Simplifying Continuous-Time Quantum Walks on Dynamic Graphs

• URL: http://arxiv.org/abs/2106.06015v2
• Date: Mon, 3 Jan 2022 19:58:21 GMT
• Title: Simplifying Continuous-Time Quantum Walks on Dynamic Graphs
• Authors: Rebekah Herrman, Thomas G. Wong
• Abstract summary: A continuous-time quantum walk on a dynamic graph evolves by Schr"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. In this paper, we give six scenarios under which a dynamic graph can be simplified.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger'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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