Hybrid oscillator-qudit quantum processors: stabilizer states and symplectic operations
- URL: http://arxiv.org/abs/2508.04819v1
- Date: Wed, 06 Aug 2025 18:57:45 GMT
- Title: Hybrid oscillator-qudit quantum processors: stabilizer states and symplectic operations
- Authors: Sayan Chakraborty, Victor V. Albert,
- Abstract summary: We construct stabilizer states and error-correcting codes on combinations of discrete- and continuous-variable systems.<n>We provide examples using commutation matrices, integer symplectic matrices, and binary codes.
- Score: 0.6138671548064355
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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. We construct general hybrid error-correcting codes by relating stabilizer codes to non-commutative tori and obtaining logical operators via Morita equivalence. We provide examples using commutation matrices, integer symplectic matrices, and binary codes.
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