Characterization of errors in a CNOT between surface code patches

• URL: http://arxiv.org/abs/2405.05337v2
• Date: Tue, 21 May 2024 09:36:48 GMT
• Title: Characterization of errors in a CNOT between surface code patches
• Authors: Bálint Domokos, Áron Márton, János K. Asbóth,
• Abstract summary: We investigate a lattice-surgery-based CNOT operation between two surface code patches. We fully characterize the two-qubit logical error channel of the lattice-surgery-based CNOT.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As current experiments already realize small quantum circuits on error corrected qubits, it is important to fully understand the effect of physical errors on the logical error channels of these fault-tolerant circuits. Here, we investigate a lattice-surgery-based CNOT operation between two surface code patches under phenomenological error models. (i) For two-qubit logical Pauli measurements -- the elementary building block of the CNOT -- we optimize the number of stabilizer measurement rounds, usually taken equal to $d$, the size (code distance) of each patch. We find that the optimal number can be greater or smaller than $d$, depending on the rate of physical and readout errors, and the separation between the code patches. (ii) We fully characterize the two-qubit logical error channel of the lattice-surgery-based CNOT. We find a symmetry of the CNOT protocol, that results in a symmetry of the logical error channel. We also find that correlations between X and Z errors on the logical level are suppressed under minimum weight decoding.

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