arXiv subjects

Daowen Qiu

Publications and source records attributed to Daowen Qiu.

At least 19 recordsLinked to original sources

arXiv2026

Distributed quantum-classical hybrid algorithm for solving K-SAT problem

Recently, Dunjko et al.(PRL, 2018) proposed an algorithm for accelerating the solution of 3-satisfiability problems using a small-scale quantum computer. In this paper, we design a distributed quantum-classical hybrid algorithm for solving K-satisfiability problems. Under resource-constrained conditions, our algorithm achieves a significant acceleration in the core term of the exponential time complexity. The proposed algorithm is a generalization of the algorithm by Dunjko et al. Compared with their algorithm, our algorithm requires a smaller number of qubits. More importantly, the proposed algorithm does not rely on any quantum communication.

quant-ph↗

arXiv2026

Low Depth Distributed Quantum Algorithms for Unordered Database Search

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-ph↗

arXiv2026

Distributed Quantum Discrete Logarithm Algorithm

Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current hardware limitations, the scale of DLP instances that can be addressed by quantum computers remains insufficient. To overcome this limitation, we propose a distributed quantum discrete logarithm algorithm that reduces the required quantum register size for solving DLPs. Specifically, we design a distributed quantum algorithm to determine whether the solution is contained in a given set. Based on this procedure, our method solves DLPs by identifying the intersection of sets containing the solution. Compared with Shor's original algorithm, our approach reduces the register size and can improve the success probability, while requiring no quantum communication.

quant-ph↗

arXiv2025

Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm

We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our algorithm is more concise than the previous exact algorithm and applies to any finite Abelian group. Second, utilizing the Chinese Remainder Theorem, we propose a distributed exact quantum algorithm for finite AHSP, which requires fewer qudits, lower quantum query complexity, and no quantum communication. We further show that our distributed approach can be extended to certain classes of non-Abelian groups. Finally, we develop a parallel exact classical algorithm for finite AHSP with reduced query complexity; even without parallel execution, the total number of queries across all nodes does not exceed that of the original centralized algorithm under mild conditions.

quant-ph↗

arXiv2025

Probabilistic Bounds on the Number of Elements to Generate Finite Nilpotent Groups and Their Applications

This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let $\varphi_k(G)$ denote the probability that $k$ random elements generate a finite nilpotent group $G$. For any $0 < \epsilon < 1$, we prove that $\varphi_k(G) \ge 1 - \epsilon$ if $k \ge \operatorname{rank}(G) + \lceil \log_2(2/\epsilon) \rceil$ (a bound based on the group rank) or if $k \ge \operatorname{len}(G) + \lceil \log_2(1/\epsilon) \rceil$ (a bound based on the group chain length). Moreover, these bounds are shown to be nearly tight. Both bounds sharpen the previously known requirement of $k \ge \lceil \log_2 |G| + \log_2(1/\epsilon) \rceil + 2$. Our results provide a foundational tool for analyzing probabilistic algorithms, enabling a better estimation of the iteration count for the finite Abelian hidden subgroup problem (AHSP) standard quantum algorithm and a reduction in the circuit repetitions required by Regev's factoring algorithm.

quant-ph↗

arXiv2025

Notes on Stack Machines and Quantum Stack Machines

Multi-stack machines and Turing machines can simulate to each other. In this note, we give a succinct definition of multi-stack machines, and from this definition it is clearly seen that pushdown automata and deterministic finite automata are special cases of multi-stack machines. Also, with this mode of definition, pushdown automata and deterministic pushdown automata are equivalent and recognize all context-free languages. In addition, we are motivated to formulate concise definitions of quantum pushdown automata and quantum stack machines.

cs.FL↗

arXiv2025

Distributed quantum approximate counting algorithm

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.

