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Prof. Jeff Yepez on "Surfing Dirac waves in Hawaii: An introduction to quantum computing for quantum simulation"
417A (Watanabe Hall)
2505 Correa Road
This is the first of two talks on the topic of using quantum computing for quantum simulation. The main purpose of this work is to establish a framework to represent quantum field theories on a Feynman quantum computer.
The quantum algorithms for modeling quantum field theories can be difficult to grasp at first because physicists are accustomed to treating quantum field theory problems analytically. Even when quantum field theories are treated numerically the typical approach taken is to perform imaginary-time simulations to obtain estimates of ground states and the lowest eigenenergies, for example using quantum Monte Carlo. Yet, borrowing from the quantum-gate-based model of quantum computation, it is possible to construct unitary evolution operators that are suited for carrying out real-time quantum simulations of fermions.
Since the purpose of this talk is to introduce the quantum computing approach, I will present a unitary algorithm for modeling Dirac particles by demonstrating a few simple problems related to their time-dependent behavior. A taste of the method's application to modeling quantum field theory is given for the case of the Thirring model. Here particle-particle and particle-antiparticle interactions can be readily demonstrated for the covariant Thirring Lagrangian in 1+1 dimensions using just a laptop computer.
Note from jgl: this is mostly HEP, but anyone interested in quantum mechanics will benefit from this vision, and enjoy the dynamical graphics. Jeff has published interesting papers in this area and is supervising two UH grad students carrying out some of this program.