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Condensed matter seminar: Preparing Bethe Ansatz Eigenstates on a Quantum Computer

John van Dyke

Virginia Tech

 Quantum computers hold promise for the simulation of quantum many-body systems, with applications in chemistry and materials research.  While small-scale demonstrations have been achieved by using variational quantum eigensolvers, the problem sizes that have been studied fall within the classically-tractable regime.  The possibility of scaling these methods beyond this limit remains unclear, while other algorithms (such as phase estimation) require significant resources.  We propose state preparation for Bethe-ansatz-solvable models as a simple problem allowing for a quantum advantage over classical computational methods at large system sizes.  This is because, despite the existence of an exact solution, some properties (such as certain correlation functions) can be difficult to extract using analytic or approximate methods.  Using the structure of the ansatz, we then present an explicit algorithm that directly produces eigenstates of the 1D XXZ chain on a quantum computer, without the need for any optimization or approximation.  The resources required for our approach compare favorably with other state-of-the-art algorithms for quantum simulation.