Simplifying continuous-time quantum walks on dynamic graphs

Rebekah Herrman; Thomas G. Wong

doi:10.1007/s11128-021-03403-7

Simplifying continuous-time quantum walks on dynamic graphs

Research output: Contribution to journal › Article › peer-review

Abstract

A continuous-time quantum walk on a dynamic graph evolves by Schrödinger’s equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that implements a quantum circuit can be quite complicated. In this paper, we give six scenarios under which a dynamic graph can be simplified, and they exploit commuting graphs, identical graphs, perfect state transfer, complementary graphs, isolated vertices, and uniform mixing on the hypercube. As examples, we simplify dynamic graphs, in some instances allowing single-qubit gates to be implemented in parallel.

Original language	English (US)
Article number	54
Journal	Quantum Information Processing
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s11128-021-03403-7
State	Published - Feb 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Statistical and Nonlinear Physics
Theoretical Computer Science
Signal Processing
Modeling and Simulation
Electrical and Electronic Engineering

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10.1007/s11128-021-03403-7

Cite this

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abstract = "A continuous-time quantum walk on a dynamic graph evolves by Schr{\"o}dinger{\textquoteright}s equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that implements a quantum circuit can be quite complicated. In this paper, we give six scenarios under which a dynamic graph can be simplified, and they exploit commuting graphs, identical graphs, perfect state transfer, complementary graphs, isolated vertices, and uniform mixing on the hypercube. As examples, we simplify dynamic graphs, in some instances allowing single-qubit gates to be implemented in parallel.",

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Simplifying continuous-time quantum walks on dynamic graphs

Abstract

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