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

Physical Review A

Monte Carlo graph search for quantum circuit optimization

Bodo Rosenhahn, Tobias J. Osborne

Published Dec 19, 2023• 15 citations
Publisher

Abstract

The authors introduce a search algorithm aimed at optimizing the arrangement of quantum gates, leveraging different sampling techniques to dynamically grow a graph that represents potential quantum circuits. They demonstrate efficacy in reducing the quantum gate count, both theoretically and numerically, albeit with acknowledged computational challenges as the graph expands.

DOI
10.1103/physreva.108.062615

Related papers

Monte Carlo Graph Search for Quantum Circuit Optimization

Bodo Rosenhahn, Tobias J. Osborne

The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of quantum gates to achieve a desired quantum algorithm for solving a specific task. This is especially challenging for quantum machine learning and signal processing. For example, it is not trivial to design a quantum Fourier transform from scratch. This work proposes a quantum architecture search algorithm which is based on a Monte Carlo graph search and measures of importance sampling. It is applicable to the optimization of gate order, both for discrete gates, as well as gates containing continuous variables. Several numerical experiments demonstrate the applicability of the proposed method for the automatic discovery of quantum circuits.

arXiv:2307.07353•Jul 14, 2023•1 citation

Dynamic Programming for Quantum Circuit Optimization

Jincheng Zhang

Quantum circuit optimization is a critical challenge in the development and execution of quantum algorithms. The exponential growth in the complexity of quantum circuits necessitates efficient optimization techniques. This paper proposes a novel approach utilizing dynamic programming to systematically explore and minimize the resources (gate count and circuit depth) required for a given quantum circuit transformation. The core mechanism involves constructing a dynamic programming table to store the optimal solutions for subproblems, leveraging the overlapping subproblems inherent in the circuit transformation process. The algorithm systematically builds solutions from smaller circuit fragments, ultimately arriving at the globally optimal transformation. The potential scalability of this approach, combined with its ability to directly address the combinatorial nature of circuit optimization, offers a promising avenue for advancing quantum computing. This work provides a theoretical framework and outlines a detailed algorithm for dynamic programming-based quantum circuit optimization.

•Aug 28, 2026•0 citations

Relational Quantum Circuit Synthesis via Topological Optimization

Jincheng Zhang

Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.

•Sep 3, 2026•0 citations

Topological Factor-Based Quantum Circuit Optimization

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. Current optimization techniques often rely on heuristics and approximations, leading to suboptimal results and significant overhead in terms of quantum gate count. This research proposes a novel approach to quantum circuit optimization based on the identification and manipulation of topological factors within quantum circuits. We define a new algorithm that leverages these topological factors to guide circuit restructuring and reduction, aiming to minimize the number of quantum gates required for a given quantum algorithm. The core idea is that circuits with inherent topological symmetries can be significantly simplified. This work explores the theoretical framework and provides a foundational understanding of this approach, outlining a potential pathway toward more efficient and robust quantum algorithms. The proposed method offers a fundamentally different perspective on circuit optimization, moving beyond traditional gate-level approaches and embracing the underlying topological structure of quantum computations. The primary goal is to demonstrate a reduction in quantum gate count without compromising the fidelity of the final computation.

•Sep 3, 2026•0 citations

Dynamic Circuit Synthesis for Quantum Computing based on Graph Representation

Jincheng Zhang

Quantum circuit synthesis is a critical step in quantum computing, aiming to translate a logical quantum circuit into an efficient physical implementation. Traditional methods often suffer from inefficiency and a lack of adaptability, particularly when dealing with varying input data. This paper introduces a novel approach to quantum circuit synthesis that leverages graph representation and dynamic adaptation. The core idea is to represent quantum circuits as graphs, allowing the system to analyze and modify the circuit structure in real-time based on the input data. This dynamic adaptation minimizes gate count and execution time, offering significant improvements over static synthesis techniques. The presented framework provides a foundation for more flexible and efficient quantum computation.

