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:2511.04945 · Journal of Computational Physics

Distributed quantum approximate counting algorithm

Huaijing Huang, Daowen Qiu

quant-phSubmitted Nov 7, 2025• Announced Nov 10, 2025• 0 citations• Revised Oct 25, 2026 (v2)
v1 · Nov 7, 2025v2 · Oct 25, 2026
arXivHTMLPDF

Abstract

In this article, we propose a distributed quantum algorithm for solving counting problem using Grover operator and a classical post-processing procedure. We apply the proposed algorithm to estimate inner products and Hamming distances. Simulations are conducted on the Qisikit platform, further demonstrating the effectiveness of our algorithm and its suitability for the NISQ era. Compared to existing counting algorithms, the proposed algorithm has advantages in terms of the number of qubits, circuit depth, and the number of quantum gates.

Related papers

Simpler quantum counting

Chu-Ryang Wie

A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states in the search space. This algorithm terminates within log(sqrt(N/M)) consecutive measurement steps when the probability p1 of measuring the state |1> is at least 0.5, and the result from the final step is used in estimating M by a classical post processing. The purpose of controlled-Grover iteration is to increase the probability p1. This algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, produces a more accurate estimate of M, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare the two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.

Quantum Information and Computation•Sep 1, 2019•31 citations

Low Depth Distributed Quantum Algorithms for Unordered Database Search

Huaijing Huang, Daowen Qiu, Ximing Hua +1 more

Grover's algorithm accelerates unstructured database search quadratically compared to classical algorithms. In the NISQ era, distributed quantum computing can decrease circuit depth and reduce noise. In this paper, an algorithm for constructing query operators for subfunctions is proposed. By dividing the target string of the search problem into several substrings and integrating the query operator of each subfunction, a low-depth distributed exact quantum search algorithm is designed. The contributions of this paper are as follows: (1) The proposed distributed algorithm has a lower circuit depth and can mitigate error accumulation compared to distributed quantum search algorithms; (2) The target can be accurately located by the proposed distributed algorithm; (3) Experiments conducted with the quantum software MindQuantum confirm the effectiveness and feasibility of the proposed distributed algorithm. Moreover, the introduction of noise to the circuit during these experiments indicates that the algorithm possesses an inherent capacity for noise resistance.

quant-pharXiv:2604.14081•Chinese Journal of Physics•Apr 16, 2026•1 citation

Distributed Quantum Algorithm for the NISQ Era: A Novel Approach to Solving Simon's Problem with Reduced Resources

Xu Zhou, Yuchen Wang, Wenxuan Tao +2 more

Abstract Distributed quantum computation has gained significant interest in the noisy intermediate‐scale quantum (NISQ) era. This paradigm requires each computing node to possess a reduced number of qubits and quantum gates. In this study, a Distributed Simon's Algorithm (DSA) is designed to tackle Simon's problem, which entails the discovery of a hidden string of a promised Boolean function , where if and only if or . Specifically, 1) our algorithm is capable of being partitioned into any nodes, where ; 2) the number of queries required by the DSA is , while that of the original Simon's algorithm (SA) is ; 3) the maximum number of qubits required by our approach at a single node is , which is fewer than the qubits required by both the SA and existing distributed Simon's algorithm. Here, denotes the number of computing qubits needed for the ‐th node and satisfies ; 4) the optimal circuit depth of the DSA is , which is reduced compared to the circuit depth of the SA, ; 5) in contrast to currently distributed schemes, the DSA eliminates the need for classical queries; 6) how the DSA solves a specific Simon's problem (e.g., ) is also simulated using MindSpore Quantum, a quantum simulation software. The simulation results show that the DSA features a shallower quantum circuit, thereby demonstrating enhanced resistance to circuit noise. This characteristic makes it more feasible for implementation in the NISQ era.

Advanced Quantum Technologies•Apr 13, 2025•1 citation

Distributed exact multi-objective quantum search algorithm

Hao Li, Daowen Qiu, Le Luo

Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design two distributed iterated operators and therefore two new distributed Grover's algorithms are obtained with the following advantages: (1) Compared to Grover's algorithm and the modified Grover's algorithm by Long, our distributed algorithms require fewer qubits; (2) Compared to the distributed Grover's algorithm proposed by Qiu et al., one of our distributed algorithms is exact. Of course, both our distributed algorithms require quite quantum communication and involve a number of more complicated unitary operators as cost, but there still may have certain advantage of physical realizability in the Noisy Intermediate-Scale Quantum (NISQ) era.

arXiv:2409.04039•Sep 6, 2024•0 citations

HAMMR-L: Noise Reduction in Quantum Outcomes Using a Richardson-Lucy Deconvolution Algorithm for Quantum State Graphs

