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.

18 pages, 22 figures

References in corpus (14)

• Quantum computational advantage using photons
• Universal computation by quantum walk
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Optimizing the discrete time quantum walk using a SU(2) coin
• Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons
• Ultra-long quantum walks via spin-orbit photonics
• Symmetry-noise interplay in quantum walk on an n-cycle
• Scalable Superconducting Architecture for Adiabatic Quantum Computation
• Generating Haar-uniform Randomness using Stochastic Quantum Walks on a Photonic Chip
• Perfect state transfer on hypercubes and its implementation using superconducting qubits

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• Quantum walk-based protocol for secure communication between any two directly connected nodes on a network
• Optimizing topology for quantum probing with discrete-time quantum walks
• Quantum walk with coherent multiple translations induces fast quantum gate operations
• Photon-Number Conserved Universal Quantum Logic Employing Continuous-Time Quantum Walk on Dual-Rail Qubit Arrays