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Five Promises from Geometric Quantum Mechanics for Efficient Quantum Simulations

John Sidles, University of Washington

(Session : Thursday from )

Abstract. Quantum simulations play a central role in modern science and engineering, but it remains a challenge to simulate the large-scale, high-temperature, and nonequilibrium quantum systems that occur in applications such as magnetic resonance imaging, condensed matter, chemistry, and nanotechnology. Geometric descriptions of quantum trajectory unraveling lead to algorithms for fast matrix-vector multiplication that can speed the numerical computation of quantum simulations for broad classes of physical systems. From an informatic and differential geometry point of view, these are order-$N$ algorithms for computing the musical isomorphism between one-forms and vectors on the Kahlerian state-space manifolds of tensor network products.

Renewing and Uniting Two Challenges of John von Neumann and Richard Feynman: Atomic-Resolution Biomicroscopy and Simulating Quantum Physics with Computers

John Sidles, University of Washington

(Session 7 : Saturday from 1:30-2:00)

Abstract. In two renowned lectures, Richard Feynman (in 1959) challenged mathematicians, scientists, and engineers to "see the individual atoms" in biological molecules and (in 1982) to "make a simulation of nature [that is] quantum mechanical." An earlier statement of these same challenges can be found in a 1946 letter from John von Neumann to Norbert Weiner. The status of these two challenges is reviewed. Atomic-resolution biomicroscopy is treated as a problem in quantum communication whose fundamental quantum limits can be calculated by combining Feynman's formalism for quantum measurement with Shannon's formalism for information channel capacity. Modern advances in quantum information theory and simulation science suggest avenues for further analysis. The assessment concludes that both of von Neumann's and Feynman's challenges are rapidly approaching scientific and technological feasibility.