Static Quantum Errors and Purification

Abstract: State preparation that initializes quantum systems in a fiducial state and measurements to read outcomes after the evolution of quantum states, both essential elements in quantum information processing in general, may contain noise from which errors, in particular, referred to as static errors, may appear even with noise-free evolution. In this work, we consider noisy resources such as faulty manufacturing and improper maintenance of systems by which static errors in state preparation and measurement are inevitable. We show how to suppress static errors and purify noiseless SPAM by repeatedly applying noisy resources. We present the purification protocol for noisy initialization and noisy measurements and verify that a few qubits are immediately cost-effective to suppress error rates up to $10^{-3}$. We also demonstrate the purification protocol in a realistic scenario. The results are readily feasible with current quantum technologies.