Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity

• URL: http://arxiv.org/abs/2207.13356v1
• Date: Wed, 27 Jul 2022 08:25:38 GMT
• Title: Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity
• Authors: A.V. Antipov, E.O. Kiktenko, A.K. Fedorov
• Abstract summary: We show that a class of "neighboring-blocks" stabilizer quantum error correction codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of three-, five-, and nine-qubits stabilizer code schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of three-, five-, and nine-qubits stabilizer code schemes. For three- and five-qubit codes suggested scheme has the property that it uses only native two-qubit CNS (CNOT-SWAP) gates, which potentially reduces the amount of non-correctable errors due to the shorter gate time. We developed efficient decoding procedures for repetition codes and the five-qubit code using a minimum weight-perfect matching approach to account for the specific order of measurements in our scheme. The analysis of noise levels for which the scheme could show improvements in the fidelity of a stored logical state in the three- and five-qubit cases is provided. We complement our results by realizing the developed scheme for a three-qubit code using a cloud-based quantum processor and the five-qubit code using the state-vector simulator.

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