  Current noisy quantum computers have multiple types of errors, which can
occur in the state preparation, measurement/readout, and gate operation, as
well as intrinsic decoherence and relaxation. Partly motivated by the booming
of intermediate-scale quantum processors, measurement and gate errors have been
recently extensively studied, and several methods of mitigating them have been
proposed and formulated in software packages (e.g., in IBM Qiskit). Despite
this, the state preparation error and the procedure to quantify it have not yet
been standardized, as state preparation and measurement errors are usually
considered not directly separable. Inspired by a recent work of Laflamme, Lin,
and Mor [Phys. Rev. A 106, 012439 (2022)], we propose a simple and
resource-efficient approach to quantify separately the state preparation and
readout error rates. With these two errors separately quantified, we also
propose methods to mitigate them separately, especially mitigating state
preparation errors with linear (with the number of qubits) complexity. As a
result of the separate mitigation, we show that the fidelity of the outcome can
be improved by an order of magnitude compared to the standard measurement error
mitigation scheme. We also show that the quantification and mitigation scheme
is resilient against gate noise and can be immediately applied to current noisy
quantum computers. To demonstrate this, we present results from cloud
experiments on IBM's superconducting quantum computers. The results indicate
that the state preparation error rate is also an important metric for qubit
metrology that can be efficiently obtained.
