2022-01-28 Seminar Report

The Quantum Matter Study Group invited Prof. Rafael Nepomechie from the University of Miami to talk about the Bethe ansatz and realizing Bethe states in quantum computers. In the beginning, he used the Heisenberg chain to introduce the coordinate Bethe ansatz. In condensed matter physics, it is extremely difficult to solve many-body Hamiltonians. For this specific Heisenberg model, Bethe came up with a judicious method for finding the exact many-body wave function. The many-body problem is transformed to solving the Bethe equations. Unfortunately, it is also hard to solve these equations completely. Prof. Nepomechie presented an alternative approach to find the exact wave function and hence the solution to the Bethe equations through quantum computation. He found that, by using specific quantum operations, the exact wave function of the Heisenberg model can be presented in the quantum computer with a probability decaying as the factorial of the number magnons that make up the wave function. It is interesting to learn about this connection between the Bethe ansatz and quantum computing. Discussions were made how to increase the probability of the discussed scheme and how to extend it to find the complete set of Bethe roots for larger systems.

Reported by Thore Posske (University of Hamburg, Germany) and Ching-Kai Chiu

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