Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity
A. V. Antipov, Evgeniy O. Kiktenko, Aleksey K. Fedorov · Physical Review A · 2023
We describe a class of neighboring-block stabilizer quantum error correction codes and demonstrate that such a 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-qubit repetition code, Laflamme's five-qubit code, and Shor's nine-qubit code. For three-qubit repetition code and Laflamme's five-qubit code, the suggested scheme has the property that it uses only native two-qubit controlled-not-swap gates, which potentially reduces the amount of noncorrectable errors due to the shorter gate time. Elements of the scheme can be used to implement surface code with near-neighbor connectivity using a single ancilla, as demonstrated in an example. We developed efficient decoding procedures for repetition codes and the Laflamme's 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 qubit in the three-qubit repetition code and Laflamme's five-qubit code cases is provided. We complement our results by realizing the developed scheme for a three-qubit code using an IBM quantum processor and the Laflamme's five-qubit code using the state-vector simulator.