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

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.

Computational power of single qubit discrete-time quantum walk

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.

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

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.

scholarly journals Universal quantum computation using the discrete-time quantum walk

2010 ◽  
Vol 81 (4) ◽  
Author(s):  
Neil B. Lovett ◽  
Sally Cooper ◽  
Matthew Everitt ◽  
Matthew Trevers ◽  
Viv Kendon
Keyword(s):  
Quantum Computation ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Quantum ◽  
Universal Quantum

scholarly journals A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Unit Circle ◽  
Stationary State ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Limit ◽  
The Other ◽  
Unitary Matrix ◽  
Initial State ◽  
Time Quantum ◽  
Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

Limitations of discrete-time quantum walk on a one-dimensional infinite chain

2018 ◽  
Vol 382 (13) ◽  
pp. 899-903
Author(s):  
Jia-Yi Lin ◽  
Xuanmin Zhu ◽  
Shengjun Wu
Keyword(s):  
Discrete Time ◽  
Quantum Walk ◽  
Infinite Chain ◽  
One Dimensional ◽  
Time Quantum

scholarly journals Measuring the Tangle of Three-Qubit States

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 436 ◽  
Author(s):  
Adrián Pérez-Salinas ◽  
Diego García-Martín ◽  
Carlos Bravo-Prieto ◽  
José Latorre
Keyword(s):  
Direct Measurement ◽  
Canonical Form ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Tripartite Entanglement ◽  
Single Qubit ◽  
Optimal Values ◽  
Random States ◽  
Qubit States ◽  
Computational Basis

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method.

scholarly journals A limit theorem for a splitting distribution of a quantum walk

2018 ◽  
Vol 16 (03) ◽  
pp. 1850023
Author(s):  
Takuya Machida
Keyword(s):  
Limit Theorem ◽  
Probability Distribution ◽  
Random Walks ◽  
Discrete Time ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Unitary Evolution ◽  
Time Quantum ◽  
Long Time

Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

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