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:2504.13532 · Quantum Machine Intelligence

Quantum walks–based adaptive distribution generation with efficient CUDA-Q acceleration

Yen-Jui Chang, Weiting Wang, Chen-Yu Liu, Yun-Yuan Wang, Ching‐Ray Chang

Published Apr 8, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract We present a novel Adaptive Distribution Generator (ADG) that leverages a quantum walks–based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with discrete-time quantum walks(DTQWs)—specifically, split-step quantum walks(SSQWs) and their entangled extensions—to dynamically tune coin parameters and drive the evolution of quantum states toward desired distributions. This enables accurate one-dimensional probability modeling for applications such as financial simulation and the generation of structured two-dimensional patterns, exemplified by digit representations (0–9). Implemented within the CUDA-Q framework, our approach exploits GPU acceleration to significantly reduce computational overhead and improve scalability relative to conventional methods. Extensive benchmarks demonstrate that our Quantum Walk–Based Adaptive Distribution Generator (QWs-based ADG) achieves high simulation fidelity and bridges the gap between theoretical quantum algorithms and practical high-performance computation.

DOI
10.1007/s42484-026-00391-8

Related papers

Preparing random state for quantum financing with quantum walks

Yen-Jui Chang, Weiting Wang, Hao-Yuan Chen +2 more

In recent years, there has been an emerging trend of combining two innovations in computer science and physics to achieve better computation capability. Exploring the potential of quantum computation to achieve highly efficient performance in various tasks is a vital development in engineering and a valuable question in sciences, as it has a significant potential to provide exponential speedups for technologically complex problems that are specifically advantageous to quantum computers. However, one key issue in unleashing this potential is constructing an efficient approach to load classical data into quantum states that can be executed by quantum computers or quantum simulators on classical hardware. Therefore, the split-step quantum walks (SSQW) algorithm was proposed to address this limitation. We facilitate SSQW to design parameterized quantum circuits (PQC) that can generate probability distributions and optimize the parameters to achieve the desired distribution using a variational solver. A practical example of implementing SSQW using Qiskit has been released as open-source software. Showing its potential as a promising method for generating desired probability amplitude distributions highlights the potential application of SSQW in option pricing through quantum simulation.

arXiv:2302.12500•Feb 24, 2023•1 citation

A novel approach for quantum financial simulation and quantum state preparation

Yen-Jui Chang, Wei‐Ting Wang, Hao-Yuan Chen +2 more

Abstract Quantum state preparation is a vital process in quantum computing and quantum information processing. The ability to accurately and reliably prepare specific quantum states is essential for a variety of applications. One of the promising applications of quantum computers is quantum simulation. This requires preparing a quantum state that represents the system we’re trying to simulate. This research introduces a novel simulation algorithm, the multi-Split-Steps Quantum Walk (multi-SSQW), designed to learn and load complicated probability distributions using parameterized quantum circuits (PQC) with a variational solver on classical simulators. The multi-SSQW algorithm is a modified version of the split-steps quantum walk, enhanced to incorporate a multi-agent decision-making process, rendering it suitable for modeling financial markets. The study provides theoretical descriptions and empirical investigations of the multi-SSQW algorithm to demonstrate its promising capabilities in probability distribution simulation and financial market modeling. Taking advantage of quantum computation, the multi-SSQW model's complex financial distributions and scenarios with high accuracy, providing valuable insights and mechanisms for financial analysis and decision-making. The multi-SSQW’s key benefits include its modeling flexibility, stable convergence, and instantaneous computation. These advantages underscore its rapid modeling and prediction potential in dynamic financial markets.

arXiv:2308.01844•Quantum Machine Intelligence•Apr 25, 2024•14 citations

On the convergence of Markov chain distribution within quantum walk circuit subspace

