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THU: Thursday Contributed Sessions

THU 2: Quantum Information: Concepts and Methods I

THU 2.8: Talk

Thursday, September 11, 2025, 16:00–16:15, ZHG002

Quantum signal processing as time evolution — •Shawn Skelton — Leibniz Universität Hannover

The quantum circuit model has become a standard tool in quantum algorithm development. However, it can be preferable to formulate quantum algorithms as the time evolution generated by a Hamiltonian, for example as is done in quantum adiabatic computing. While adiabatic quantum computation can be polynomially mapped to the circuit model, algorithms developed in the circuit model and adiabatic quantum computation remain conceptually and practically separate.

In this talk, I consider a template for quantum algorithm development in the circuit model, known as quantum signal processing (QP). I derive the generator and time-evolved operator corresponding to a given QSP circuit. I then show how, for a restricted class of Hamiltonians, any QSP circuit can be implemented with a quantum adiabatic evolution. Algorithms have been developed for every major quantum computation problem with QSP, and it is known that QSP can solve BQP-complete problems. Thus, my work provides a pathway for many quantum algorithms to be reformulated in terms of well-understood physical time evolution.

Keywords: quantum adiabtic theorem; quantum computing; quantum signal processing