Spin squeezed GKP codes for quantum error correction in atomic ensembles
- URL: http://arxiv.org/abs/2211.05181v2
- Date: Mon, 19 Jun 2023 19:58:35 GMT
- Title: Spin squeezed GKP codes for quantum error correction in atomic ensembles
- Authors: Sivaprasad Omanakuttan and T.J. Volkoff
- Abstract summary: GKP codes encode a qubit in displaced phase space of a quantum system.
We propose atomic ensemble analogues of the single-mode CV GKP code.
We find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: GKP codes encode a qubit in displaced phase space combs of a
continuous-variable (CV) quantum system and are useful for correcting a variety
of high-weight photonic errors. Here we propose atomic ensemble analogues of
the single-mode CV GKP code by using the quantum central limit theorem to pull
back the phase space structure of a CV system to the compact phase space of a
quantum spin system. We study the optimal recovery performance of these codes
under error channels described by stochastic relaxation and isotropic ballistic
dephasing processes using the diversity combining approach for calculating
channel fidelity. We find that the spin GKP codes outperform other spin system
codes such as cat codes or binomial codes. Our spin GKP codes based on the
two-axis countertwisting interaction and superpositions of SU(2) coherent
states are direct spin analogues of the finite-energy CV GKP codes, whereas our
codes based on one-axis twisting do not yet have well-studied CV analogues. An
implementation of the spin GKP codes is proposed which uses the linear
combination of unitaries method, applicable to both the CV and spin GKP
settings. Finally, we discuss a fault-tolerant approximate gate set for quantum
computing with spin GKP-encoded qubits, obtained by translating gates from the
CV GKP setting using quantum central limit theorem.
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