Aingeru Ramos, Jose Antonio Pascual, Javier Navaridas +1 more

Abstract Markov chain Monte Carlo (MCMC) methods are a family of algorithms designed to approximate probability distributions that are otherwise intractable to sample from directly. However, as the dimensionality and complexity of the target distribution increase, the convergence of these methods can slow considerably, demanding substantial computational resources. In this context, quantum computing emerges as a promising framework to address this limitation, with different quantum circuit constructions serving as quantum MCMC methods. In this work, we present a quantum circuit based on the discrete quantum walk (DQW) algorithm that implements the algorithmic steps of the Metropolis–Hastings method, encoding the target distribution in a position quantum register. The circuit incorporates auxiliary registers to compute and discretize the acceptance probability, and uses controlled operations to modulate the walker’s evolution accordingly. Simulation results show that the marginal probability distribution encoded in the position register converges asymptotically toward the discretized target distribution for both single and multimodal distributions. We further analyze the effect of circuit parameters on convergence behavior and approximation quality, refining the construction by enabling the evaluation of multiple candidate moves per iteration, therefore reducing the number of iterations required for convergence within our implementation. Finally, we provide a qualitative comparison of our approach with related quantum MCMC methods, namely Szegedy’s quantum walk and QAOA, and discuss structural differences as well as the potential incorporation of adaptive proposal techniques within the proposed circuit framework.

arXiv:2504.12089•Quantum Information Processing•Apr 27, 2026•1 citation

A hybrid quantum walk model unifying discrete and continuous quantum walks

Tianen Chen, Yun Shang

Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures, we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying K adjacency matrices of n -vertex regular graphs with time complexity O ( n 2 d 1 ⋯ d K ), outperforming classical matrix multiplication ( O ( n 2.371552 )) when vertex degrees d i are bounded. The algorithm’s efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.

arXiv:2509.09221•npj Quantum Information•Dec 30, 2025•2 citations

Quantum State Generator (QGS)

Jincheng Zhang

Quantum State Generator (QGS) presents a novel algorithmic approach to quantum computation, leveraging the power of quantum state generators to generate specific quantum states with enhanced probability distributions. This research explores the design and implementation of a QGS, focusing on its ability to improve quantum computation efficiency and resource utilization. The core mechanism centers around the creation of a dynamic quantum state generator that adapts to input parameters, enabling precise control over the generated quantum states. This approach directly addresses the limitations of traditional quantum computing by reducing the operational complexity and increasing the potential for effective quantum algorithms. The paper details the architecture of the QGS, including the quantum state generator's design and the subsequent probabilistic distribution algorithms. The resulting QGS demonstrates significant improvements in quantum computation performance through targeted probability refinement. This work provides a foundation for future advancements in quantum computing, offering a practical pathway towards achieving substantial gains in efficiency and scalability.

•Sep 4, 2026•0 citations

Dynamic Probability Distribution Generation and Quantum Computing Integration

Jincheng Zhang

This paper explores the integration of dynamic probability distribution generation with quantum computing to achieve unprecedented precision in generating complex Gaussian distributions. Traditional methods often struggle with high-dimensional distributions, limiting their applicability. We propose a novel approach that leverages quantum computing for precise calculations within the generation process, significantly improving the accuracy and computational efficiency of the resulting probability distributions. This work addresses the limitations of existing techniques by presenting a robust and scalable framework for generating high-fidelity Gaussian distributions utilizing quantum computation.

