Doctoral Dissertations

Orcid ID


Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Data Science and Engineering

Major Professor

Travis Humble

Committee Members

Dr. Travis Humble, Dr. Russell Lee Zaretzki, Dr. Himanshu Thapliyal, Dr. Rebekah Herrman


Quantum computing faces a persistent challenge with noise. This dissertation addresses the fundamental question of how to define and differentiate computational accuracy, result reproducibility, output stability, and device reliability amidst spatio-temporal non-stationarity in quantum registers. It explores characterizing spatial and temporal noise statistics, estimating performance limits via characterization data, mitigating time-varying quantum noise with adaptive algorithms, and understanding trade-offs when using unreliable devices. Sources of noise include interaction between qubits and the environment, as well as imperfections in implementing quantum logic gates, leading to decoherence (the loss of coherence) in quantum states. Quantum states' survival is brief, making reliable output a challenge. Probabilistic error cancellation can estimate observables for highly entangled states beyond classical supercomputers' capabilities, showcasing quantum computers' utility even with noise. The challenge lies in non-stationary noise distribution, varying across time and qubits. Precise definitions of computational accuracy, device reliability, outcome stability, and result reproducibility are essential to tackle noisy quantum output. The dissertation provides a statistical framework to disentangle these concepts and foster a comprehensive understanding within the context of noisy quantum computations. The dissertation demonstrates the non-stationarity of noise in current quantum computers and analyzes the reliability of transmon devices through systematic data gathering. It investigates estimating output stability by leveraging device characterization data and develops analytical bounds for effective stability estimation. Dynamic quantum channel estimation becomes significant due to time-varying noise, and adaptive algorithms like Bayesian Inference play a crucial role in stabilizing mitigated outputs. The approach is demonstrated using Probabilistic Error Cancellation with a Pauli noise channel. Additionally, the relationship between accuracy, stability, and reproducibility is explored, highlighting their distinct meanings and potential trade-offs. The dissertation addresses noise averaging and potential misleading results when channel estimation time-scales surpass mitigation application. In conclusion, this dissertation advances the understanding of challenges posed by non-stationary noise in quantum computing and offers insights for estimating and enhancing output stability amid temporally and spatially varying quantum noise.

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