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+---
+tags: VQE, Hamiltonian-level, NISQ, Noise, Numerical, Theory
+title: 'PhD thesis: "Optimal Hamiltonian control for variational quantum algorithms: On spin-qubit quantum processors"'
+sort-date: 2026-05-29
+---
+
+[[/index|Christopher K. Long]]
+
+Supervisors:
+Crispin H. W. Barnes,
+Frederico Martins,
+David R. M. Arvidsson-Shukur,
+and Normann Mertig
+
+Examiners: Alex J. W. Thom
+and Simon C. Benjamin
+
+Submitted: 29 May 2026
+
+Viva: 6 August 2026
+
+Download will be available soon.
+
+# Abstract
+
+> Variational quantum algorithms (VQAs) were once believed to be the fastest route to demonstrating practical quantum advantage. VQAs use a parameterized quantum circuit to perform a machine-learning task. For example, VQAs can employ the Rayleigh–Ritz method to estimate a molecule's eigenenergies. While VQAs are already used to bootstrap quantum processors, their utility for quantum chemistry tasks has been questioned. The three main concerns are runtime, noise on near-term devices, and optimizability. This thesis presents data to corroborate these concerns before making progress on addressing all three. First, I present numerical runtime estimates and quantify the noise-induced errors for a class of VQAs that is believed to be readily optimizable: adaptive derivative-assembled pseudo-Trotter variational quantum eigensolvers (ADAPT-VQEs). These initial results demonstrate that VQAs will only become feasible when device noise levels fall below typical fault-tolerance thresholds. Second, to overcome these concerns, I replace the gate-based quantum circuit approach with a Hamiltonian-control approach. This necessitates a device model. Herein, I focus on quantum-dot spin-qubit devices with electron and hole spins. To perform a study of Hamiltonian control on these processors, I developed a performant software suite that includes an integrator and automatic differentiation. Using this software, I estimate the minimal evolution times for state preparation. This demonstrates Hamiltonian-level VQAs can run up to $100$ times faster than the fastest gate-based VQAs. Next, I numerically demonstrate that Hamiltonian-level VQAs are robust to device imperfections and leakage, and up to $10^5$ times less susceptible to decoherence than the state-of-the-art VQAs. Finally, I consider the scalability of Hamiltonian-level VQAs in four ways: (i) Increasing the expressibility of the device Hamiltonian by developing a technique for adding terms virtually. (ii) Demonstrating, via Lie algebraic methods, that the microwave antenna, used for single-qubit control via electron spin resonance, is a redundant component. (Similarly, electric-dipole–spin-resonance controls can be removed.) (iii) Calibrating modules with Hamiltonian-control techniques to enhance scalability. (iv) Designing an adaptive control technique to limit the *ansatz* parameter count. This thesis restores much of the lost belief in variational quantum algorithms.
+
+# Citation
+
+Christopher K. Long. Optimal Hamiltonian control for variational quantum algorithms: On spin-qubit quantum processors, PhD thesis, University of Cambridge, 2026.
+
+## BibTeX
+
+```bibtex
+@phdthesis{long2026,
+ author = {Long, Christopher K.},
+ title = {Optimal Hamiltonian control for variational quantum algorithms: on spin-qubit quantum processors},
+ school = "University of Cambridge",
+ address = "Cambridge, UK",
+ year = 2026,
+ type = {PhD thesis}
+}
+```
+
+# Software
+
+- [[/Software/From-virtual-Z-gates-to-virtual-Z-pulses-source-code/index|From-virtual-Z-gates-to-virtual-Z-pulses-source-code]] [@long_2025_17149989]
+- [[/Software/Minimal-state-preparation-times-for-silicon-spin-qubits-source-code/index|Minimal-state-preparation-times-for-silicon-spin-qubits-source-code]] [@long_2025_17340395]
+- [[/Software/QuGradLab/index|QuGradLab]] [@QuGradLab]
+- [[/Software/QuGrad/index|QuGrad]] [@QuGrad]
+- [[/Software/PySTE/index|PySTE]] [@PySTE]
+- [[/Software/Suzuki-Trotter-Evolver/index|Suzuki-Trotter-Evolver]] [@SuzukiTrotterEvolver]
+
+# Data
+
+- [[/Datasets/From-virtual-Z-gates-to-virtual-Z-pulses-data]] [@long_2025_17113740]
+- [[/Datasets/Minimal state-preparation times for silicon spin qubits data]] [@long_2025_15676408]
+
+# Social media posts
+
+## Bluesky
+
+On Friday, I submitted my PhD thesis! I'm looking forward to defending in August and sharing the thesis with the rest of you.
— Christopher K. Long (@christopher-k-long.bsky.social) 1 June 2026 at 11:06
+
+Since finishing my PhD viva on the 6th, with minor corrections, life has been busy. The discussion with Alex Thom and Simon Benjamin during my viva was insightful, and I'll have a better thesis as a result—thank you! My corrections are now done, but were slowed down by an accident on the 17th.
— Christopher K. Long (@christopher-k-long.bsky.social) 25 August 2026 at 11:04
+
+## LinkedIn
+
+On Friday, I submitted my PhD thesis! I'm looking forward to defending in August and sharing the thesis with the rest of you.
+
+I have had an amazing time at the Cavendish Laboratory - Department of Physics at the University of Cambridge over the last 8 years! I am excited to be starting as a Presidential Postdoctoral Fellow at Virginia Tech with Ed Barnes and Sophia Economou in late August!
— Christopher K. Long (LinkedIn) 1 June 2026
+
+Since finishing my PhD viva on the 6th, with minor corrections, life has been busy, and I didn't get around to posting. The discussion with Alex Thom and Simon Benjamin during my viva was insightful, and I'll have a better thesis as a result—thank you! My corrections are now done, but were slowed down by an accident on the 17th. I was water skiing, and during a fall, instead of my foot binding releasing cleanly, it broke, damaging my foot. Now post surgery, it looks like I can't walk or fly for at least 6 weeks, so the start of my postdoc at Virginia Tech will be delayed until October.
— Christopher K. Long (LinkedIn) 25 August 2026
+
+## X
+
+
+
+
+
+
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