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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.
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1 The Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X); Homi Bhabha National Institute, Mumbai, India (GRID:grid.450257.1) (ISNI:0000 0004 1775 9822)
2 The Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X); FNSPE, Czech Technical University in Prague, Prague, Czech Republic (GRID:grid.6652.7) (ISNI:0000000121738213)
3 The Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X); BITS-Pilani, Goa, India (GRID:grid.418391.6) (ISNI:0000 0001 1015 3164)
4 The Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X); Birla Institute of Technology and Science, Pilani, India (GRID:grid.418391.6) (ISNI:0000 0001 1015 3164)
5 The Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X); Homi Bhabha National Institute, Mumbai, India (GRID:grid.450257.1) (ISNI:0000 0004 1775 9822); Indian Institute of Science, Quantum Optics and Quantum Information, Department of Instrumentation and Applied Physics, Bengaluru, India (GRID:grid.34980.36) (ISNI:0000 0001 0482 5067)