Quantum State Tomography for Hardware Verification of Quantum Computers

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, traditionally employed in research laboratories with highly controlled environments. However, the burgeoning field of quantum computing faces the significant challenge of deploying and verifying quantum hardware in the presence of noise and decoherence, characteristics inherent in current Noisy Intermediate-Scale Quantum (NISQ) devices. This paper proposes an adapted QST algorithm designed to overcome these limitations. The core idea is to systematically reconstruct the density matrix of a qubit or a small quantum system using a series of carefully designed measurements. We address the impact of noise by incorporating error mitigation strategies within the reconstruction process. The algorithm's performance is evaluated through theoretical analysis and conceptual implementation, highlighting its potential to provide a practical and efficient method for hardware verification of NISQ computers. This work establishes a novel approach for characterizing and debugging NISQ hardware, a critical step toward realizing the full potential of quantum computation.

DOI: 10.5281/zenodo.22460078

Related papers

Quantum State Tomography with Measurement Device Independent Quantum Computing

Jincheng Zhang

Quantum state tomography (QST) is a critical technique for characterizing the state of quantum systems, particularly in the context of quantum computing. Traditional QST protocols rely heavily on precise knowledge of the measurement devices used, introducing significant vulnerabilities to systematic errors and device imperfections. This paper proposes a novel measurement device-independent (MDI) quantum state tomography protocol designed specifically for multi-qubit systems. The core principle of this approach is the strategic utilization of entanglement to minimize the impact of device-specific biases, thereby achieving a more robust and accurate reconstruction of the quantum state. The protocol involves a carefully designed series of measurements performed by multiple, potentially imperfect, measurement devices. Through analyzing the correlations generated by these measurements, we can, with a high degree of certainty, deduce the underlying quantum state without requiring perfect knowledge of each individual device. This MDI QST method represents a significant advancement in overcoming the limitations of conventional QST, paving the way for more reliable and scalable quantum state characterization in complex quantum computing architectures. The theoretical framework and key equations are presented, demonstrating the feasibility and advantages of this approach.

Sep 5, 20260 citations

Hyperdimensional Computing for Quantum State Tomography

Jincheng Zhang

Quantum state tomography (QST) is a fundamental technique for characterizing quantum systems, but it often suffers from significant experimental challenges, including high measurement complexity and resource demands. This paper explores the potential of hyperdimensional computing (HDC) as a viable alternative to traditional QST. HDC leverages high-dimensional vectors to represent and manipulate quantum states, allowing for the development of algorithms that exploit inherent correlations to reconstruct quantum state information with reduced measurement requirements. The core claim is that HDC offers a potentially efficient and scalable approach to QST. This work details the theoretical framework, outlining key algorithms and highlighting the advantages of utilizing HDC for quantum state characterization. The focus is on demonstrating the feasibility of this approach through conceptual design, emphasizing the reduced complexity compared to conventional QST methods. We propose a framework for representing quantum states within HDC vectors and present a simplified reconstruction algorithm.

Aug 28, 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

Convergence of a Reconstructed Density Matrix to a Pure State Using the Maximal Entropy Approach

Rishabh Gupta, Raphael David Levine, Sabre Kais

Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than 1000-qubits by the end of 2023, efficient validation techniques are also being developed for testing quantum processing on these devices. The characterization of a quantum state is done by experimental measurements through the process called quantum state tomography (QST) which scales exponentially with the size of the system. However, QST performed using incomplete measurements is aptly suited for characterizing these quantum technologies especially with the current nature of noisy intermediate-scale quantum (NISQ) devices where not all mean measurements are available with high fidelity. We, hereby, propose an alternative approach to QST for the complete reconstruction of the density matrix of a quantum system in a pure state for any number of qubits by applying the maximal entropy formalism on the pairwise combinations of the known mean measurements. This approach provides the best estimate of the target state when we know the complete set of observables, which is the case of convergence of the reconstructed density matrix to a pure state. Our goal is to provide a practical inference of a quantum system in a pure state that can find its applications in the field of quantum error mitigation on a real quantum computer that we intend to investigate further.

arXiv:2107.01191The Journal of Physical Chemistry AAug 19, 202116 citations

Probabilistic Programming for Quantum State Tomography

Jincheng Zhang

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.

Sep 5, 20260 citations

Quantum State Tomography with Entangled Photon Sources

Jincheng Zhang

Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, crucial for validating quantum technologies. However, traditional QST methods often suffer from limitations in measurement efficiency and accuracy, particularly when dealing with complex quantum systems. This work presents an advanced approach to QST utilizing entangled photon sources and a meticulously designed measurement strategy. The core of this method lies in exploiting the correlations inherent in entangled photon pairs to significantly enhance the reconstruction process. We detail a novel scheme that minimizes measurement errors and maximizes the information extracted from each measurement, leading to a substantial improvement in both the accuracy and resolution of the reconstructed quantum state. The theoretical framework outlines the key equations and algorithms used for state reconstruction, focusing on a practical implementation. The results presented suggest a pathway towards more robust and reliable QST, paving the way for more accurate characterization of quantum systems and the development of advanced quantum applications.

Aug 28, 20260 citations