  Enhancing the lifetime of qubits with quantum code-based memories on
different quantum hardware is a significant step towards fault-tolerant quantum
computing. We theoretically show that the break-even point, i.e., preserving
arbitrary quantum information longer than the lifetime of a single idle qubit,
can be beaten even with the quantum phase-flip repetition code in a
dephasing-time-limited system. Applying circuit-based analytical calculation,
we determine the efficiency of the phase-flip code as a quantum memory in the
presence of relaxation, dephasing, and faulty quantum gates. Considering
current platforms for quantum computing, we identify the gate error
probabilities and optimal repetition number of quantum error correction cycles
to reach the break-even point.
