Quantum adiabatic computation via bifurcation for solving combinatorial problems

Quantum adiabatic computing is a promising framework for tackling combinatorial optimization problems by exploiting quantum mechanical principles such as superposition and the adiabatic theorem. In this context, a method of quantum computation based on bifurcations in quantum nonlinear oscillators was proposed, enabling the generation of cat states. This approach demonstrated that it can be used to solve combinatorial problems such as the Ising model.
This master’s thesis provides a concise review of the bifurcation-based quantum computation recently proposed and, as one of the thesis’s objectives, extends this approach by implementing the method in a novel model of quantum oscillators defined within a dissipative environment. The mean-field equations of these dissipative oscillators are analysed for both single and coupled cases, to study the dynamics of the system and how it changes with the couplings. Moreover, numerical simulations are conducted to examine the Ising model with random couplings and the Hopfield network, with emphasis on memory storage and the resulting ground-state degeneracy. Finally, the method, using both types of oscillators, is applied to the determination of eigenvectors of a matrix M.

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