TY - JOUR
T1 - Simplifying continuous-time quantum walks on dynamic graphs
AU - Herrman, Rebekah
AU - Wong, Thomas G.
N1 - Funding Information:
R.H. was supported by DARPA ONISQ program under award W911NF-20-2-0051. The authors thank the organizers of the “Quantum Information on Graphs” session of the 2019 Canadian Mathematical Society Winter Meeting, where their collaboration on this research was initiated.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/2
Y1 - 2022/2
N2 - 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.
AB - 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.
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U2 - 10.1007/s11128-021-03403-7
DO - 10.1007/s11128-021-03403-7
M3 - Article
AN - SCOPUS:85123032372
VL - 21
JO - Quantum Information Processing
JF - Quantum Information Processing
SN - 1570-0755
IS - 2
M1 - 54
ER -