Bose-Hubbard model for universal quantum-walk-based computation

Multiphoton propagation in connected structures—a quantum walk—offers the potential of simulating complex physical systems and provides a route to universal quantum computation. Increasing the complexity of quantum photonic networks where the walk occurs is essential for many applications. We implement a quantum walk of indistinguishable photon pairs in a multimode fiber supporting 380 modes. Using wavefront shaping, we control the propagation of the two-photon state through the fiber in which all modes are coupled. Excitation of arbitrary output modes of the system is realized by controlling classical and quantum interferences. This report demonstrates a highly multimode platform for multiphoton interference experiments and provides a powerful method to program a general high-dimensional multiport optical circuit. This work paves the way for the next generation of photonic devices for quantum simulation, computing, and communication.

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Floquet-engineered quantum walks

Scientific Reports ◽

10.1038/s41598-020-74418-w ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Haruna Katayama ◽

Noriyuki Hatakenaka ◽

Toshiyuki Fujii

Keyword(s):

Quantum Computation ◽

Computational Models ◽

Quantum Algorithms ◽

Quantum Walk ◽

Quantum Walks ◽

Research Areas ◽

Wide Range ◽

Mechanical Analogue ◽

Universal Quantum ◽

Walking Mechanism

Abstract The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

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

Scientific Reports ◽

10.1038/s41598-021-91033-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Shivani Singh ◽

Prateek Chawla ◽

Anupam Sarkar ◽

C. M. Chandrashekar

Keyword(s):

Hilbert Space ◽

Discrete Time ◽

Single Particle ◽

Quantum Walk ◽

Quantum Gates ◽

Position Space ◽

Single Qubit ◽

Time Quantum ◽

Universal Quantum ◽

Qubit States

AbstractQuantum 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.

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Universal quantum computation by discontinuous quantum walk

Physical Review A ◽

10.1103/physreva.82.042304 ◽

2010 ◽

Vol 82 (4) ◽

Cited By ~ 23

Author(s):

Michael S. Underwood ◽

David L. Feder

Keyword(s):

Quantum Computation ◽

Quantum Walk ◽

Universal Quantum

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Computational power of single qubit discrete-time quantum walk

10.21203/rs.3.rs-226618/v1 ◽

2021 ◽

Author(s):

Shivani Singh ◽

Prateek Chawla ◽

Anupam Sarkar ◽

C. M. Chandrashekar

Keyword(s):

Discrete Time ◽

Quantum Walk ◽

Quantum Gates ◽

Computational Power ◽

Position Space ◽

Single Qubit ◽

Qubit System ◽

Time Quantum ◽

Universal Quantum ◽

Qubit States

Abstract Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal set of gates on two-and three-qubit system. The idea is to reap the effective Hilbert space of the single qubit and the position space on which it evolves in superposition of position space in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates in the form of 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.

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Discrete-time quantum walk on circular graph: Simulations and effect of gate depth and errors

International Journal of Quantum Information ◽

10.1142/s0219749921500088 ◽

2021 ◽

pp. 2150008

Author(s):

Iyed Ben Slimen ◽

Amor Gueddana ◽

Vasudevan Lakshminarayanan

Keyword(s):

Discrete Time ◽

Quantum Computer ◽

Quantum Walk ◽

Quantum Walks ◽

Quantum Circuits ◽

Time Quantum ◽

Universal Quantum ◽

Circuit Decomposition ◽

Circular Graph ◽

The Impact

We investigate the counterparts of random walks in universal quantum computing and their implementation using standard quantum circuits. Quantum walks have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1D graph, namely a circle, and show how to implement a discrete-time quantum walk in quantum circuits built with universal CNOT and single qubit gates. We review elementary quantum gates and circuit decomposition techniques and propose a generalized version of all CNOT-based circuits of the quantum walk. We simulated these circuits on five different qubits IBM-Q quantum devices. This quantum computer has nonperfect gates based on superconducting qubits, and, therefore, we analyzed the impact of the CNOT errors and CNOT-depth on the fidelity of the circuit.

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