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

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 3-qubit repetition code, Laflamme's 5-qubit code, and Shor's 9-qubit code. For 3-qubit repetition code and Laflamme's 5-qubit code suggested scheme has the property that it uses only native two-qubit CNS gates, which potentially reduces the amount of non-correctable errors due to the shorter gate time. Elements of the scheme can be used to implement surface code with near-neighbour connectivity using single ancilla, as demonstrated in an example. We developed efficient decoding procedures for repetition codes and the Laflamme's 5-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 3-qubit repetition code and Laflamme's 5-qubit code cases is provided. We complement our results by realizing the developed scheme for a 3-qubit code using an IBM quantum processor and the Laflamme's 5-qubit code using the state-vector simulator.

27 pages, 33 figures

References in corpus (9)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Surface codes: Towards practical large-scale quantum computation
• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Removing leakage-induced correlated errors in superconducting quantum error correction
• A leakage-resilient approach to fault-tolerant quantum computing with superconducting elements
• Tailored XZZX codes for biased noise
• Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings

Cited by in corpus (4)

• Low-overhead quantum error correction codes with a cyclic topology
• Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions
• MIRAGE: Quantum Circuit Decomposition and Routing Collaborative Design using Mirror Gates
• Suppressing decoherence in quantum state transfer with unitary operations