Abstract
We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys. Rev. A {\bf 73}, 012325 (2006)]. We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches. Furthermore, we show that the expected total displacement error incurred in multiple rounds of error followed by syndrome extraction is bounded by $2\sqrt{\pi}$. By recompiling the syndrome-extraction circuits, we show that all squeezing operations can be subsumed into auxiliary state preparation, reducing them to beamsplitter transformations and quadrature measurements.
Highlights
Encoding and manipulating quantum information in continuous variable (CV) systems [1,2,3] is a promising route to realizing a useful quantum computing device
We have described an explicit protocol for GKP quantum error correction that provides improved protection from
We have shown that GKP states undergo a is taoptaplrodxisipmlaacteelmy ebnotu(nadneddthbeyre2f√orπe require a correction) that in each quadrature, after multiple rounds of error-syndrome extraction
Summary
Encoding and manipulating quantum information in continuous variable (CV) systems [1,2,3] is a promising route to realizing a useful quantum computing device. Albert et al [15] showed that the GKP code outperforms a number of other bosonic codes when states are exposed to amplitude damping and Gaussian random displacement errors. Where the operator D (α) shifts the state in phase space by Re{α}, Im{α} in the q and p quadratures, respectively, and the width σ0 quantifies the extent of the error This error model describes amplitude damping that is preceded by an offsetting preamplification [16], and it is highly relevant to many experimental platforms. Despite this potential, explicit error correction protocols for accessible approximate states are currently lacking. We recompile the syndrome extraction circuit in an experimentally friendly way, such that squeezing need only be applied to auxiliary states which can be prepared offline
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