Universal quantum computing using single-particle discrete-time quantum walk

Shivani Singh,C M Chandrashekar,Prateek Chawla,Anupam Sarkar

doi:10.1038/s41598-021-91033-5

Shivani Singh, C M Chandrashekar + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-91033-5

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Abstract

Quantum walk has been regarded as a primitive to universal quantum computation. In this paper, we demonstrate the realization of the universal set of quantum gates on two- and three-qubit systems by using the operations required to describe the single particle discrete-time quantum walk on a position space. The idea is to utilize the effective Hilbert space of the single qubit and the position space on which it evolves in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates and engineering arbitrary states is simpler in the proposed quantum walk model when compared to the circuit based model of computation. We will also discuss the scalability of the model and some propositions for using lesser number of qubits in realizing larger qubit systems.

Highlights

Quantum walk has been regarded as a primitive to universal quantum computation
To perform the operations of universal set of gates on two qubit system, the particle will execute a quantum walk on an open graph of two vertices such that particle itself will act as first qubit with two internal degrees of freedom, span{|0, |1 } representing the state of the first qubit
By using the provision of engineering the presence of a single particle in superposition of position space using discrete-time quantum walk, we have demonstrated the realization of universal quantum gates in a multi-qubit system

Summary

Introduction

We demonstrate the realization of the universal set of quantum gates on two- and three-qubit systems by using the operations required to describe the single particle discrete-time quantum walk on a position space. The idea is to increase the control over the dynamics of walk by using appropriate evolution operators and driving the particles’ state towards the desired qudit state This technique can be used to prepare any high-dimensional quantum state and experimentally, a six-dimensional qudit state has been prepared and measured. Quantum computing has been shown on both forms of quantum walks, i.e., continuous-time[19] and discretetime quantum w alks[20], where the position space of the particle represents quantum wires They give a way of programming a quantum computer rather than modelling or mimicking one and do not exhibit a potential towards designing a physical architecture. Our model, based on the discrete-time quantum walk, gives a physical and logical building block to model a quantum computer on lattice based system or Scientific Reports | (2021) 11:11551

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