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Quantum state tomography (QST) is a crucial ingredient for almost all aspects of experimental quantum information processing. As an analog of the imaging technique in the quantum settings, QST is born to be a data science problem, where machine learning techniques, noticeably neural networks, have been applied extensively. In this work, we build an integrated all-optical setup for neural network QST, based on an all-optical neural network (AONN). Our AONN is equipped with built-in nonlinear activation function, which is based on electromagnetically induced transparency. Experiment results demonstrate the validity and efficiency of the all-optical setup, indicating that AONN can mitigate the state-preparation-and-measurement error and predict the phase parameter in the quantum state accurately. Given that optical setups are highly desired for future quantum networks, our all-optical setup of integrated AONN-QST may shed light on replenishing the all-optical quantum network with the last brick.
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Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as in terms of the computational time to analyze those measurements. In this paper, we address the problem of analysis speed and flexibility, introducing textit{Neural Adaptive Quantum State Tomography} (NA-QST), a machine learning based algorithm for quantum state tomography that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. Our algorithm is inspired by particle swarm optimization and Bayesian particle-filter based adaptive methods, which we extend and enhance using neural networks. The resampling step, in which a bank of candidate solutions -- particles -- is refined, is in our case learned directly from data, removing the computational bottleneck of standard methods. We successfully replace the Bayesian calculation that requires computational time of $O(mathrm{poly}(n))$ with a learned heuristic whose time complexity empirically scales as $O(log(n))$ with the number of copies measured $n$, while retaining the same reconstruction accuracy. This corresponds to a factor of a million speedup for $10^7$ copies measured. We demonstrate that our algorithm learns to work with basis, symmetric informationally complete (SIC), as well as other types of POVMs. We discuss the value of measurement adaptivity for each POVM type, demonstrating that its effect is significant only for basis POVMs. Our algorithm can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems. It can also adapt to a subset of possible states, a choice of the type of measurement, and other experimental details.
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states, which exhibit dominant eigenstates and thus lend themselves to low-rank approximations. The developed scheme is applicable to any pure-state tomography method, promoting it to mixed-state tomography. Here, we demonstrate it with machine learning-inspired pure-state tomography based on neural-network representations of quantum states. The latter have been shown to efficiently approximate generic classes of complex (pure) states of large quantum systems. We test our method by applying it to experimental data from trapped ion experiments with four to eight qubits.
Continuous-variable quantum information processing through quantum optics offers a promising platform for building the next generation of scalable fault-tolerant information processors. To achieve quantum computational advantages and fault tolerance,
non-Gaussian resources are essential. In this work, we propose and analyze a method to generate a variety of non-Gaussian states using coherent photon subtraction from a two-mode squeezed state followed by photon-number-resolving measurements. The proposed method offers a promising way to generate rotation-symmetric states conventionally used for quantum error correction with binomial codes and truncated Schr{o}dinger cat codes. We consider the deleterious effects of experimental imperfections such as detection inefficiencies and losses in the state engineering protocol. Our method can be readily implemented with current quantum photonic technologies.
We propose and experimentally demonstrate a quantum state tomography protocol that generalizes the Wallentowitz-Vogel-Banaszek-Wodkiewicz point-by-point Wigner function reconstruction. The full density operator of an arbitrary quantum state is efficiently reconstructed in the Fock basis, using semidefinite programming, after interference with a small set of calibrated coherent states. This new protocol is resource- and computationally efficient, is robust against noise, does not rely on approximate state displacements, and ensures the physicality of results.
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.
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