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

arXiv:2307.11027 · The European Physical Journal D

Cycle discrete-time quantum walks on a noisy quantum computer

Vivek Wadhia, Nicholas Chancellor, Viv M. Kendon

Published Mar 1, 2024• 8 citations
arXivHTMLPDF

Abstract

Abstract The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as , the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity. Graphic abstract

DOI
10.1140/epjd/s10053-023-00795-2

Related papers

Experimental Implementation of Discrete Time Quantum Walk with the IBM Qiskit Library

Pierriccardo Olivieri, Mehrnoosh Askarpour, Elisabetta Di Nitto

This paper presents an implementation of quantum random walk using the Qiskit library, given the quantum circuits extracted from the literature. We started by implementing an instance of Coined Discrete Quantum Walk on an 8-node cyclic graph. Observing the limitations of this implementation, we experimented a different approach by proposing an implementation for Szegedy Quantum Walk in the IBM Qiskit library [1]. The proposed solution could be used as a building block to construct quantum implementation of other classic algorithms.

IEEE/ACM International Workshop on Quantum Software Engineering (Q-SE)•Jun 1, 2021•4 citations

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

Luca Razzoli, Gabriele Cenedese, Maria Bondani +1 more

Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2n-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O(n2+nt) two-qubit gates compared to the O(n2t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers.

arXiv:2402.01854•Entropy•Apr 2, 2024•16 citations

Implementation of a quantum walk in a cycle of four nodes using an alternative method based on the Swap gate

Dagoberto S. Freitas, Aisis Rodrigues Barbosa

This work has the objective of implementing quantum random walks in a graph with 4 nodes represented by a circle. It was observed that during the implementation of a discrete-time quantum walk, based on Hadamard's coin, the simulated results diverge from the theoretically expected results. In order to correct the discrepancies between the processed and theoretically expected results we use an alternative method based on the Swap port. To perform the simulation of the algorithms, the Qiskit framework and a real processor provided by IBM through remote access was used. The simulations performed in the real processor showed small fluctuations, however the quantum states were obtained with satisfactory probabilities.

Sitientibus Série Ciências Físicas•Oct 5, 2023•0 citations

Practical Guide to Quantum Computing: Building Noise Models with IBM Quantum Simulators # 4

Mikhail Pavlov

Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.

•Mar 4, 2026•0 citations

Practical Guide to Quantum Computing: IBM Quantum Cloud Simulators # 3

Mikhail Pavlov

Abstract This practical guide explores the use of IBM Quantum cloud simulators for modeling and analyzing quantum circuits under realistic conditions. Using the IBM Q platform and Qiskit Runtime, the work demonstrates how to configure the ibmq_qasm_simulator and map a basic noise model derived from a physical IBM Quantum™ device. The guide focuses on: Setting up the ibmq_qasm_simulator in Qiskit. Extracting and applying a hardware-based noise model from a real IBM Quantum backend. Performing noisy simulations of QuantumCircuits. Using Sampler and Estimator primitives in Qiskit Runtime to analyze circuit outputs. Studying the impact of realistic quantum errors such as decoherence, gate infidelity, and readout noise. By incorporating noise models into simulations, researchers and developers can better understand how quantum circuits behave on real hardware, optimize algorithms before deployment, and design more robust quantum programs. This approach bridges the gap between idealized simulations and physical quantum devices, making it a critical step toward practical quantum application development.

•Mar 4, 2026•0 citations

Implementation of quantum random walk on a real quantum computer

Warat Puengtambol, Prapong Prechaprapranwong, Unchalisa Taetragool

Abstract A random walk is one of the widely adopted random processes for simulation and approximation in multiple areas of science and engineering. Quantum random walk is an analog version of the classical random walk. It was first introduced in 1993 by Y. Aharonov et al. They presented that, with the nature of quantum characteristic, the average length of the walking path on a line is possible to larger than a classical random walk can produce. Therefore, the quantum random walk can be used as a tool to construct many other quantum algorithms. Moreover, it can solve graph problems that many real-world problems can be formulated. However, quantum algorithms are only useful in practice if we can implement them efficiently on a quantum computer. In this study, we are then interested in designing and implementing a quantum circuit that can be run on a real quantum computing device. We firstly focus on the most straightforward, which is a one-dimension, quantum random walk algorithm. Then, the quantum circuits are developed and implemented on a real quantum computer and a quantum computing simulator using software development kits provided by IBM. Lastly, the performance and results of the quantum circuits tested on both computing platforms are presented.

Journal of Physics Conference Series•Jan 1, 2021•11 citations
Abstract The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as , the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity. Graphic abstract
This paper presents an implementation of quantum random walk using the Qiskit library, given the quantum circuits extracted from the literature. We started by implementing an instance of Coined Discrete Quantum Walk on an 8-node cyclic graph. Observing the limitations of this implementation, we experimented a different approach by proposing an implementation for Szegedy Quantum Walk in the IBM Qiskit library [1]. The proposed solution could be used as a building block to construct quantum implementation of other classic algorithms.
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2n-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O(n2+nt) two-qubit gates compared to the O(n2t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers.
This work has the objective of implementing quantum random walks in a graph with 4 nodes represented by a circle. It was observed that during the implementation of a discrete-time quantum walk, based on Hadamard's coin, the simulated results diverge from the theoretically expected results. In order to correct the discrepancies between the processed and theoretically expected results we use an alternative method based on the Swap port. To perform the simulation of the algorithms, the Qiskit framework and a real processor provided by IBM through remote access was used. The simulations performed in the real processor showed small fluctuations, however the quantum states were obtained with satisfactory probabilities.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.
Abstract This practical guide explores the use of IBM Quantum cloud simulators for modeling and analyzing quantum circuits under realistic conditions. Using the IBM Q platform and Qiskit Runtime, the work demonstrates how to configure the ibmq_qasm_simulator and map a basic noise model derived from a physical IBM Quantum™ device. The guide focuses on: Setting up the ibmq_qasm_simulator in Qiskit. Extracting and applying a hardware-based noise model from a real IBM Quantum backend. Performing noisy simulations of QuantumCircuits. Using Sampler and Estimator primitives in Qiskit Runtime to analyze circuit outputs. Studying the impact of realistic quantum errors such as decoherence, gate infidelity, and readout noise. By incorporating noise models into simulations, researchers and developers can better understand how quantum circuits behave on real hardware, optimize algorithms before deployment, and design more robust quantum programs. This approach bridges the gap between idealized simulations and physical quantum devices, making it a critical step toward practical quantum application development.
Abstract A random walk is one of the widely adopted random processes for simulation and approximation in multiple areas of science and engineering. Quantum random walk is an analog version of the classical random walk. It was first introduced in 1993 by Y. Aharonov et al. They presented that, with the nature of quantum characteristic, the average length of the walking path on a line is possible to larger than a classical random walk can produce. Therefore, the quantum random walk can be used as a tool to construct many other quantum algorithms. Moreover, it can solve graph problems that many real-world problems can be formulated. However, quantum algorithms are only useful in practice if we can implement them efficiently on a quantum computer. In this study, we are then interested in designing and implementing a quantum circuit that can be run on a real quantum computing device. We firstly focus on the most straightforward, which is a one-dimension, quantum random walk algorithm. Then, the quantum circuits are developed and implemented on a real quantum computer and a quantum computing simulator using software development kits provided by IBM. Lastly, the performance and results of the quantum circuits tested on both computing platforms are presented.