Break-even point of the phase-flip error correcting code

Abstract

Abstract In this theoretical study, we explore the use of quantum code-based memories to enhance the lifetime of qubits and exceed the break-even point, which is critical for the implementation of fault-tolerant quantum computing. Specifically, we investigate the quantum phase-flip repetition code as a quantum memory and theoretically demonstrate that it can preserve arbitrary quantum information longer than the lifetime of a single idle qubit in a dephasing-time-limited system, e.g. in semiconductor qubits. Our circuit-based analytical calculations show the efficiency of the phase-flip code as a quantum memory in the presence of relaxation, dephasing, and faulty quantum gates. Moreover, we identify the optimal repetition number of quantum error correction cycles required to reach the break-even point by considering the gate error probabilities of current platforms for quantum computing. Our results provide guidelines for developing quantum memories in semiconductor quantum devices.