Jake Scally, Austin Myers, Ryan Carmichael +2 more

Current quantum computers present significant noise, especially as circuit depth and qubit count increase. Prior work has demonstrated that erroneous outcomes exhibit some behavior in Hamming space, enabling improvements in the output distributions of NISQ-era computers. We present HAMMR-L: a principled post-processing technique for improving the fidelity of output distributions by applying Richardson-Lucy image deconvolution on a state graph of measurement results connected by Hamming distance. We show that this preliminary implementation of HAMMR-L outperforms existing cutting-edge Hamming-based post-processors such as QBEEP while being circuit and hardware agnostic, which QBEEP is not. HAMMR-L also demonstrates clear potential for future improvements and we discuss how such improvements might be realized while highlighting the strengths, limitations, and generality of the underlying concept.

quant-pharXiv:2603.28821•Mar 31, 2026•0 citations

Noise-Aware Distributed Quantum Approximate Optimization Algorithm on Near-Term Quantum Hardware

Kuan‐Cheng Chen, Xiaotian Xu, Felix Burt +3 more

This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple Quantum Processing Units (QPUs) to enhance scalability and performance. The noise-aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•20 citations
In this article, we propose a distributed quantum algorithm for solving counting problem using Grover operator and a classical post-processing procedure. We apply the proposed algorithm to estimate inner products and Hamming distances. Simulations are conducted on the Qisikit platform, further demonstrating the effectiveness of our algorithm and its suitability for the NISQ era. Compared to existing counting algorithms, the proposed algorithm has advantages in terms of the number of qubits, circuit depth, and the number of quantum gates.
A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states in the search space. This algorithm terminates within log(sqrt(N/M)) consecutive measurement steps when the probability p1 of measuring the state |1> is at least 0.5, and the result from the final step is used in estimating M by a classical post processing. The purpose of controlled-Grover iteration is to increase the probability p1. This algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, produces a more accurate estimate of M, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare the two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.
Grover's algorithm accelerates unstructured database search quadratically compared to classical algorithms. In the NISQ era, distributed quantum computing can decrease circuit depth and reduce noise. In this paper, an algorithm for constructing query operators for subfunctions is proposed. By dividing the target string of the search problem into several substrings and integrating the query operator of each subfunction, a low-depth distributed exact quantum search algorithm is designed. The contributions of this paper are as follows: (1) The proposed distributed algorithm has a lower circuit depth and can mitigate error accumulation compared to distributed quantum search algorithms; (2) The target can be accurately located by the proposed distributed algorithm; (3) Experiments conducted with the quantum software MindQuantum confirm the effectiveness and feasibility of the proposed distributed algorithm. Moreover, the introduction of noise to the circuit during these experiments indicates that the algorithm possesses an inherent capacity for noise resistance.
Abstract Distributed quantum computation has gained significant interest in the noisy intermediate‐scale quantum (NISQ) era. This paradigm requires each computing node to possess a reduced number of qubits and quantum gates. In this study, a Distributed Simon's Algorithm (DSA) is designed to tackle Simon's problem, which entails the discovery of a hidden string of a promised Boolean function , where if and only if or . Specifically, 1) our algorithm is capable of being partitioned into any nodes, where ; 2) the number of queries required by the DSA is , while that of the original Simon's algorithm (SA) is ; 3) the maximum number of qubits required by our approach at a single node is , which is fewer than the qubits required by both the SA and existing distributed Simon's algorithm. Here, denotes the number of computing qubits needed for the ‐th node and satisfies ; 4) the optimal circuit depth of the DSA is , which is reduced compared to the circuit depth of the SA, ; 5) in contrast to currently distributed schemes, the DSA eliminates the need for classical queries; 6) how the DSA solves a specific Simon's problem (e.g., ) is also simulated using MindSpore Quantum, a quantum simulation software. The simulation results show that the DSA features a shallower quantum circuit, thereby demonstrating enhanced resistance to circuit noise. This characteristic makes it more feasible for implementation in the NISQ era.
Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design two distributed iterated operators and therefore two new distributed Grover's algorithms are obtained with the following advantages: (1) Compared to Grover's algorithm and the modified Grover's algorithm by Long, our distributed algorithms require fewer qubits; (2) Compared to the distributed Grover's algorithm proposed by Qiu et al., one of our distributed algorithms is exact. Of course, both our distributed algorithms require quite quantum communication and involve a number of more complicated unitary operators as cost, but there still may have certain advantage of physical realizability in the Noisy Intermediate-Scale Quantum (NISQ) era.
Current quantum computers present significant noise, especially as circuit depth and qubit count increase. Prior work has demonstrated that erroneous outcomes exhibit some behavior in Hamming space, enabling improvements in the output distributions of NISQ-era computers. We present HAMMR-L: a principled post-processing technique for improving the fidelity of output distributions by applying Richardson-Lucy image deconvolution on a state graph of measurement results connected by Hamming distance. We show that this preliminary implementation of HAMMR-L outperforms existing cutting-edge Hamming-based post-processors such as QBEEP while being circuit and hardware agnostic, which QBEEP is not. HAMMR-L also demonstrates clear potential for future improvements and we discuss how such improvements might be realized while highlighting the strengths, limitations, and generality of the underlying concept.
This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple Quantum Processing Units (QPUs) to enhance scalability and performance. The noise-aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.