The key challenge to useful quantum information processing is the deleterious effects of noise on intricate and fragile quantum states that are extraordinarily sensitive to environmental variations. The problem of quantum noise will be surmounted by quantum computer engineering. I propose a three step approach to the engineering problem 1) understand the noise and its nature, 2) remove all controllable sources of errors, and 3) correct for uncontrollable sources of error, ie., characterize, calibrate, and correct which are the three C's in the title of this thesis and form the three core parts of this work. In order to produce useful techniques, I have made great efforts to design an approach that is efficient in both classical and quantum computational resources.
Characterization concerns the definition and estimation of quantum noise models. A complete tomographic theory, such as that provided by gate set tomography, is theoretically useful, but efficiency constraints motivate reduced protocols such as phase estimation. Calibration deals with techniques to control a quantum processor and minimize its operational error. For this purpose, I adapt the celebrated ``linear, quadratic, Gaussian''(LQG) control of classical theory in the context of quantum calibration for the first time. LQG is the optimal control algorithm when model assumptions are met. Correction removes any remaining error, which is usually incoherent sources that cannot be corrected for with optimal classical control. I introduce a novel metric of code performance that can be used to identify optimal codes for efficient correction of errors under non-uniform noise distributions. The techniques presented in this work address foundational issues in quantum computer engineering.
