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.
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.
A distinctive feature of Quantum Reservoir Computing (QRC) is the ability to directly embed quantum input states into the reservoir dynamics. However, the resulting output is fundamentally linear for a single input state, preventing QRC from naturally computing nonlinear functionals such as purity or entropy. We overcome this limitation with a quantum-classical hybrid architecture combining a qubit quantum reservoir with a classical echo state network (ESN), allowing both nonlinear functional approximation and effective temporal processing. We systematically study performance under two information regimes: full-tomography and partial information (single-axis measurements), with the latter demonstrating that the hybrid system outperforms its standalone components in both linear and nonlinear tasks due to the enhanced information retrieval provided by the quantum reservoir. Building on these results, we apply an online monitoring protocol that explicitly accounts for measurement back-action and finite measurement ensembles, enabling a realistic assessment of performance under experimental conditions. These results establish hybrid quantum-classical reservoir computing (HRC) architectures as a practical and scalable route for enhanced quantum machine learning on near-term qubit hardware.
Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous-variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introduce a method for detecting the quantum capacity of continuous-variable communication channels and memories without performing a full process tomography. Our method works in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can change dynamically under the control of a malicious adversary. The method is experimentally friendly and can be implemented using only finitely squeezed states and homodyne measurements.
Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced feedback-based quantum reservoir systems, which process temporal information with comparatively fewer components and enable real-time computation while preserving the input history. Motivated by their promising empirical performance, in this work, we study the approximation capabilities of feedback-based quantum reservoir computing. More specifically, we are concerned with recurrent quantum neural networks, which are quantum analogues of classical recurrent neural networks. Our results show that regular state-space systems can be approximated using quantum recurrent neural networks without the curse of dimensionality and with the number of qubits only growing logarithmically in the reciprocal of the prescribed approximation accuracy. Notably, our analysis demonstrates that quantum recurrent neural networks are universal with linear readouts, making them both powerful and experimentally accessible. These results pave the way for practical and theoretically grounded quantum reservoir computing with real-time processing capabilities.
Over the last decade, researchers have studied the interplay between quantum computing and classical machine learning algorithms. However, measurements often disturb or destroy quantum states, requiring multiple repetitions of data processing to estimate observable values. In particular, this prevents online (real-time, single-shot) processing of temporal data as measurements are commonly performed during intermediate stages. Recently, it was proposed to sidestep this issue by focusing on tasks with quantum output, eliminating the need for detectors. Inspired by reservoir computers, a model was proposed where only a subset of the internal parameters are trained while keeping the others fixed at random values. Here, we also process quantum time series, but we do so using a Recurrent Gaussian Quantum Network (RGQN) of which all internal interactions can be trained. As expected, this increased flexibility yields higher performance in benchmark tasks. Building on this, we show that the RGQN can tackle two quantum communication tasks, while also removing some hardware restrictions of the currently available methods. First, our approach is more resource efficient to enhance the transmission rate of quantum channels that experience certain memory effects. Second, it can counteract similar memory effects if they are unwanted, a task that could previously only be solved when redundantly encoded input signals could be provided. Finally, we run a small-scale version of the last task on Xanadu's photonic processor Borealis.
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.
Over the last decade, researchers have studied the synergy between quantum computing (QC) and classical machine learning (ML) algorithms. However, measurements in QC often disturb or destroy quantum states, requiring multiple repetitions of data processing to estimate observable values. In particular, this prevents online (i.e., real-time, single-shot) processing of temporal data as measurements are commonly performed during intermediate stages. Recently, it was proposed to sidestep this issue by focusing on tasks with quantum output, thereby removing the need for detectors. Inspired by reservoir computers, a model was proposed where only a subset of the internal parameters are optimized while keeping the others fixed at random values. Here, we also process quantum time series, but we do so using a quantum optical recurrent neural network (QORNN) of which all internal interactions can be trained. As expected, this approach yields higher performance, as long as training the QORNN is feasible. We further show that our model can enhance the transmission rate of quantum channels that experience certain memory effects. Moreover, it can counteract similar memory effects if they are unwanted, a task that could previously only be solved when redundantly encoded input signals were available. Finally, we run a small-scale version of this last task on the photonic processor Borealis, demonstrating that our QORNN can be constructed using currently existing hardware.