Assessing Quantum Computers' Performance in the NISQ Era

Quantum dynamics in the presence of an external environment are susceptible to decoherence and dissipation, which are primary error sources in current quantum processors. The decay of quantum state fidelity — a measure of the correlation between the ideal and imperfect states — characterizes inevitable degradation in practical quantum processes. Understanding how this decay depends on the nature and severity of errors helps in understanding decoherence and improving algorithms.

However, average fidelity decay overlooks significant dynamic aspects, which this thesis aims to address. The first part examines fidelity decay in a random quantum circuit with errors from imperfect two-qubit gates and qubit permutations. We show that fidelity decays exponentially with both circuit depth and number of qubits raised to an architecture-dependent power, and estimate decay rates based on the amplitude of the errors.

These findings assist in benchmarking quantum computers using Quantum Volume - a figure of merit for quantum processors - and suggest strategies for enhancing performance. In the second part, we study how dissipation impacts chaotic and regular dynamics. We find that average fidelity decay does not differentiate chaotic from regular systems, so we analyze the spectral properties of dissipative maps.

By examining various regular dynamics, we find that spectral features unique to non-dissipative systems persist up to a dissipation threshold, which can help distinguish between regular and chaotic maps. This thesis assists in characterizing error accumulation in quantum circuits and provides insights into the influence of noise in chaotic and regular quantum channels.