Multi-qubit quantum computing using discrete-time quantum walks on closed graphs

Abstract

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover’s algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

“…The great potential of exploiting the peculiar features of quantum walks-quantum superposition of multiple paths, ballistic spread (faster than the diffusive spread of a classical random walker), and entanglement-for algorithmic purposes [4][5][6] has been immediately clear since their introduction. Nowadays, quantum walks have proven to be a universal model for quantum computation [7][8][9][10][11], and examples of their use include algorithms for quantum search [12][13][14][15]; the solving of hard K-SAT instances [16]; graph isomorphism problems [17][18][19]; algorithms in complex networks [20,21] such as link prediction [22,23] and community detection [24,25]; and quantum simulation [26][27][28][29][30]. Furthermore, quantum communication protocols based on quantum walks have been put forward [31][32][33][34][35][36][37][38][39].…”

Quantum walk-based protocol for secure communication between any two directly connected nodes on a network

“…One of the methods to implement various network-based protocols is to use the toolkit of the quantum walk formalism. Quantum walks on networks have been used for various applications such as search problems [28][29][30][31], state transfer and quantum routing [32][33][34][35], evaluation of information flow through networks [36][37][38][39], training of neural networks [40,41], properties of percolation graphs [42][43][44], and universal quantum computation [45][46][47][48].…”