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Physical Review Research

Nonperturbative leakage elimination for a logical qubit encoded in a mechanical oscillator

Shasha Zheng, Qiongyi He, Mark Byrd, Lian-Ao Wu

Published Sep 9, 2020• 5 citations
Publisher

Abstract

This work presents a theoretical scheme to suppress decoherence-induced leakage errors of a single-mode harmonic oscillator used to encode a qubit in continuous-variable systems by introducing a nonperturbative leakage elimination operator.
DOI
10.1103/physrevresearch.2.033378

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In , Gottesman, Kitaev, and Preskill described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This encoding provides a natural error-correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We then use these bounds to constrain the quality of input qubit and ancilla states.
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.
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