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Enhancing the lifetime of qubits with quantum code-based memories ondifferent quantum hardware is a significant step towards fault-tolerant quantumcomputing. We theoretically show that the break-even point, i.e., preservingarbitrary quantum information longer than the lifetime of a single idle qubit,can be beaten even with the quantum phase-flip repetition code in adephasing-time-limited system. Applying circuit-based analytical calculation,we determine the efficiency of the phase-flip code as a quantum memory in thepresence of relaxation, dephasing, and faulty quantum gates. Consideringcurrent platforms for quantum computing, we identify the gate errorprobabilities and optimal repetition number of quantum error correction cyclesto reach the break-even point.

Break-even point of the quantum repetition code