PhD Seminar • Algorithms and Complexity — Revisiting the Simulation of Quantum Turing Machines by Quantum CircuitsExport this event to calendar

Wednesday, November 21, 2018 — 1:30 PM EST

Abel Molina, PhD candidate
David R. Cheriton School of Computer Science

Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: t >= n steps of a quantum Turing machine running on an input of length n can be simulated by a uniformly generated family of quantum circuits with size quadratic in t, and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time.

We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in t, rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of a method of Arrighi, Nesme, and Werner (2011) that allows for the localization of causal unitary evolutions. This talk will not require a background in quantum computing.

Location 
DC - William G. Davis Computer Research Centre
1304
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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