Devising accreditation protocols for near-term quantum computing devices

In theory, perfect quantum computers can solve certain problems that are con- sidered intractable with classical computers. In practice, quantum computers are imperfect, since their internal components are afflicted by noise. The aim of this thesis is to devise protocols to verify the correctness of the outputs of quantum computations implemented on the Noisy Intermediate-Scale Quantum (NISQ) com- puting devices currently being built. We begin by optimizing some of the existing protocols based on interactive proof systems. Moving beyond these protocols (which are impractical for NISQ devices due to their overhead in qubits and gates), we then present a protocol (that we name \accreditation protocol") that encompasses all the main limitations of NISQ devices, including the limited availability of qubits and noisy gates. The accreditation protocol returns an upper-bound on the variation distance between ideal and noisy probability distributions of the outputs of an arbitrary quantum computation. Relying on the accuracy of single-qubit gates (which are the least noisy components in all currently available NISQ devices), the accreditation protocol can detect all types of noise in state-preparation, measurements and two-qubit gates. To conclude our work, we present a modified version of the accreditation protocol that relies on more assumptions on the noise (motivated by empirical evidence) and provides tighter bounds on the variation distance. Our accreditation protocols are scalable, unlike the protocols based on classi- cal simulations of quantum circuits. They are practical for implementation on NISQ devices, unlike the protocols based on interactive proof systems. Moreover, they can detect noise that may be missed by protocols based on quantum process tomogra- phy and randomized benchmarking. Thus, they represent the state-of-the-art of circuit characterization, and we expect them to be widely used in future quantum computations