Implementation of quantum walks on IBM quantum computers
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Implementation of quantum walks on IBM quantum computers F. Acasiete1 · F. P. Agostini2 · J. Khatibi Moqadam1 · R. Portugal1 Received: 15 March 2020 / Accepted: 11 November 2020 / Published online: 24 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now it 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. Keywords Quantum computing · Quantum walks · Quantum circuits · IBM Q experience · Qiskit
1 Introduction Quantum walks are considered the quantum analogue of classical walks, which are useful for developing classical randomized algorithms [1]. Quantum walks have already
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R. Portugal [email protected] F. Acasiete [email protected] F. P. Agostini [email protected] J. Khatibi Moqadam [email protected]
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National Laboratory of Scientific Computing - LNCC, Av. Getúlio Vargas 333, Petrópolis, RJ 25651-075, Brazil
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National Institute of Metrology, Quality, and Technology - Inmetro, Av. Nossa Senhora das Graças 50, Duque de Caxias, RJ 25250-020, Brazil
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proved useful for designing quantum algorithms [2]. The most general definition of a quantum walk on a graph demands that its time evolution obeys the laws of quantum mechanics and is constrained by graph locality [3]. A quantum computer that can realize computational tasks that the largest supercomputers available nowadays cannot simulate has been recently built [4], opening a broad highway to implement quantum walks efficiently. The implementation of quantum walks on quantum computers requires log2 N qubits, where N is the number of nodes of the graph around which the walkers ramble. On the other hand, in many forms of implementing quantum walk in laboratories, the number of devices the experimenter puts on the table scales with the number of nodes of the graph [5], though the required resources are decreased by resorting to classical realization of quantum walks with optical systems [6–8]. Quantum computers provide us with an exponential advantage; however, indicating by the noisy intermediate-scale quantum (NISQ) era, the available quantum computers are prone to errors above the threshold required to implement quantum error correcting codes [9]. That obviously limits the depth of the circuits that would simulate the quantum walk reasonably well. The time evolution of quantum walks on graphs can be continuo
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