Most of the publications on Quantum Computing and its main building block; the Qubit, rely on the Quantum Theory and use its terminologies. It is therefore not an easy task for the Electrical Engineers to fully understand the concept of the qubits, and how they are designed, controlled, readout, and used for computation. The primary aim of this paper is to show that the physical quantities describing the superconducting Transmons-the microwave realizations of the qubits-are just noisy signals similar to those encountered in e.g. Mobile and Satellite Communications. The nature of the noise in the qubit case, which will be simply called Quantum Noise, is essentially different from that of e.g. the thermal one. Contrary to the well-studied Thermal Noise, the Quantum one enjoys precise probability distributions and can interfere coherently. In particular, the so-called Stationary States resemble individually pure noise. However, a superposition of at least two of them results in a noisy signal, whose signal-to-noise ratio improves (goes higher) as more stationary states enter the superposition. Furthermore, the excitation (control) and readout of the qubits will be treated from the perspectives of the Electrical Engineering.
Recent progress in quantum signal processing (QSP) and its generalization, quantum singular value transformation, has led to a grand unification of quantum algorithms. However, inherent experimental noise in quantum devices severely limits the length of realizable QSP sequences. We consider a model of QSP with generic perturbative noise in the signal processing basis and present a diagrammatic notation useful for analyzing such errors. To demonstrate our technique, we study a specific coherent error, that of under- or overrotation of the signal processing operator parametrized by $\ensuremath{\epsilon}\ensuremath{\ll}1$. For this coherent error model, it is shown that while Pauli
Z errors are not recoverable without additional resources, Pauli
X and
Y errors can be arbitrarily suppressed by coherently appending a noisy recovery QSP without the use of additional resources or ancillas. Furthermore, through a careful accounting of errors using our diagrammatic tools, we provide an upper and lower bound on the length of this recovery QSP operator. We anticipate that the perturbative technique and the diagrammatic notation proposed here will facilitate future study of generic noise in QSP and quantum algorithms.