation, quantum computation and quantum state synthesis
- Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
- Performance and structure of single-mode bosonic codes
- Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
- All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
- Fidelity of Single Qubit Maps
- Quantum computing with rotation-symmetric bosonic codes
- Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
- Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- Entangling Bosonic Modes via an Engineered Exchange Interaction
- Towards Scalable Bosonic Quantum Error Correction
- Single-Mode Displacement Sensor
- Analog quantum error correction with encoding a qubit into an oscillator
- Cat codes with optimal decoherence suppression for a lossy bosonic channel
- Error Analysis For Encoding A Qubit In An Oscillator
- Encoding an oscillator into many oscillators
- Continuous-variable gate teleportation and bosonic-code error correction
- Quantum error correction against photon loss using NOON states
- All-Optical Long-Distance Quantum Communication with Gottesman-Kitaev-Preskill qubits
- Fault-tolerant quantum computation with static linear optics
- Exact Performance of Concatenated Quantum Codes
- Modular Bosonic Subsystem Codes
- 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