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Seminar Series with David Gosset
Qiskit Qiskit Seminar Series with David Gosset
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Speaker: David Gosset
Host: Dr. Zlatko Minev
Slides: https://www.dropbox.com/s/d5e8gc6rqy48pyj/David%20Gosset%20Slides.pdf?dl=0
Abstract:
In this work we provide new techniques for a fundamental and ubiquitous task: simulating measurement of a quantum state in the standard basis. Our algorithms reduce the sampling task to computing poly(n) amplitudes of n-qubit states; unlike previously known techniques they do not require computation of marginal probabilities. First we consider the case where the state of interest is the output state of an m-gate quantum circuit U. We propose an exact sampling algorithm which involves computing O(m) amplitudes of n-qubit states generated by subcircuits of U spanned by the first t=1,2,…,m gates. We show that our algorithm can significantly accelerate quantum circuit simulations based on tensor network contraction methods or low-rank stabilizer decompositions. Second, we consider the case in which ψ is the unique ground state of a local Hamiltonian with a spectral gap that is lower bounded by an inverse polynomial function of n. We prove convergence guarantees for a simple Metropolis-Hastings Markov Chain as well as a more involved continuous-time Markov chain that is related to the so-called fixed node Hamiltonian approach from the quantum Monte Carlo community. This talk is based on joint works arXiv:2112.08499 and arXiv:2207.07044 with Sergey Bravyi, Giuseppe Carleo, and Yinchen Liu.
Bio:
David Gosset is a quantum computer scientist who is interested in quantum algorithms and complexity theory.
He has worked on theoretical questions relevant to small quantum computers, including understanding the computational power of constant-depth quantum circuits and the limits of classical simulation algorithms. He has also investigated the computational power and complexity of quantum many-body systems, and the application of physics-inspired tools from these areas to quantum computer science.
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