quant-ph↗

arXiv2025

Distributed Quantum Computing Based on Fixed-point Quantum Search

Fixed-point quantum search can find target strings without knowing their initial success probability and can be applied to the design of distributed quantum algorithms. This paper makes the following contributions to the integration of distributed quantum computing and the fixed-point quantum search: (1) An inherent relationship between a given Boolean function and its sub-functions is discovered. (2) In particular, a distributed quantum amplitude amplification algorithm based on the fixed-point search is proposed. The algorithm has advantages in the number of qubits and circuit depth, requires no quantum communication, and is simulated by means of Qiskit to show good noise resistance. (3) Inspired by the proposed algorithm, a general model for applying the fixed-point quantum search to distributed quantum computing is formulated.

quant-ph↗

arXiv2025

Universal Error Correction for Distributed Quantum Computing

In distributed quantum computing, the final solution of a problem is usually achieved by catenating these partial solutions resulted from different computing nodes, but intolerable errors likely yield in this catenation process. In this paper, we propose a universal error correction scheme to reduce errors and obtain effective solutions. Then, we apply this error correction scheme to designing a distributed phase estimation algorithm that presents a basic tool for studying distributed Shor's algorithm and distributed discrete logarithm algorithm as well as other distributed quantum algorithms. Our method may provide a universal strategy of error correction for a kind of distributed quantum computing.

quant-ph↗

arXiv2025

Distributed quantum algorithm for discrete logarithm problem

The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era. The main contributions of this paper are as follows: (1) A distributed quantum algorithm for discrete logarithm problem is designed, and its space complexity and success probability exhibit certain advantages to some extent; (2) The classical error correction technique proposed by Xiao and Qiu et al. is generalized by extending three bits to more than three bits.

quant-ph↗

arXiv2025

Improved distributed quantum algorithm for Simon's problem

Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large number of qubits was employed. In this paper, we design an improved distributed quantum algorithm for Simon's problem without using sorting operators, and our algorithm has the advantage of reducing half number of qubits required for a single computing node. Moreover, our algorithm does not involve the classical search process.

quant-ph↗

arXiv2025

New Insights into the Decidability of Opacity in Timed Automata

This paper investigates the decidability of opacity in timed automata (TA), a property that has been proven to be undecidable in general. First, we address a theoretical gap in recent work by J. An et al. (FM 2024) by providing necessary and sufficient conditions for the decidability of location-based opacity in TA. Based on these conditions, we identify a new decidable subclass of TA, called timed automata with integer resets (IRTA), where clock resets are restricted to occurring at integer time points. We also present a verification algorithm for opacity in IRTA. On the other hand, we consider achieving decidable timed opacity by weakening the capabilities of intruders. Specifically, we show that opacity in general TA becomes decidable under the assumption that intruders can only observe time in discrete units. These results establish theoretical foundations for modeling timed systems and intruders in security analysis, enabling an effective balance between expressiveness and decidability.

eess.SY↗

arXiv2025

Free-space Continuous-variable Quantum Secret Sharing

Free-space quantum cryptography has the potential to enable global quantum communication. However, most existing continuous-variable quantum secret sharing (CV-QSS) schemes rely on fiber channels. In this paper, we present a CV-QSS protocol designed for free-space transmission and construct models of crucial parameters, including channel transmittance, excess noise, and interruption probability, thus deriving the bound of the secret key rate. In particular, we provide a multi-source excess noise model for free-space CV-QSS based on the local local oscillator (LLO) scheme and a straightforward optimization of the noise. Furthermore, our research considers the impact of atmospheric turbulence on the protocol. Simulation results demonstrate that the intensification of atmospheric turbulence adversely affects the aforementioned crucial parameters, leading to a significant reduction in the key rate. However, our protocol shows its capability to securely share secrets over a distance of exceeding $60$ km among five participants in the presence of turbulence with $C^2_n=1\times 10^{-15}m^{-2/3}$, while maintaining a high key rate of approximately $0.55$ bit/pulse over a distance of $10$ km across twenty participants. These findings suggest that efficient CV-QSS in free space is indeed achievable. This research may serve as a reference for the design and optimization of the practical CV-QSS system.

