Quantum State Vector Reconstruction via Bayesian Inference

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Quantum state vector reconstruction is a fundamental problem in quantum information theory, crucial for tasks like quantum state tomography and quantum error correction. Traditional methods often struggle with noisy measurements and lack a principled framework for uncertainty quantification. This paper introduces a novel algorithm, Quantum State Vector Reconstruction via Bayesian Inference, that leverages Bayesian inference to reconstruct a quantum state vector from a set of measurements, enhancing accuracy and offering a more robust approach compared to existing methods. We detail the core mechanism, emphasizing the integration of Bayesian estimation for uncertainty quantification and refinement of the reconstruction process. The algorithm incorporates a probabilistic approach to estimate the state vector distribution, improving reconstruction by incorporating uncertainty estimates directly into the reconstruction process. This results in a more reliable and accurate state vector reconstruction, particularly when dealing with noisy measurements. This work addresses the limitations of conventional methods by providing a principled Bayesian framework for state vector reconstruction, offering a significant advancement in this field.

DOI: 10.5281/zenodo.22265125

Related papers

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 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 Bayesian Inference for Uncertainty Quantification in Machine Learning

Jincheng Zhang

Quantum Bayesian Inference (QBI) offers a promising approach to quantifying uncertainty in machine learning models, particularly in the face of adversarial examples. This paper introduces a novel framework for QBI that leverages quantum mechanics to enhance model robustness. We demonstrate improvements in uncertainty quantification through a rigorous analysis of the impact of quantum noise on model predictions. The core mechanism involves utilizing quantum state tomography to construct a quantum representation of the model's uncertainty, which is then used to generate robust predictions. We also explore the potential of QBI to mitigate adversarial examples through a novel defense mechanism based on quantum entanglement. This work presents a significant advancement in uncertainty quantification techniques, addressing limitations of existing methods and opening new avenues for reliable machine learning.

Sep 2, 20260 citations

Quantum-Inspired Bayesian Inference for Uncertainty Quantification

Jincheng Zhang

This paper introduces a novel approach to Bayesian inference, termed Quantum-Inspired Bayesian Inference (QIBI), which leverages principles from quantum mechanics to address the limitations of classical Bayesian methods in complex, high-dimensional scenarios. Traditional Bayesian inference often struggles with computational cost and scalability, particularly when dealing with distributions exhibiting significant uncertainty. QIBI addresses this by employing an "amplitude" representation for probability distributions, inspired by the concept of superposition, and a quantum-inspired sampling strategy designed to efficiently explore the entire probability space. The core idea is to treat probability amplitudes as analogous to quantum wave amplitudes, allowing for interference effects that can guide the sampling process towards regions of higher probability. This approach aims to provide significant speedups and potentially improve the accuracy of uncertainty quantification compared to standard Bayesian methods. The paper details the theoretical framework, outlines the proposed QIBI algorithm, and discusses potential applications.

Sep 6, 20260 citations

Quantum-Inspired Bayesian Inference with Superposition

Jincheng Zhang

This paper introduces a novel approach to Bayesian inference that draws inspiration from the principles of quantum mechanics, specifically superposition and decoherence. Traditional Bayesian inference often struggles with exploring the vast and complex inference landscape, leading to slow convergence and potential inaccuracies. Our method utilizes a quantum-inspired representation of probability distributions as quantum states, enabling the simultaneous consideration of multiple hypotheses within a superposition. Controlled decoherence protocols are then employed to guide the inference process, effectively selecting the most probable hypothesis while minimizing computational cost. We demonstrate, through theoretical analysis and mathematical formulations, that this approach can dramatically improve the exploration of the inference landscape, resulting in faster convergence and enhanced accuracy compared to conventional Bayesian methods. The core of this work lies in the mapping of Bayesian model parameters to quantum states and the implementation of controlled decoherence, offering a fundamentally new perspective on probabilistic reasoning. This research aims to provide a framework for tackling complex Bayesian problems efficiently and effectively, potentially unlocking new possibilities in various fields, including machine learning, statistics, and scientific discovery.

Sep 1, 20260 citations

Quantum Bayesian Inference for Statistical Machine Learning

Jincheng Zhang

Quantum Bayesian Inference (QBI) presents a novel approach to statistical machine learning, utilizing the principles of quantum mechanics to enhance the accuracy and robustness of models, particularly when dealing with high-dimensional data and complex Bayesian frameworks. This paper introduces a quantum algorithm designed to efficiently estimate the posterior distribution of parameters in a Bayesian model through the application of quantum superposition and entanglement, aiming to overcome the limitations of classical methods. We explore the potential of this paradigm shift to deliver exponential speedups in inference tasks, offering a compelling path towards more accurate and reliable statistical machine learning algorithms.

Aug 29, 20260 citations