Enlarging the GKP stabilizer group for enhanced noise protection

Abstract

Encoding a qubit in a larger Hilbert space of an oscillator is an efficient way to protect its quantum information against decoherence. Promising examples of such bosonic encodings are the Gottesman-Kitaev-Preskill (GKP) codes. In this work, we investigate how redefining the stabilizer group of the GKP codes to include all operations with trivial action on the code space can contribute to the search for an optimal implementation of a logical circuit when it is affected by noise. We find the generators of the Gaussian stabilizer group, allowing us to search for different physical implementations of a Clifford operation. We then propose an algorithm that finds the optimal implementation of a given logical Clifford circuit on GKP codes, such that the state is less affected by loss errors during the computation. Finally, we demonstrate numerically, with logical randomized benchmarking, that such a compiler can increase the lifetime of square-GKP qubits while running Clifford circuits, compared to a random walk compiler.

References in corpus (25)

• Gaussian Quantum Information
• Encoding a qubit in an oscillator
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Randomized Benchmarking of Quantum Gates
• Scalable Noise Estimation with Random Unitary Operators
• Real-time quantum error correction beyond break-even
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill 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
• A general framework for randomized benchmarking
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Achievable rates for the Gaussian quantum channel
• On symplectic eigenvalues of positive definite matrices
• Quantum Error Correction of Qudits Beyond Break-even
• Encoding qubits in multimode grid states
• Quantum capacity and codes for the bosonic loss-dephasing channel
• Robust and Deterministic Preparation of Bosonic Logical States in a Trapped Ion
• Matrix decompositions in Quantum Optics: Takagi/Autonne, Bloch-Messiah/Euler, Iwasawa, and Williamson
• A Non-Commuting Stabilizer Formalism
• Logical Clifford Synthesis for Stabilizer Codes
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Chasing shadows with Gottesman-Kitaev-Preskill codes
• Using a Kerr interaction for GKP magic state preparation
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction