Impact of control noise on a variational quantum eigensolver

Abstract

Quantum computers promise advantages over classical systems for problems such as molecular simulation, fueling the development of hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE). VQE is particularly attractive for noisy intermediate-scale quantum (NISQ) devices due to its shallow circuit depth and partial resilience to noise. Silicon-based spin qubits, with their compatibility with existing semiconductor technologies, are strong candidates for scalable quantum computation. However, their performance is constrained by hardware imperfections—chiefly charge noise and voltage miscalibration—that manifest as fluctuations or offsets in gate electrode voltages. These disturbances degrade quantum gate fidelities and, in turn, the accuracy of algorithmic results, presenting significant challenges for practical applications. In this thesis, we develop a comprehensive hardware-algorithm co-simulation framework to quantify the impact of voltage noise on silicon quantum dot systems. Charge noise is modeled using an ensemble of random telegraph noise processes to emulate realistic 1/f-like spectra. We systematically investigate the effects of stochastic noise and systematic miscalibration at both the gate level and algorithm level. For individual quantum gates—including RX, Hadamard, CZ, and RootSWAP—we characterize noise-induced fidelity loss and derive analytical expressions for error sensitivity, revealing contrasting robustness between detuning-driven and exchange-driven gates. Quantum process tomography and Kraus operator decomposition further elucidate dominant error channels, distinguishing coherent and incoherent contributions from different noise regimes. Extending the analysis to algorithm performance, we simulate VQE for the hydrogen molecule and identify a practical noise tolerance window within which high-accuracy energy estimation is maintained. These advances underscore the progress in bridging device physics and quantum algorithm implementation for silicon spin qubits, offering quantitative guidance on error budgeting, control calibration, and the development of noise-resilient algorithms for near-term quantum processors.