Stability of Quantum Computers

Quantum computing's potential is immense, promising super-polynomial reductions in execution time, energy use, and memory requirements compared to classical computers. This technology has the power to revolutionize scientific applications such as simulating many-body quantum systems for molecular structure understanding, factorization of large integers, enhance machine learning, and in the process, disrupt industries like telecommunications, material science, pharmaceuticals and artificial intelligence. However, quantum computing's potential is curtailed by noise, further complicated by non-stationary noise parameter distributions across time and qubits. This dissertation focuses on the persistent issue of noise in quantum computing, particularly non-stationarity of noise parameters in transmon processors. It establishes a framework comprising computational accuracy, device reliability, outcome stability, and result reproducibility for assessing noisy outcomes amidst time-varying quantum noise. It further aims to determine the upper and lower bounds for this framework using available noise characterization data, in terms of the distance between time-varying noise densities. Using real data from a transmon processor, it validates the bounds on a test quantum circuit. It also demonstrates that if the physical platform's noise stays within the bounds determined by the analysis, experimental reproducibility can be guaranteed with a high degree of certainty. Furthermore, it develops a Bayesian algorithm to enhance outcome stability and accuracy for probabilistic error cancellation (PEC) in presence of time-varying quantum noise. The results obtained from experiments using a 5-qubit implementation of the Bernstein-Vazirani algorithm conducted on the ibmq_kolkata device, underscore the effectiveness of the adaptive algorithm, showing a 42% improvement in accuracy over non-adaptive PEC and a 60% improvement in stability. Considering the time-varying stochastic nature of quantum noise, integrating adaptive estimation in error mitigation is crucial. In summary, by delving into the complexities of non-stationary noise in quantum computing, this dissertation provides valuable insights into quantifying and enhancing stability of outcomes from noisy quantum computers.