Dynamic Programming for Quantum Circuit Optimization with Uncertainty

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Quantum circuit optimization is a crucial step in realizing the full potential of quantum computing. However, the inherent uncertainty in quantum gate fidelities and measurement outcomes presents a significant challenge. Traditional optimization methods often fail to adequately address this probabilistic nature. This paper proposes a novel dynamic programming approach for quantum circuit optimization that explicitly incorporates uncertainty. The algorithm constructs an optimal circuit path by minimizing the expected cost, which accounts for the potential error associated with each gate operation and measurement. This framework allows for a more accurate and robust optimization process, leading to circuits with reduced error and improved performance. The core claim is that dynamic programming can be effectively applied to quantum circuit optimization, acknowledging and utilizing the probabilistic elements. The key mechanism involves a structured, iterative process to evaluate and select the best circuit paths based on a quantified uncertainty model. This approach avoids the limitations of purely deterministic optimization techniques when dealing with quantum systems.

DOI: 10.5281/zenodo.22581767

Related papers

Dynamic Programming for Quantum Circuit Compilation with Uncertainty

Jincheng Zhang

Quantum circuit compilation is a critical step in the process of translating high-level quantum algorithms into executable instructions on quantum hardware. Traditional compilation techniques often rely on deterministic models of gate operations and measurement outcomes, which can lead to suboptimal results and inaccurate performance estimates. This paper introduces a novel dynamic programming approach to quantum circuit compilation that explicitly addresses the inherent uncertainty associated with qubit measurements and gate operations. The algorithm utilizes probabilistic models to represent the likelihood of measurement outcomes and gate errors, optimizing the circuit design for the *expected* performance, considering the statistical nature of quantum computation. The core contribution lies in shifting the focus from worst-case scenarios to expected outcomes, leading to more realistic and potentially more efficient quantum circuit designs. The methodology provides a framework for incorporating uncertainty directly into the compilation process, a crucial step towards achieving robust and reliable quantum computation.

Aug 31, 20260 citations

Dynamic Programming for Quantum Circuit Optimization with Error Modeling

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. However, the inherent noise and decoherence present in quantum systems introduce significant challenges to traditional optimization techniques. This paper proposes a novel approach that leverages dynamic programming (DP) to optimize quantum circuits while explicitly incorporating probabilistic error models. The core idea is to extend the DP table to represent not only the cost (gate count) of minimizing the circuit but also the estimated error probability associated with each sub-circuit. This allows for a more accurate assessment of the trade-off between circuit complexity and fidelity. The algorithm iteratively builds the DP table, considering different circuit decompositions and their corresponding error rates. The resulting optimized quantum circuit minimizes the overall expected error, providing a more robust solution compared to purely gate-count-based optimization. The methodology is presented with detailed formulas and mathematical notation, providing a comprehensive understanding of the approach. This work addresses a key limitation of existing optimization methods by integrating error modeling directly into the dynamic programming framework.

Sep 5, 20260 citations

Dynamic Programming for Probabilistic Circuit Optimization

Jincheng Zhang

Quantum circuit optimization remains a critical challenge in the development of quantum computing. Traditional dynamic programming (DP) methods, while effective for deterministic circuit design, fail to adequately address the inherent probabilistic nature of quantum operations. This paper proposes a novel approach that extends DP algorithms by explicitly incorporating probabilistic models representing uncertainties in quantum gate operations and qubit measurements. The core idea is to leverage Monte Carlo simulations to estimate expected costs and rewards within the DP framework. This allows for a more realistic and potentially efficient solution to the circuit optimization problem, considering the statistical fluctuations that are fundamental to quantum computing. We demonstrate the feasibility of this method conceptually, outlining the key components and algorithmic steps. Further research and implementation will be necessary to fully realize the potential of this approach.

Sep 7, 20260 citations

Probabilistic Programming for Quantum Circuit Optimization

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. However, traditional optimization methods often struggle to account for the inherent uncertainties present in quantum systems, such as noise, decoherence, and incomplete knowledge of circuit parameters. This paper proposes a novel approach leveraging probabilistic programming to address this challenge. We demonstrate how probabilistic programming languages can be used to model and reason about these uncertainties, leading to more robust and efficient optimization strategies. The core concept involves defining a probabilistic model of the quantum circuit optimization problem, incorporating parameters with associated probability distributions. This allows for the exploration of the solution space in a statistically informed manner, ultimately leading to better-optimized quantum circuits. The developed framework offers a pathway for more reliable and adaptive optimization, particularly relevant for near-term quantum devices where noise and errors are unavoidable.

Aug 31, 20260 citations

Dynamic Programming for Quantum Circuit Optimization with Error Mitigation

Jincheng Zhang

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. Traditional optimization methods often struggle to effectively balance circuit depth, gate complexity, and the inherent noise associated with quantum systems. This paper proposes a novel dynamic programming (DP) framework that integrates circuit optimization with error mitigation strategies. The core idea is to recursively explore all possible circuit transformations, incorporating error mitigation techniques as constraints within the DP search space. This approach allows for simultaneous consideration of both gate operations and error mitigation, leading to optimized circuits with reduced depth and enhanced fidelity. The algorithm is formulated as a state transition function, where each state represents a partial circuit transformation, and the objective is to minimize a cost function that combines circuit depth and an error mitigation metric. We demonstrate the feasibility and potential efficiency of this framework through a conceptual analysis and outline the key components of the implementation. Future work will focus on developing a fully optimized implementation and exploring the framework's applicability to various quantum algorithms.

Sep 3, 20260 citations

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, 20260 citations