Demonstration of low-overhead quantum error correction codes

Abstract

Quantum computers hold the potential to surpass classical computers in solving complex computational problems. The fragility of quantum information and the error-prone nature of quantum operations necessitate the use of quantum error correction codes to achieve fault-tolerant quantum computing. However, most codes that have been demonstrated so far suffer from low encoding efficiency, and their scalability is hindered by prohibitively high resource overheads. Here we use a 32-qubit quantum processor to demonstrate two low-overhead quantum low-density parity-check codes, a distance-4 bivariate bicycle code and a distance-3 punctured bivariate bicycle code. Utilizing a two-dimensional architecture with overlapping long-range couplers connecting the qubits, we demonstrate the simultaneous measurements of all non-local weight-6 stabilizers via the periodic execution of an efficient syndrome extraction circuit. We achieve a logical error rate per logical qubit per cycle of (8.91 ± 0.17)% for the bivariate bicycle code with four logical qubits and (7.77 ± 0.12)% for the punctured bivariate bicycle code with six logical qubits. Our results establish the feasibility of performing quantum error correction with long-range coupled superconducting processors, demonstrating the viability of low-overhead quantum error correction. Quantum low-density parity-check error correction codes are anticipated to deliver high performance, but require long-range qubit–qubit interactions. Two of these error correction codes have now been successfully implemented on a superconducting device.