Probabilistic Programming for Quantum State Tomography

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Quantum state tomography (QST) is a crucial technique for characterizing quantum states, vital for verifying quantum device performance and implementing quantum information processing. However, traditional QST methods are notoriously computationally demanding, requiring extensive experimental data acquisition and subsequent processing, often leading to high resource consumption. This work presents a novel framework for QST utilizing probabilistic programming. The core idea is to model the quantum state as a probability distribution and employ Bayesian inference, coupled with variational methods, to efficiently infer the density matrix from limited measurement data. We demonstrate the efficacy of this approach, showcasing its potential to significantly reduce experimental costs and improve the accuracy of QST. The framework's automation and optimization capabilities represent a substantial advancement in the field, paving the way for more accessible and efficient quantum state characterization.

DOI: 10.5281/zenodo.22315096

Related papers

Quantum State Tomography with Limited Measurements

Jincheng Zhang

Quantum state tomography (QST) is a crucial technique for characterizing quantum states, forming the bedrock of quantum information processing and quantum metrology. However, traditional QST relies on a large number of measurements, making it computationally expensive and experimentally demanding. This work addresses this challenge by proposing a novel algorithm that integrates compressed sensing (CS) and Bayesian inference to achieve accurate quantum state reconstruction from limited measurement data. The core idea is to exploit the inherent sparsity of quantum states and leverage CS principles to significantly reduce the required measurement count. The algorithm utilizes a sparse dictionary learned from prior knowledge of the quantum state and employs Bayesian inference to estimate the state parameters, providing a robust and efficient reconstruction process. The results demonstrate the feasibility and effectiveness of this approach, offering a pathway towards more practical and accessible QST methods. Key mathematical formulations are presented, including the Bayesian inference framework and the CS reconstruction process.

Sep 5, 20260 citations

Quantum State Tomography via Variational Quantum Algorithms

Jincheng Zhang

Quantum state tomography (QST) is a fundamental technique in quantum information science, aiming to reconstruct the density matrix of an unknown quantum state from experimental measurements. However, traditional QST methods often suffer from significant computational demands and are highly susceptible to measurement noise, hindering their practical application, particularly with near-term quantum computers. This work proposes a novel approach to QST utilizing variational quantum algorithms (VQAs). VQAs iteratively optimize a parameterized quantum circuit to minimize a cost function related to the fidelity between the desired state and the state predicted by the circuit. This approach dramatically reduces the number of required measurements and offers the potential for achieving high-fidelity state reconstruction with lower quantum resource requirements. We detail the theoretical framework, outlining the core algorithms and mathematical formulations. The key advantage lies in the ability to learn the state directly, mitigating the limitations of traditional methods. We explore the optimization landscape and discuss strategies for improving convergence and robustness. The results demonstrate a promising path toward scalable and robust QST on quantum devices.

Aug 29, 20260 citations

Dynamic Programming for Quantum State Tomography with Entangled Photon Sources

Jincheng Zhang

Quantum state tomography (QST) is a fundamental procedure in quantum information science, enabling the precise characterization of quantum states. Traditional QST methods often require a prohibitive number of measurements, particularly for complex quantum states, significantly limiting their practical application. This work presents a novel approach to QST leveraging dynamic programming. The core idea is to iteratively refine a quantum state estimate based on measurement data, minimizing the total number of measurements needed to achieve a desired level of accuracy. The algorithm constructs a dynamic programming table, storing partial state estimates and their associated probabilities, allowing for efficient exploration of the state space. We demonstrate the efficacy of this approach through theoretical analysis and illustrate its potential advantages over conventional methods. The key contribution lies in the algorithm's ability to adaptively adjust the measurement strategy, focusing on regions of the state space with the highest uncertainty, leading to a substantial reduction in measurement requirements. The performance of the algorithm is discussed in terms of computational complexity and accuracy achieved.

Sep 5, 20260 citations

Quantum-Enhanced Bayesian Inference for Uncertainty Quantification

Jincheng Zhang

Quantum-enhanced Bayesian inference offers a promising approach to address the computational challenges associated with uncertainty quantification, particularly in situations demanding high accuracy and speed. This paper explores the design and implementation of a quantum algorithm, quantum state tomography, to enhance Bayesian inference, aiming to mitigate the inherent cost of traditional methods. We detail the theoretical framework underpinning this approach, highlighting its potential to significantly improve reliability and speed. The core claim centers on leveraging quantum state tomography to achieve a more precise estimate of the system state, thereby bolstering the accuracy of Bayesian inference. This work represents a novel investigation into the application of quantum mechanics to Bayesian inference, with the potential to deliver substantial improvements in computational efficiency and robustness.

Sep 1, 20260 citations

Quantum State Tomography via Compressed Sensing

Jincheng Zhang

Quantum state tomography (QST) is a crucial technique for characterizing the state of quantum systems. However, traditional QST requires a large number of measurements, leading to significant experimental overhead in terms of time, resources, and data acquisition. This work proposes a novel approach to QST by leveraging compressed sensing (CS) techniques. CS allows for accurate reconstruction of the quantum state from a significantly reduced set of measurements, thereby mitigating the experimental burden. We employ sparsity regularization, a key component of CS, to minimize the number of measurements needed. The theoretical framework and the underlying principles are presented, focusing on the mathematical formulation of the problem and the optimization strategies involved. This method offers a pathway to more efficient and cost-effective QST, particularly for complex quantum states or when limited experimental resources are available. We demonstrate the potential of this approach through a detailed mathematical analysis.

Sep 5, 20260 citations

Fractal Information Theory for Quantum State Tomography

Jincheng Zhang

Quantum state tomography (QST) is a fundamental technique for characterizing the state of a quantum system. However, traditional QST protocols often suffer from significant measurement complexity and resource demands, particularly when dealing with high-dimensional quantum states. This work proposes a novel approach to QST that leverages the inherent fractal structure observed in measurement outcomes. We introduce a framework utilizing fractal dimension analysis to guide the acquisition of more efficient and accurate tomography protocols. The core idea is to adaptively refine measurement strategies based on the fractal characteristics revealed in the measurement data. This approach aims to reduce the overall number of measurements required while simultaneously improving the fidelity of the reconstructed quantum state. We demonstrate the theoretical feasibility and potential benefits of this methodology, offering a promising direction for advancing QST techniques.

Aug 31, 20260 citations