Experimental Implementation of Quantum Walks on IBM Quantum Computers

Abstract

The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and to obtain results with significant fidelity. Quantum walks are good candidates to be implemented on the available quantum computers. In this work, we implement discrete-time quantum walks with one and two interacting walkers on cycles, two-dimensional lattices, and complete graphs on IBM quantum computers. We are able to obtain meaningful results using the cycle, the two-dimensional lattice, and the complete graph with 16 nodes each, which require 4-qubit quantum circuits up to depth 100.

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• Circuit Implementation of Discrete-Time Quantum Walks via the Shunt Decomposition Method
• Circuit Design for $k$-coloring Problem and Its Implementation in Any Dimensional Quantum System
• Parametrized constant-depth quantum neuron
• Circuit Design for Clique Problem and Its Implementation on Quantum Computer
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• United Nation Security Council in Quantum World: Experimental Realization of Quantum Anonymous Veto Protocols using IBM Quantum Computer
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