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Differentiable Quantum Circuit Simulator

Jincheng Zhang

Published Aug 29, 2026• 0 citations
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Abstract

This paper presents a novel approach to simulating quantum circuits with differentiability, enabling gradient-based optimization for quantum algorithms. The core of the method lies in combining the accuracy of quantum circuit Monte Carlo simulation with the efficiency of automatic differentiation. We introduce a framework where the quantum circuit's evolution is simulated using Monte Carlo techniques, and the resulting expectation values are computed using automatic differentiation. This allows us to calculate gradients with respect to the circuit's parameters, which can then be used with standard optimization algorithms to refine the circuit's design. The key innovation is the seamless integration of these two techniques, offering a pathway to directly optimize quantum circuits for improved performance. The presented methodology provides a foundation for exploring advanced quantum algorithms and improving their efficiency through gradient-based approaches.

DOI
10.5281/zenodo.22156685

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This paper introduces a novel approach to optimizing quantum circuits by directly calculating and applying gradients. Traditional quantum algorithm optimization relies heavily on simulating the quantum circuit on classical computers, which is computationally expensive and limits the scalability of these algorithms. Our work proposes a framework for differentiable quantum circuit optimization, treating quantum circuits as differentiable functions and employing gradient-based optimization techniques. We outline a methodology for computing gradients of the expectation values of quantum circuits with respect to their adjustable parameters. This allows for the direct optimization of quantum circuits using algorithms such as gradient descent, potentially leading to significant improvements in the efficiency and accuracy of quantum algorithms. The core contribution lies in providing a mathematically rigorous foundation for this differentiable approach, paving the way for automated quantum algorithm design and enhancement. The presented method offers a viable alternative to classical simulation, addressing a key bottleneck in the practical implementation of quantum algorithms.
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Simulating the evolution of quantum circuits is a computationally intensive task, fundamentally limited by the need to explore the exponentially large Hilbert space associated with quantum systems. This work introduces a novel approach utilizing probabilistic programming to efficiently model and simulate quantum circuit dynamics. The core idea involves representing quantum circuit operations as probabilistic functions, enabling the use of Monte Carlo methods for estimating circuit evolution with significantly reduced computational overhead. This approach provides a flexible and scalable framework for exploring complex quantum systems, particularly those where traditional deterministic simulation methods become intractable. The method's effectiveness is demonstrated through theoretical analysis and a conceptual outline of implementation, highlighting potential benefits and future research directions. Key mathematical concepts employed include probability theory, Markov chains, and Monte Carlo integration. The primary goal is to offer a practical alternative to standard quantum simulation techniques, particularly for scenarios requiring approximate solutions or exploration of large parameter spaces.
We develop a backpropagation algorithm for evaluating parameter gradients in quantum circuits using Pauli propagation simulation. The method has computational complexity comparable to that of standard sparse Pauli simulation techniques, while producing gradients whose accuracy is of the same order as the corresponding observable expectation values. By exploiting the reversibility of quantum circuits, the algorithm reduces the memory cost by a factor of O(nparam)\mathcal{O}(n_\text{param})O(nparam​) compared with conventional reverse-mode automatic differentiation, where nparamn_\text{param}nparam​ denotes the number of parameters in the circuit. Compared with finite difference methods, the algorithm is O(nparam)\mathcal{O}(n_\text{param})O(nparam​) more efficient in function evaluations. These features enable efficient and accurate classical optimization of quantum circuits for applications such as state preparation and time-evolution compression, while also allowing operator-complexity measures such as the operator stabilizer Rényi entropy to be monitored and regularized during optimization. We demonstrate the method by optimizing low-energy state-preparation circuits for transverse-field Ising models in one, two, and three dimensions and for the three-dimensional Heisenberg model, and by compressing two-dimensional time-evolution circuits.
This paper introduces a novel approach to quantum circuit optimization based on adaptive parameter adjustment. Traditional optimization methods often rely on static parameters, struggling with complex and non-linear circuits. Our algorithm dynamically adjusts circuit parameters through a simulated computational process, enabling automated optimization and improved circuit performance. The core mechanism involves learning a mapping between circuit characteristics and resulting computations, allowing for continuous parameter refinement. This adaptive strategy is expected to significantly enhance the efficiency and robustness of quantum circuit design and execution.
This paper presents a novel methodology for optimizing quantum circuit design utilizing topological optimization techniques. The core idea revolves around representing quantum circuits as topological networks and employing topological optimization algorithms to refine their structure. This approach aims to minimize the number of quantum gates required, thereby enhancing the efficiency and scalability of quantum computation. The research explores the potential of this method to significantly reduce circuit complexity and improve overall performance. The primary contribution lies in the application of topological optimization to the inherently complex domain of quantum circuit design, offering a potentially transformative approach to quantum computing. Mathematical formulations and key concepts are presented to illustrate the method's principles and demonstrate its feasibility.