•Sep 4, 2026•0 citations
Abstract We present a novel Adaptive Distribution Generator (ADG) that leverages a quantum walks–based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with discrete-time quantum walks(DTQWs)—specifically, split-step quantum walks(SSQWs) and their entangled extensions—to dynamically tune coin parameters and drive the evolution of quantum states toward desired distributions. This enables accurate one-dimensional probability modeling for applications such as financial simulation and the generation of structured two-dimensional patterns, exemplified by digit representations (0–9). Implemented within the CUDA-Q framework, our approach exploits GPU acceleration to significantly reduce computational overhead and improve scalability relative to conventional methods. Extensive benchmarks demonstrate that our Quantum Walk–Based Adaptive Distribution Generator (QWs-based ADG) achieves high simulation fidelity and bridges the gap between theoretical quantum algorithms and practical high-performance computation.
In recent years, there has been an emerging trend of combining two innovations in computer science and physics to achieve better computation capability. Exploring the potential of quantum computation to achieve highly efficient performance in various tasks is a vital development in engineering and a valuable question in sciences, as it has a significant potential to provide exponential speedups for technologically complex problems that are specifically advantageous to quantum computers. However, one key issue in unleashing this potential is constructing an efficient approach to load classical data into quantum states that can be executed by quantum computers or quantum simulators on classical hardware. Therefore, the split-step quantum walks (SSQW) algorithm was proposed to address this limitation. We facilitate SSQW to design parameterized quantum circuits (PQC) that can generate probability distributions and optimize the parameters to achieve the desired distribution using a variational solver. A practical example of implementing SSQW using Qiskit has been released as open-source software. Showing its potential as a promising method for generating desired probability amplitude distributions highlights the potential application of SSQW in option pricing through quantum simulation.
Abstract Quantum state preparation is a vital process in quantum computing and quantum information processing. The ability to accurately and reliably prepare specific quantum states is essential for a variety of applications. One of the promising applications of quantum computers is quantum simulation. This requires preparing a quantum state that represents the system we’re trying to simulate. This research introduces a novel simulation algorithm, the multi-Split-Steps Quantum Walk (multi-SSQW), designed to learn and load complicated probability distributions using parameterized quantum circuits (PQC) with a variational solver on classical simulators. The multi-SSQW algorithm is a modified version of the split-steps quantum walk, enhanced to incorporate a multi-agent decision-making process, rendering it suitable for modeling financial markets. The study provides theoretical descriptions and empirical investigations of the multi-SSQW algorithm to demonstrate its promising capabilities in probability distribution simulation and financial market modeling. Taking advantage of quantum computation, the multi-SSQW model's complex financial distributions and scenarios with high accuracy, providing valuable insights and mechanisms for financial analysis and decision-making. The multi-SSQW’s key benefits include its modeling flexibility, stable convergence, and instantaneous computation. These advantages underscore its rapid modeling and prediction potential in dynamic financial markets.
Abstract Markov chain Monte Carlo (MCMC) methods are a family of algorithms designed to approximate probability distributions that are otherwise intractable to sample from directly. However, as the dimensionality and complexity of the target distribution increase, the convergence of these methods can slow considerably, demanding substantial computational resources. In this context, quantum computing emerges as a promising framework to address this limitation, with different quantum circuit constructions serving as quantum MCMC methods. In this work, we present a quantum circuit based on the discrete quantum walk (DQW) algorithm that implements the algorithmic steps of the Metropolis–Hastings method, encoding the target distribution in a position quantum register. The circuit incorporates auxiliary registers to compute and discretize the acceptance probability, and uses controlled operations to modulate the walker’s evolution accordingly. Simulation results show that the marginal probability distribution encoded in the position register converges asymptotically toward the discretized target distribution for both single and multimodal distributions. We further analyze the effect of circuit parameters on convergence behavior and approximation quality, refining the construction by enabling the evaluation of multiple candidate moves per iteration, therefore reducing the number of iterations required for convergence within our implementation. Finally, we provide a qualitative comparison of our approach with related quantum MCMC methods, namely Szegedy’s quantum walk and QAOA, and discuss structural differences as well as the potential incorporation of adaptive proposal techniques within the proposed circuit framework.
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures, we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying K adjacency matrices of n -vertex regular graphs with time complexity O ( n 2 d 1 ⋯ d K ), outperforming classical matrix multiplication ( O ( n 2.371552 )) when vertex degrees d i are bounded. The algorithm’s efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.
Quantum State Generator (QGS) presents a novel algorithmic approach to quantum computation, leveraging the power of quantum state generators to generate specific quantum states with enhanced probability distributions. This research explores the design and implementation of a QGS, focusing on its ability to improve quantum computation efficiency and resource utilization. The core mechanism centers around the creation of a dynamic quantum state generator that adapts to input parameters, enabling precise control over the generated quantum states. This approach directly addresses the limitations of traditional quantum computing by reducing the operational complexity and increasing the potential for effective quantum algorithms. The paper details the architecture of the QGS, including the quantum state generator's design and the subsequent probabilistic distribution algorithms. The resulting QGS demonstrates significant improvements in quantum computation performance through targeted probability refinement. This work provides a foundation for future advancements in quantum computing, offering a practical pathway towards achieving substantial gains in efficiency and scalability.
This paper explores the integration of dynamic probability distribution generation with quantum computing to achieve unprecedented precision in generating complex Gaussian distributions. Traditional methods often struggle with high-dimensional distributions, limiting their applicability. We propose a novel approach that leverages quantum computing for precise calculations within the generation process, significantly improving the accuracy and computational efficiency of the resulting probability distributions. This work addresses the limitations of existing techniques by presenting a robust and scalable framework for generating high-fidelity Gaussian distributions utilizing quantum computation.