par Cunningham, Joseph 
Président du jury Oreshkov, Ognyan
Promoteur Roland, Jérémie
Publication Non publié, 2025-10-17
Président du jury Oreshkov, Ognyan
Promoteur Roland, Jérémie
Publication Non publié, 2025-10-17
Thèse de doctorat
| Résumé : | Adiabatic Quantum Computing (AQC) is a powerful framework for designing quantum algorithms, yet its practical implementation is often hampered by the difficulty of engineering precise, continuous time-dependent Hamiltonians or the substantial computational overhead of time discretisation. This thesis develops alternative adiabatic frameworks based on dissipative and stochastic quantum evolution to circumvent these challenges.The core methodology introduces novel dynamics where discrete quantum operations, such as time-independent Hamiltonian evolution with Poisson-distributed phase randomisation or randomised unitary applications (qubitization), replace continuous evolution. This stochastic approach allows the system’s average behaviour to be rigorously analysed using new, generalised adiabatic theorems, including the development of novel quantitative bounds for unbounded Hamiltonians and specialised dissipative generators.Algorithmically, this work demonstrates that these discrete, stochastic procedures can achieve the optimal asymptotic time complexity of continuous AQC while mitigating discretisation costs. Specifically, adapted-schedule implementations are shown to yield optimal scaling for the Quantum Linear Systems Problem (QLSP), achieving complexity proportional to the condition number $O(\kappa)$, and $O(\sqrt{N/M})$ scaling for unstructured search. By establishing highly efficient, implementable alternatives to continuous AQC, this research offers a significant pathway toward robust and scalable quantum computation. The study also investigates the general family of diagonal Hamiltonians for optimisation problems, revealing that finding the optimal scheduling required for peak performance is, in general, an NP-hard problem. |
