The development of practical quantum algorithms hinges critically on the ability to efficiently manage and compress quantum states. Noisy Intermediate-Scale Quantum (NISQ) computers, characterized by limited qubit counts and inherent noise, exacerbate this challenge. This paper proposes a novel quantum state compression technique utilizing tensor decomposition and variational quantum algorithms to minimize qubit requirements while mitigating error accumulation. The core idea involves transforming a complex quantum state into a lower-rank tensor representation, subsequently optimized using a variational quantum algorithm. This approach aims to capture the essential information within the original state, reducing computational overhead and enhancing the feasibility of running quantum algorithms on NISQ devices. We outline the theoretical framework, detailing the mathematical formulation of the compression process, including the tensor representation, variational optimization, and error correction strategies. The paper explores the key parameters influencing the compression ratio and error rates, ultimately demonstrating the potential of this technique to unlock the computational power of NISQ computers.
The development of practical quantum algorithms hinges critically on the ability to efficiently manage and compress quantum states. Noisy Intermediate-Scale Quantum (NISQ) computers, characterized by limited qubit counts and inherent noise, exacerbate this challenge. This paper proposes a novel quantum state compression technique utilizing tensor decomposition and variational quantum algorithms to minimize qubit requirements while mitigating error accumulation. The core idea involves transforming a complex quantum state into a lower-rank tensor representation, subsequently optimized using a variational quantum algorithm. This approach aims to capture the essential information within the original state, reducing computational overhead and enhancing the feasibility of running quantum algorithms on NISQ devices. We outline the theoretical framework, detailing the mathematical formulation of the compression process, including the tensor representation, variational optimization, and error correction strategies. The paper explores the key parameters influencing the compression ratio and error rates, ultimately demonstrating the potential of this technique to unlock the computational power of NISQ computers.
Variational quantum algorithms (VQAs) can potentially solve practical problems using contemporary Noisy Intermediate Scale Quantum (NISQ) computers. VQAs find near-optimal solutions in the presence of qubit errors by classically optimizing a loss function computed by parameterized quantum circuits. However, developing and testing VQAs is challenging due to the limited availability of quantum hardware, their high error rates, and the significant overhead of classical simulations. Furthermore, VQA researchers must pick the right initialization for circuit parameters, utilize suitable classical optimizer configurations, and deploy appropriate error mitigation methods. Unfortunately, these tasks are done in an ad-hoc manner today, as there are no software tools to configure and tune the VQA hyperparameters.
Variational quantum algorithms (VQAs) have emerged as a promising candidate for realizing quantum advantage in machine learning and optimization tasks on noisy intermediate-scale quantum (NISQ) devices. Despite significant theoretical promise, the practical impact of VQAs is constrained by the exponential growth in computational resources required for classical simulation, the onset of barren plateaus in parameterized landscapes, and the inherent difficulties of scaling classical optimization routines to circuits with many qubits and layers. Addressing these intertwined challenges is essential for both advancing quantum algorithm development and extracting actionable physical insights from modern quantum hardware.This dissertation develops, analyzes, and validates an efficient framework based on approximate tensor ring decompositions for the classical simulation, training, and benchmarking of variational quantum circuits and eigensolvers. The first component of this work formalizes the representation of quantum states and gates within a cyclic tensor ring structure, enabling the compression of parameterized quantum circuits to linear scaling in both qubit number and circuit depth, while preserving essential quantum correlations and entanglement structure. Gate operations are efficiently approximated via truncated singular value decomposition, and novel algorithms for forward propagation and gradient-based training in the tensor ring domain are developed. These methodological advances are systematically benchmarked on standard supervised learning tasks, including Iris and MNIST datasets, and compared to conventional statevector and matrix product state baselines, resulting in competitive accuracy and orders-of-magnitude reductions in simulation cost. Extending this framework, the dissertation also introduces a scalable method for gradient evaluation in variational quantum eigensolvers (VQE) using the approximate tensor ring representation. This approach enables the simulation and training of large circuits for combinatorial optimization problems, supporting practical qubit counts and circuit depths inaccessible to traditional simulation methods. Detailed experiments on the Maximum-Cut optimization problem demonstrate both the computational efficiency and robustness of the tensor ring framework in nontrivial optimization landscapes.Collectively, the results establish approximate tensor ring decomposition as a versatile and powerful framework for advancing quantum machine learning and discrete optimization, supporting both pre-deployment benchmarking on classical hardware and algorithm design for next-generation quantum devices. This work provides a foundation for the further exploration of scalable quantum-classical hybrid algorithms, with implications for quantum simulation, optimization, and beyond.
This paper presents a novel approach to information compression leveraging quantum state reorganization. The core idea is to exploit the inherent correlations within quantum states to achieve compression rates surpassing those attainable by conventional classical methods. This method utilizes quantum entanglement and quantum state reorganization techniques to encode information across multiple qubits. By intelligently manipulating these quantum correlations, we demonstrate a potential for significantly enhanced compression efficiency. The theoretical framework is presented, outlining the key principles and mathematical formulations underpinning this approach. We introduce a new algorithm based on iterative state reorganization, aiming to minimize the quantum state representation while preserving the maximum amount of information. The success of this method hinges on the ability to identify and exploit redundant or correlated quantum states, a process we formalize with mathematical models. The presented framework offers a promising direction for future research in quantum information processing and compression.
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.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
This paper explores a novel approach to high-dimensional data compression by leveraging concepts from quantum mechanics, specifically entanglement and superposition, within the framework of tensor decomposition. Traditional tensor decomposition methods, while effective for dimensionality reduction and feature extraction, often struggle with the computational complexity inherent in large-scale datasets. Our approach introduces a modified tensor decomposition algorithm guided by quantum-inspired principles, aiming to enhance compression efficiency and potentially improve representation accuracy. The core idea is to mimic the correlations observed in quantum entanglement to inform the iterative process of tensor factorization. We outline the theoretical foundations, detail the proposed algorithm, and discuss the potential benefits and challenges of this hybrid approach. The primary contribution lies in the integration of quantum-inspired concepts into a practical tensor decomposition method, opening new avenues for data compression in high-dimensional scenarios.