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Implementation of Continuous-Time Quantum Walks on Quantum Computers
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Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are interesting candidates to be implemented on quantum computers. In this work, we describe efficient circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms on three graph classes: complete graphs, complete bipartite graphs, and hypercubes. For the class of complete and complete bipartite graphs, the circuits implement the evolution operator exactly. For the class of hypercubes, the circuit implements an approximate evolution operator, which tends to the exact evolution operator when the number of vertices is large. Our Qiskit simulations show that the implementation is successful at finding the marked vertex even for low-dimensional hypercubes.
Forward citations
Cited by 2 Pith papers
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A matching decomposition algorithm for simulating quantum walk Hamiltonians
Matching decomposition with edge compression builds quantum-walk circuits that need up to 43% fewer CX gates and 54% less depth than Pauli decomposition on tested sparse graphs.
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High-dimensional graphs convolution for quantum walks photonic applications
The authors claim that hypercubes, cycles, tori, and lattices can be convolved into smaller weighted graphs while preserving continuous-time quantum walk dynamics.
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