Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Globecom Workshops (GC Wkshps)

Quantum Walks with Entangled Coins and Walkers in Superposition

Salvador Elías Venegas-Andraca

Published Dec 1, 2018• 2 citations
Publisher

Abstract

We introduce a generalization of quantum walks with entangled coins consisting of a model of discrete quantum walks with coin pairs under various degrees of entanglement and walkers in quantum superposition as initial states. We introduce novel position probability distributions that may be used for algorithm development based on quantum-mechanical phenomena. Also, we numerically show that the skewness of position probability distribution produced by using coin initial state with various degrees of entanglement cannot be easily inferred.

DOI
10.1109/glocomw.2018.8644206

Related papers

Quantum Walk-based Generation of Entanglement Between Two Walkers

Salvador Elías Venegas-Andraca, Sougato Bose

Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.

arXiv:0901.3946•Jan 26, 2009•12 citations

Coined quantum walk on a quantum network

Jigyen Bhavsar, Shashank Shekhar, Siddhartha Santra

We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker moves originates from the unitary interaction of the walker coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand and, on the other, between the network qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker position with higher initial network entanglement. A potential application of these results as a characterization tool for quantum network properties is suggested.

arXiv:2406.01558•Physical Review A•Nov 20, 2024•2 citations

Revisiting one-dimensional discrete-time quantum walks with general coin

Mahesh N. Jayakody, Chandrakala Meena, Priodyuti Pradhan

Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the one-dimensional discrete-time QW and discuss basic steps in detail by incorporating the most general coin operator, constant in both space and time, and a localized initial state using numerical modeling. We investigate the impact of each parameter of the general coin operator on the probability distribution of the quantum walker. We show that by tuning the parameters of the general coin, one can regulate the probability distribution of the walker. We provide an algorithm for the one-dimensional quantum walk driven by the general coin operator. The study on general coin operators also includes the popular coins – Hadamard, Grover, and Fourier.

Physics Open•Nov 10, 2023•9 citations

Experimental demonstration of quantum walks with initial superposition states

Qi-Ping Su, Yu Zhang, Li Yu +9 more

Abstract The preparation of initial superposition states of discrete-time quantum walks (DTQWs) is necessary for the study and applications of DTQWs. Based on an encoding method, here, we propose a DTQW protocol in linear optics, which enables the preparation of arbitrary initial superposition states of the walker and the coin and enables to obtain the states of the DTQW in addition to the probability distribution of the walker. With this protocol, we experimentally demonstrate the DTQW in the polarization space with both the walker and the coin initially in superposition states, by using only passive linear-optical elements. The effects of the walker’s different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQWs are very different from those of DTQWs starting with a single position. Our findings reveal different properties of DTQWs and pave an avenue to study DTQWs with arbitrary initial states. Moreover, this encoding method enables one to encode an arbitrary high-dimensional quantum state, using a single physical qubit, and may be adopted to implement other quantum information tasks.

arXiv:1805.09784•npj Quantum Information•May 17, 2019•34 citations

Quantum walks

Steven Anatolievich Duplij, Raimund Vogl

We investigate quantum walks which play an important role in the modelling of many phenomena. The detailed and thorough description is given to the discrete quantum walks on a line, where the total quantum state consists of quantum states of the walker and the coin. In addition to the standard walker probability distribution, we introduce the coin probability distribution which gives more complete quantum walk description and novel visualization in terms of the so called polyanders (analogs of trianders in DNA visualization). The methods of final states computation and the Fourier transform are presented for the Hadamard quantum walk.

Institute of Physics eBooks•Nov 1, 2023•0 citations

Entangled Quantum Walkers for Secure Quantum Key Distribution

Lai, Chia-Tso

Quantum Key Distribution (QKD) is an emerging cryptographic method designed for secure key sharing. Its security is theoretically guaranteed by fundamental principles of quantum mechanics, making it a leading candidate for future communication protocols. Quantum Random Walks (QRWs), on the other hand, are quantum processes that exhibit intriguing phenomena such as interference and superposition, enabling the generation of decentralized and asymmetric probability distributions. Inspired by both fields of study, we propose a novel QKD protocol based on two entangled quantum walkers. Our protocol exploits the unique correlations between the walkers at extremal positions of the walk to establish secret keys shared exclusively by the two parties. The security of the protocol is augmented by analyzing the joint probability distributions of the walkers' measured positions and their associated coin states.

arXiv:2508.05593•Aug 7, 2025•0 citations
We introduce a generalization of quantum walks with entangled coins consisting of a model of discrete quantum walks with coin pairs under various degrees of entanglement and walkers in quantum superposition as initial states. We introduce novel position probability distributions that may be used for algorithm development based on quantum-mechanical phenomena. Also, we numerically show that the skewness of position probability distribution produced by using coin initial state with various degrees of entanglement cannot be easily inferred.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker moves originates from the unitary interaction of the walker coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand and, on the other, between the network qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker position with higher initial network entanglement. A potential application of these results as a characterization tool for quantum network properties is suggested.
Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the one-dimensional discrete-time QW and discuss basic steps in detail by incorporating the most general coin operator, constant in both space and time, and a localized initial state using numerical modeling. We investigate the impact of each parameter of the general coin operator on the probability distribution of the quantum walker. We show that by tuning the parameters of the general coin, one can regulate the probability distribution of the walker. We provide an algorithm for the one-dimensional quantum walk driven by the general coin operator. The study on general coin operators also includes the popular coins – Hadamard, Grover, and Fourier.
Abstract The preparation of initial superposition states of discrete-time quantum walks (DTQWs) is necessary for the study and applications of DTQWs. Based on an encoding method, here, we propose a DTQW protocol in linear optics, which enables the preparation of arbitrary initial superposition states of the walker and the coin and enables to obtain the states of the DTQW in addition to the probability distribution of the walker. With this protocol, we experimentally demonstrate the DTQW in the polarization space with both the walker and the coin initially in superposition states, by using only passive linear-optical elements. The effects of the walker’s different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQWs are very different from those of DTQWs starting with a single position. Our findings reveal different properties of DTQWs and pave an avenue to study DTQWs with arbitrary initial states. Moreover, this encoding method enables one to encode an arbitrary high-dimensional quantum state, using a single physical qubit, and may be adopted to implement other quantum information tasks.
We investigate quantum walks which play an important role in the modelling of many phenomena. The detailed and thorough description is given to the discrete quantum walks on a line, where the total quantum state consists of quantum states of the walker and the coin. In addition to the standard walker probability distribution, we introduce the coin probability distribution which gives more complete quantum walk description and novel visualization in terms of the so called polyanders (analogs of trianders in DNA visualization). The methods of final states computation and the Fourier transform are presented for the Hadamard quantum walk.
Quantum Key Distribution (QKD) is an emerging cryptographic method designed for secure key sharing. Its security is theoretically guaranteed by fundamental principles of quantum mechanics, making it a leading candidate for future communication protocols. Quantum Random Walks (QRWs), on the other hand, are quantum processes that exhibit intriguing phenomena such as interference and superposition, enabling the generation of decentralized and asymmetric probability distributions. Inspired by both fields of study, we propose a novel QKD protocol based on two entangled quantum walkers. Our protocol exploits the unique correlations between the walkers at extremal positions of the walk to establish secret keys shared exclusively by the two parties. The security of the protocol is augmented by analyzing the joint probability distributions of the walkers' measured positions and their associated coin states.