The evaluation of unknown states for a given quantum system is one of the key problems in quantum information processing. The most efficient method of state characterization is quantum state tomography (QST), where the full-density matrices are reconstructed from the experimental measurements or numerical simulations performed on quantum states. The improvement of the computational performance in quantum state tomography and its related problems is a challenging task for modern theoretical physics. The general scheme of computing deals with the input information that goes into a quantum reservoir through a recurrent evolution. After the evolution, the final output is obtained as the linear combination of the readout elements. In our approach, the quantum reservoir is modeled with the Lindbladian equation. The control over performance is made by the coherent coupling parameter between the input quantum state and the reservoir. The control feedback algorithm is represented with the set of Kolesnikov’s target attractor algorithm to drive certain parameters of quantum state tomography, particularly, the outputs for the density matrix. Here we formulate the target attractor feedback in a discrete form to improve the training performance of QST and then develop a basic example of the state tomography for the quantum system of spin 1/2. We conclude by mentioning the basic features of our algorithm and its possible development.
The evaluation of unknown states for a given quantum system is one of the key problems in quantum information processing. The most efficient method of state characterization is quantum state tomography (QST), where the full-density matrices are reconstructed from the experimental measurements or numerical simulations performed on quantum states. The improvement of the computational performance in quantum state tomography and its related problems is a challenging task for modern theoretical physics. The general scheme of computing deals with the input information that goes into a quantum reservoir through a recurrent evolution. After the evolution, the final output is obtained as the linear combination of the readout elements. In our approach, the quantum reservoir is modeled with the Lindbladian equation. The control over performance is made by the coherent coupling parameter between the input quantum state and the reservoir. The control feedback algorithm is represented with the set of Kolesnikov’s target attractor algorithm to drive certain parameters of quantum state tomography, particularly, the outputs for the density matrix. Here we formulate the target attractor feedback in a discrete form to improve the training performance of QST and then develop a basic example of the state tomography for the quantum system of spin 1/2. We conclude by mentioning the basic features of our algorithm and its possible development.
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which requires a vast number of resources. However, tomography for a quantum device with temporal processing, which is fundamentally different from standard tomography, has not been formulated. We develop a practical and approximate tomography method using a recurrent machine learning framework for this intriguing situation. The method is based on repeated quantum interactions between a system called quantum reservoir with a stream of quantum states. Measurement data from the reservoir are connected to a linear readout to train a recurrent relation between quantum channels applied to the input stream. We demonstrate our algorithms for representative quantum learning tasks, followed by the proposal of a quantum memory capacity to evaluate the temporal processing ability of near-term quantum devices.
Quantum state tomography (QST) is a fundamental technique in quantum information science, used to characterize the density matrix of an unknown quantum state. However, traditional QST methods are often computationally intensive, requiring a large number of measurements and sophisticated data analysis techniques. This paper proposes a novel approach utilizing self-organizing neural networks (SONNs) for direct quantum state reconstruction. The core idea is to train a SONN to learn the mapping between experimental measurement data and the corresponding density matrix, thereby bypassing the need for precise control over the quantum system and significantly reducing the computational burden. We detail the architecture of the SONN, the training process, and demonstrate the potential of this method to achieve accurate state reconstruction with fewer measurements. The proposed method offers a promising path towards more efficient and scalable QST, particularly for complex quantum systems.
Abstract Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the number of qubits, rendering experimental implementation and data post-processing arduous even for moderately sized systems. Here, we introduce gradient-descent (GD) algorithms for the post-processing step of QST in discrete- and continuous-variable systems. To ensure physically valid state reconstruction at each iteration step of the algorithm, we use various density-matrix parameterizations: Cholesky decomposition, Stiefel manifold, and projective normalization. These parameterizations have the added benefit of enabling a rank-controlled ansatz, which simplifies reconstruction when there is prior information about the system. We benchmark the performance of our GD-QST techniques against state-of-the-art methods, including constrained convex optimization, conditional generative adversarial networks, and iterative maximum likelihood estimation. Our comparison focuses on time complexity, iteration counts, data requirements, state rank, and robustness against noise. We find that rank-controlled ansatzes in our stochastic mini-batch GD-QST algorithms effectively handle noisy and incomplete data sets, yielding significantly higher reconstruction fidelity than other methods. Simulations achieving full-rank seven-qubit QST in under three minutes on a standard laptop, with 18 GB of RAM and no dedicated GPU, highlight that GD-QST is computationally more efficient and outperforms other techniques in most scenarios, offering a promising avenue for characterizing noisy intermediate-scale quantum devices. Our Python code for GD-QST algorithms is publicly available at github.com/mstorresh/GD-QST .
Quantum state tomography (QST) is a fundamental technique for characterizing the state of a quantum system. However, traditional QST protocols often require a large number of measurements, leading to significant experimental overhead and uncertainties in the reconstructed state. This paper proposes a novel approach to QST that leverages reinforcement learning (RL) to dynamically adapt measurement strategies. The core idea is to train an RL agent to control the parameters of the QST experiment, learning to optimize the measurement process based on feedback from the acquired data. The agent learns to select measurement bases and angles that minimize the uncertainty in the reconstructed quantum state. This adaptive strategy significantly reduces the number of measurements needed compared to traditional QST while maintaining high accuracy. We present a theoretical framework for this approach, outlining the key components and demonstrating its potential for improved QST performance. The proposed method offers a promising direction for enhancing the efficiency and reliability of QST, contributing to the advancement of quantum information processing.
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.
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.