[CS] Today: Chris Kang MS PresentationApr 23, 2025

[via cs]

This is an announcement of Chris Kang's MS Presentation
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Candidate: Chris Kang

Date: Wednesday, April 23, 2025

Time: 11 am CST

Remote Location: https://uchicago.zoom.us/j/96585809367?pwd=ZmwvVGtFVjgzdTB6Z0VwVGNHWnQ5UT09 Meeting ID: 965 8580 9367 Passcode: 235711

Location: JCL 223

Title: Quantum matrix arithmetics in the Hamiltonian model

Abstract: Quantum computers are intrinsically governed by matrix arithmetics; naturally, one would expect quantum algorithms for linear algebra to be a compelling candidate for quantum advantage. A unifying framework for quantum linear algebra is the Quantum Singular Value Transformation (QSVT) algorithm (Gilyén, Su, Low, and Wiebe, ‘19), recovering prior results in matrix inversion (Harrow, Hassidim, and Lloyd, ‘09) and Hamiltonian simulation (Low and Chuang, ‘19). QSVT computes matrix polynomials via queries to a unitary “block-encoding”, i.e. an embedding of input data within a unitary acting upon a larger Hilbert space. Unfortunately, the space overheads required to load and manipulate data can be significant, posing a challenge for qubit-limited systems. 

In this talk, we conceive of quantum matrix arithmetics in the Hamiltonian model. We introduce the notion of a Hamiltonian block-encoding, instead embedding data within the Hamiltonian of a unitary. In contrast to the unitary model, the Hamiltonian model requires at most two ancilla qubits to load, manipulate, and read out data; under certain conditions, we find that just a single ancilla suffices. We describe potential applications, including inverting matrices, evaluating Green’s functions, and simulating Hamiltonians, all with just a single ancilla.

Advisors: Fred Chong

Committee Members: Fred Chong, Bill Fefferman, Nathan Wiebe