•Sep 3, 2026•0 citations

Exact and Practical Pattern Matching for Quantum Circuit Optimization

Raban Iten, Romain Moyard, Tony Metger +2 more

Quantum computations are typically performed as a sequence of basic operations, called quantum gates. Different gate sequences, called quantum circuits, can implement the same overall quantum computation. Since every additional quantum gate takes time and introduces noise into the system, it is important to find the smallest possible quantum circuit that implements a given computation, especially for near-term quantum devices that can execute only a limited number of quantum gates before noise renders the computation useless. An important building block for many quantum circuit optimization techniques is pattern matching: given a large and small quantum circuit, we would like to find all maximal matches of the small circuit, called a pattern , in the large circuit, considering pairwise commutation of quantum gates. In this work, we present the first classical algorithm for pattern matching that provably finds all maximal matches and is efficient enough to be practical for circuit sizes typical for near-term devices. We demonstrate numerically 1 that combining our algorithm with known pattern-matching-based circuit optimization techniques reduces the gate count of a random quantum circuit by ∼ 30% and can further improve practically relevant quantum circuits that were already optimized with state-of-the-art techniques.

arXiv:1909.05270•ACM Transactions on Quantum Computing•Jan 22, 2022•45 citations
The authors introduce a search algorithm aimed at optimizing the arrangement of quantum gates, leveraging different sampling techniques to dynamically grow a graph that represents potential quantum circuits. They demonstrate efficacy in reducing the quantum gate count, both theoretically and numerically, albeit with acknowledged computational challenges as the graph expands.
The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of quantum gates to achieve a desired quantum algorithm for solving a specific task. This is especially challenging for quantum machine learning and signal processing. For example, it is not trivial to design a quantum Fourier transform from scratch. This work proposes a quantum architecture search algorithm which is based on a Monte Carlo graph search and measures of importance sampling. It is applicable to the optimization of gate order, both for discrete gates, as well as gates containing continuous variables. Several numerical experiments demonstrate the applicability of the proposed method for the automatic discovery of quantum circuits.
Quantum circuit optimization is a critical challenge in the development and execution of quantum algorithms. The exponential growth in the complexity of quantum circuits necessitates efficient optimization techniques. This paper proposes a novel approach utilizing dynamic programming to systematically explore and minimize the resources (gate count and circuit depth) required for a given quantum circuit transformation. The core mechanism involves constructing a dynamic programming table to store the optimal solutions for subproblems, leveraging the overlapping subproblems inherent in the circuit transformation process. The algorithm systematically builds solutions from smaller circuit fragments, ultimately arriving at the globally optimal transformation. The potential scalability of this approach, combined with its ability to directly address the combinatorial nature of circuit optimization, offers a promising avenue for advancing quantum computing. This work provides a theoretical framework and outlines a detailed algorithm for dynamic programming-based quantum circuit optimization.
Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.
Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. Current optimization techniques often rely on heuristics and approximations, leading to suboptimal results and significant overhead in terms of quantum gate count. This research proposes a novel approach to quantum circuit optimization based on the identification and manipulation of topological factors within quantum circuits. We define a new algorithm that leverages these topological factors to guide circuit restructuring and reduction, aiming to minimize the number of quantum gates required for a given quantum algorithm. The core idea is that circuits with inherent topological symmetries can be significantly simplified. This work explores the theoretical framework and provides a foundational understanding of this approach, outlining a potential pathway toward more efficient and robust quantum algorithms. The proposed method offers a fundamentally different perspective on circuit optimization, moving beyond traditional gate-level approaches and embracing the underlying topological structure of quantum computations. The primary goal is to demonstrate a reduction in quantum gate count without compromising the fidelity of the final computation.
Quantum circuit synthesis is a critical step in quantum computing, aiming to translate a logical quantum circuit into an efficient physical implementation. Traditional methods often suffer from inefficiency and a lack of adaptability, particularly when dealing with varying input data. This paper introduces a novel approach to quantum circuit synthesis that leverages graph representation and dynamic adaptation. The core idea is to represent quantum circuits as graphs, allowing the system to analyze and modify the circuit structure in real-time based on the input data. This dynamic adaptation minimizes gate count and execution time, offering significant improvements over static synthesis techniques. The presented framework provides a foundation for more flexible and efficient quantum computation.
Quantum computations are typically performed as a sequence of basic operations, called quantum gates. Different gate sequences, called quantum circuits, can implement the same overall quantum computation. Since every additional quantum gate takes time and introduces noise into the system, it is important to find the smallest possible quantum circuit that implements a given computation, especially for near-term quantum devices that can execute only a limited number of quantum gates before noise renders the computation useless. An important building block for many quantum circuit optimization techniques is pattern matching: given a large and small quantum circuit, we would like to find all maximal matches of the small circuit, called a pattern , in the large circuit, considering pairwise commutation of quantum gates. In this work, we present the first classical algorithm for pattern matching that provably finds all maximal matches and is efficient enough to be practical for circuit sizes typical for near-term devices. We demonstrate numerically 1 that combining our algorithm with known pattern-matching-based circuit optimization techniques reduces the gate count of a random quantum circuit by ∼ 30% and can further improve practically relevant quantum circuits that were already optimized with state-of-the-art techniques.