quant-ph↗

arXiv2024

Distributed exact multi-objective quantum search algorithm

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.

quant-ph↗

arXiv2023

Learning Quantum Finite Automata with Queries

{\it Learning finite automata} (termed as {\it model learning}) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite memory. Due to their simplicity, QFA have well physical realizability, but one-way QFA still have essential advantages over classical finite automata with regard to state complexity (two-way QFA are more powerful than classical finite automata in computation ability as well). As a different problem in {\it quantum learning theory} and {\it quantum machine learning}, in this paper, our purpose is to initiate the study of {\it learning QFA with queries} (naturally it may be termed as {\it quantum model learning}), and the main results are regarding learning two basic one-way QFA: (1) We propose a learning algorithm for measure-once one-way QFA (MO-1QFA) with query complexity of polynomial time; (2) We propose a learning algorithm for measure-many one-way QFA (MM-1QFA) with query complexity of polynomial-time, as well.

quant-ph↗

arXiv2023

Exact distributed quantum algorithm for generalized Simon's problem

Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and also a special hidden subgroup problem. In this paper, we present two key contributions. Firstly, we characterize the structure of the generalized Simon's problem in distributed scenario and introduce a corresponding distributed quantum algorithm. Secondly, we refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique. Our algorithm offers exponential acceleration compared to the distributed classical algorithm. When contrasted with the centralized quantum algorithm for the generalized Simon's problem, our algorithm's oracle requires fewer qubits, thus making it easier to be physically implemented. Particularly, the exact distributed quantum algorithm we develop for the generalized Simon's problem outperforms the best previously proposed distributed quantum algorithm for Simon's problem in terms of generalizability and exactness.

quant-ph↗

arXiv2023

Opacity of Parametric Discrete Event Systems: Models, Decidability, and Algorithms

Finite automata (FAs) model is a popular tool to characterize discrete event systems (DESs) due to its succinctness. However, for some complex systems, it is difficult to describe the necessary details by means of FAs model. In this paper, we consider a kind of extended finite automata (EFAs) in which each transition carries a predicate over state and event parameters. We also consider a type of simplified EFAs, called Event-Parameters EFAs (EP-EFAs), where the state parameters are removed. Based upon these two parametric models, we investigate the problem of opacity analysis for parametric DESs. First of all, it is shown that EFAs model is more expressive than EP-EFAs model. Secondly, it is proved that the opacity properties for EFAs are undecidable in general. Moreover, the decidable opacity properties for EP-EFAs are investigated. We present the verification algorithms for current-state opacity, initial-state opacity and infinite-step opacity, and then discuss the complexity. This paper establishes a preliminary theory for the opacity of parametric DESs, which lays a foundation for the opacity analysis of complex systems.

cs.FL↗

arXiv2023

Supervisory Control of Quantum Discrete Event Systems

Discrete event systems (DES) have been deeply developed and applied in practice, but state complexity in DES still is an important problem to be better solved with innovative methods. With the development of quantum computing and quantum control, a natural problem is to simulate DES by means of quantum computing models and to establish {\it quantum DES} (QDES). The motivation is twofold: on the one hand, QDES have potential applications when DES are simulated and processed by quantum computers, where quantum systems are employed to simulate the evolution of states driven by discrete events, and on the other hand, QDES may have essential advantages over DES concerning state complexity for imitating some practical problems. So, the goal of this paper is to establish a basic framework of QDES by using {\it quantum finite automata} (QFA) as the modelling formalisms, and the supervisory control theorems of QDES are established and proved. Then we present a polynomial-time algorithm to decide whether or not the controllability condition holds. In particular, we construct a number of new examples of QFA to illustrate the supervisory control of QDES and to verify the essential advantages of QDES over classical DES in state complexity.

quant-ph↗