Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
arXiv:2602.24102 · doi:10.1103/yh45-pj3r
Abstract
Bosonic quantum error-correcting codes encode logical information in a harmonic oscillator, with the Gottesman-Kitaev-Preskill (GKP) and number-phase (NP) codes representing two fundamentally different encoding paradigms. Although both have been extensively studied, it remains unclear under what physical noise conditions (including photon loss and dephasing) one encoding intrinsically outperforms the other. Here we estimate a quantitative performance boundary between GKP and NP codes under general photon loss-dephasing noise. By optimizing code parameters within each encoding family, we identify the noise regimes in which each code exhibits a fundamental advantage. In particular, we find that the crossover occurs when the dephasing strength is approximately two orders of magnitude smaller than the loss strength, revealing a sharp separation between operational regimes. Beyond this specific comparison, our work establishes a practical and extensible methodology for benchmarking bosonic codes and optimizing their parameters, providing concrete guidance for the experimental selection and deployment of bosonic encodings in realistic noise environments.
References in corpus (35)
- Encoding a qubit in an oscillator
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- Performance and structure of single-mode bosonic codes
- Hardware-efficient autonomous quantum error correction
- Bosonic Quantum Codes for Amplitude Damping
- Error correction for continuous quantum variables
- Beating the break-even point with a discrete-variable-encoded logical qubit
- Analog quantum error correction
- Quantum computing with rotation-symmetric bosonic codes
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Optimum Quantum Error Recovery using Semidefinite Programming
- Iterative Optimization of Quantum Error Correcting Codes
- Quantum error correction against photon loss using NOON states
- Dual-rail encoding with superconducting cavities
- Optimizing Completely Positive Maps using Semidefinite Programming
- Robust Quantum Error Correction via Convex Optimization
- Quantum Error Correction of Qudits Beyond Break-even
- Experimentally feasible quantum erasure-correcting code for continuous variables
- Approximate Autonomous Quantum Error Correction with Reinforcement Learning
- Quantum capacity and codes for the bosonic loss-dephasing channel
- Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
- Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
- Protecting quantum entanglement between error-corrected logical qubits
- Semi-definite programming and quantum information
- Quantum spherical codes
- Spacetime replication of continuous variable quantum information
- The Near-optimal Performance of Quantum Error Correction Codes
- Quantum communication on the bosonic loss-dephasing channel
- Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code
- Taming numerical errors in simulations of continuous variable non-Gaussian state preparation
- Trade-offs on number and phase shift resilience in bosonic quantum codes
- Bosonic quantum error correction using squeezed Fock states
- Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction