Hybrid Oscillator-Qudit Quantum Processors: stabilizer states, stabilizer codes, symplectic operations, and non-commutative geometry

Sayan Chakraborty and Victor V. Albert · 2025 · arXiv

| 编号 QE029 | 主题 基础理论 | 链接 arXiv:2508.04819 |

摘要

摘要保留原文（英文）

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We construct stabilizer states and error-correcting codes on combinations of discrete- and continuous-variable systems, generalizing the Gottesman-Kitaev-Preskill (GKP) quantum lattice formalism. Our framework absorbs the discrete phase space of a qudit into a hybrid phase space parameterizable entirely by the continuous variables of a harmonic oscillator. The unit cell of a hybrid quantum lattice grows with the qudit dimension, yielding a way to simultaneously measure an arbitrarily large range of non-commuting position and momentum displacements. Simple hybrid states can be obtained by applying a conditional displacement to a Gottesman-Kitaev-Preskill (GKP) state and a Pauli eigenstate, or by encoding some of the physical qudits of a stabilizer state into a GKP code. The states’oscillator-qudit entanglement cannot be generated using symplectic (i.e., Gaussian-Clifford) operations, distinguishing them as a resource from tensor products of oscillator and qudit stabilizer states. Simple hybrid codes can be thought of as subsystem GKP codes whose gauge factor is entangled with a qudit. Our numerical investigations suggest that such codes can sometimes outperform GKP codes against phy

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