Abstract Quantum state tomography is one of the core techniques in quantum information science, aiming to reconstruct the density matrix of an unknown quantum state from measurement data. To address the limitations of conventional quantum state reconstruction methods in terms of noise resistance and computational efficiency, this work proposes an innovative Residual-Convolutional Quantum Denoising Autoencoder model (RC-QDAE). The results demonstrate that the model can reconstruct physical density matrices with fidelities comparable to those achieved by traditional full-data methods while requiring only 80% of the tomographic measurement data, thereby significantly alleviating the dependence on measurement resources in large-scale quantum system characterization. In three-qubit systems, the reconstruction speed of the proposed model achieves an improvement of three orders of magnitude over the maximum likelihood estimation method, effectively overcoming the excessive computational overhead inherent to traditional approaches. Moreover, the model incorporates a joint training mechanism with multiple typical noise types during the training phase, exhibiting stronger robustness when processing cross-noise data. Further evaluations show that under different noise intensities, the model consistently produces density matrices with higher fidelities than those obtained by conventional methods, highlighting its superior noise resistance and generalization capability.
Abstract Quantum state tomography is one of the core techniques in quantum information science, aiming to reconstruct the density matrix of an unknown quantum state from measurement data. To address the limitations of conventional quantum state reconstruction methods in terms of noise resistance and computational efficiency, this work proposes an innovative Residual-Convolutional Quantum Denoising Autoencoder model (RC-QDAE). The results demonstrate that the model can reconstruct physical density matrices with fidelities comparable to those achieved by traditional full-data methods while requiring only 80% of the tomographic measurement data, thereby significantly alleviating the dependence on measurement resources in large-scale quantum system characterization. In three-qubit systems, the reconstruction speed of the proposed model achieves an improvement of three orders of magnitude over the maximum likelihood estimation method, effectively overcoming the excessive computational overhead inherent to traditional approaches. Moreover, the model incorporates a joint training mechanism with multiple typical noise types during the training phase, exhibiting stronger robustness when processing cross-noise data. Further evaluations show that under different noise intensities, the model consistently produces density matrices with higher fidelities than those obtained by conventional methods, highlighting its superior noise resistance and generalization capability.
Quantum state tomography (QST) is the gold standard for estimating the unknown state of quantum systems but suffers from the longstanding problem of exponentially growing measurements. Recent deep learning approaches alleviate the problem by training neural networks in a data-driven manner without theoretical convergence guarantees. They lack reliability in tomography quality and are restricted by retraining when generalized to extensive quantum systems with varying realizations in different environments. To address this issue, we propose the first generalized deep learning method for QST, named HD-QST, that leverages hybrid denoising priors with well-established convergence guarantees to fit extensive quantum states and environments. Hybrid denoising priors are achieved with the convex combination of analytic low-rank denoiser and neural network-based smooth denoiser dynamically determined via reinforcement learning. We demonstrate in theory that, when characterizing a quantum system, HD-QST guarantees a geometric convergence rate under the relaxed condition that the true density matrix is the fixed point of any one denoiser rather than the shared fixed point of multiple denoisers. Extensive experiments show that, compared with existing methods, HD-QST consistently obtains superior fidelity for pure and mixed quantum states in both single-device simulations and cross-device applications. Remarkably, it achieves state-of-the-art fidelity in QST of real-world W states by trapped ions and precise evaluation and comparison on cross-device QST on IBM quantum computers.
In this paper, we propose a method for denoising experimental density matrices that combines standard quantum state tomography with an attention-based neural network architecture. The algorithm learns the noise from the data itself, without knowledge of its sources. Firstly, we show how the proposed protocol can improve the averaged fidelity of reconstruction over linear inversion and maximum likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. Next, we demonstrate its use for out-of-distribution data in realistic scenarios. In particular, we consider squeezed states of few spins in the presence of depolarizing noise and measurement/calibration errors and certify its metrologically useful entanglement content. The protocol introduced here targets experiments involving few degrees of freedom and afflicted by a significant amount of unspecified noise. These include NISQ devices and platforms such as trapped ions or photonic qudits. Published by the American Physical Society 2024
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 noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and complex syndrome decoding, we propose a machine learning approach that directly reconstructs clean quantum states from noisy density matrices without additional qubits. We formulate quantum noise reduction as a supervised learning problem using a convolutional neural network (CNN) autoencoder architecture with a novel fidelity-aware composite loss function. Our method is trained and evaluated on a comprehensive synthetic dataset of 10,000 density matrices derived from random 5-qubit quantum circuits, encompassing five noise types (depolarizing, amplitude damping, phase damping, bit-flip, and mixed noise) across four intensity levels (0.05-0.20). The CNN successfully reconstructs quantum states across all noise conditions, achieving an average fidelity improvement from 0.298 to 0.774 (Δ = 0.476). Notably, the model demonstrates superior performance on complex mixed noise scenarios and higher noise intensities, with mixed noise showing the highest corrected fidelity (0.807) and improvement (0.567). The approach effectively preserves both diagonal elements (populations) and off-diagonal elements (quantum coherences), making it suitable for entanglement-dependent quantum algorithms. While phase damping presents fundamental information-theoretic limitations, our results suggest that CNN-based density matrix reconstruction offers a promising, resource-efficient alternative to traditional quantum error correction for NISQ-era devices. This data-driven approach could enable practical quantum advantage with fewer physical qubits than conventional error correction schemes require.
Abstract Quantum compressed sensing is a fundamental technique for tomographic reconstruction of low-rank density matrices in informationally incomplete scenarios. However, when the available measurement data is insufficient, standard compressed sensing, like other algorithmic estimators such as maximum-likelihood, can yield imprecise or noisy estimates. To mitigate this, we propose a deep neural network-based post-processing to enhance the initial reconstruction. By treating the compressed sensing-estimated quantum state as a noisy input, the network performs a supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate the effectiveness of our method through numerical experiments. Additionally, we explore iterative application of the inference process to further enhance performance, and we analyze the network’s generalization ability by testing its performance on states and noise models not seen during training.
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.