Trade-offs on number and phase shift resilience in bosonic quantum codes

• URL: http://arxiv.org/abs/2008.12576v3
• Date: Tue, 10 Aug 2021 02:40:49 GMT
• Title: Trade-offs on number and phase shift resilience in bosonic quantum codes
• Authors: Yingkai Ouyang and Earl T. Campbell
• Abstract summary: One quantum error correction solution is to encode quantum information into one or more bosonic modes. We show that by using arbitrarily many modes, $g$-gapped multi-mode codes can yield good approximate quantum error correction codes.
• Score: 10.66048003460524
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum codes typically rely on large numbers of degrees of freedom to achieve low error rates. However each additional degree of freedom introduces a new set of error mechanisms. Hence minimizing the degrees of freedom that a quantum code utilizes is helpful. One quantum error correction solution is to encode quantum information into one or more bosonic modes. We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer $g$ apart, and the gap $g$ imparts number shift resilience to these codes. Intuitively, since phase operators and number shift operators do not commute, one expects a trade-off between resilience to number-shift and rotation errors. Here, we obtain results pertaining to the non-existence of approximate quantum error correcting $g$-gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using arbitrarily many modes, $g$-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing and amplitude damping errors.

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