System and method for control

Abstract

A control system comprises a neural-network encoder configured to output a series of latent feature vectors, based on input vectors and based on trainable coefficients, the latent feature vectors having reduced dimensionality with respect to the input vectors. The system further comprises a trainable parameterized quantum processing circuit configured to encode the latent feature vectors into input quantum states, and to process the input quantum states to produce an output control signal for application to the controlled system. The system may further comprise a neural-network decoder configured to transform the latent feature vectors into reconstructed vectors having the same dimensionality as the input vectors, and optimization processing circuitry configured to estimate reconstruction loss metrics, based on the reconstructed vectors, and train coefficients of the neural-network encoder and / or parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics from the controlled system.

Description

[0001] SYSTEM AND METHOD FOR CONTROL

[0002] TECHNICAL FIELD

[0003] The present disclosure is generally related to machine learning for use in control systems, and is more particularly related to control systems based on quantum reinforcement learning.

[0004] BACKGROUND

[0005] Autoencoders (AEs) are a widely used class of classical machine learning models proven to be highly effective in, for example, data compression. The latent space of autoencoders can be used for extraction of relevant low-dimensional features from highdimensional complex problem spaces.

[0006] AEs have been successfully used in reinforcement learning tasks, where the observation space is high dimensional, which means that non-trivial feature extraction is required to enable a reinforcement learning (RL) solution, or for an agent to efficiently solve the problem. See, e.g., S. Lange and M. Riedmiller, "Deep auto-encoder neural networks in reinforcement learning," The 2010 International Joint Conference on Neural Networks (IJCNN), 2010, pp. 1-8, doi: 10.1109 / IJCNN.2010.5596468, and H. van Hoof, N. Chen, M. Karl, R van der Smagt and J. Peters, "Stable reinforcement learning with autoencoders for tactile and visual data," 2016 IEEE / RSJ International Conference on Intelligent Robots and Systems (IROS), 2016, pp. 3928-3934, doi: 10.1109 / IROS.2016.7759578.

[0007] Quantum machine learning (QML) is a rapidly growing field, with the potential to be more efficient and effective than classical machine learning approaches. Quantum reinforcement learning (QRL) is a subfield of quantum machine learning that focuses on developing algorithms for training reinforcement learning models by leveraging quantum computational resources.

[0008] QRL agents have been recently used to solve standard baseline problems in classical control benchmark environments of continuous control problems. See, Daniel Nagy, Zsolt Tabi, Peter Haga, Zsofia Kallus and Zoltan Zimboras, “Photonic Quantum Policy Learning in OpenAI Gym”, preprint: arXiv:2108.12926, (2021).

[0009] There are various problems associated with both classical machine learning models and QML. For example, classical RL solutions need accelerators: RL as applied to real- world, high-dimensional, complex systems cannot learn patterns necessary for control problems without heuristic simplifications of the problem space. On the other hand, current QPUs can only process low-dimensional data: therefore, they cannot currently be used for applications that solve real-world problems of high dimensional problem spaces. Accordingly, improvements to systems employing QML are needed to achieve the goal of applying these systems to real-world problems such as the control of complex mobile telecommunications systems. It is an object of the present disclosure to provide such an improvement.

[0010] SUMMARY

[0011] Specific problems with QRL include that manual feature selection by domain experts used for QRL is very time-consuming and inefficient, and in most cases impossible to realize. In addition, separately trained feature extraction methods are suboptimal for control tasks. Pre-trained autoencoders or algorithmic methods such as principal components analysis (PCA) are often unable to find the best low-dimensional features for a given control problem, as these methods are optimized for compression / embedding and not for the control task itself.

[0012] In the context of controlling a mobile network, such as a 5G system as standardized by members of the 3rd-Generation Partnership Project, a mobile network state descriptor cannot generally be compressed using a simple method, as this state descriptor is formed from a diverse set of data of mixed types - i.e. , of both categorical and real- valued types, which would require separate treatment in a cost function-based definition of optimization.

[0013] We propose an end-to-end hybrid quantum-classical system and a training method for training and inference of QRL agents in classical control tasks of Mobile NWs. The proposed system comprises a set of classical autoencoders as a dimension reduction and feature extraction algorithm, a tunable parametric quantum circuit as an agent for control task, and a classical optimizer algorithm which is jointly optimizing the parameters of both the quantum and the classical part of the system for optimal control decision.

[0014] Embodiments of the techniques, apparatuses, and systems described herein address these problems by implementing a joint training of a hybrid system comprising a classical autoencoder and a quantum agent in the same training loop. Separated autoencoders may be used to process the complex data structure of a typical multidomain state vector in a complex system, such as a mobile network. The described architecture enables quantum agents to be used in cases where the problem's dimensionality would be prohibitively high for previous approaches which do not use autoencoding. In addition, the joint training enables optimal compression with regards to the control problem, rather than to the compression task itself.

[0015] An example embodiment described herein is a control system, comprising a neural- network circuit and a trainable parameterized quantum processing circuit. The neural- network circuit comprises a neural-network encoder, which is configured to receive a series of input vectors of system state features, the system state features comprising measurements and / or parameters of a controlled system, and to output a series of latent feature vectors, based on the series of input vectors and based on trainable coefficients of the neural-network encoder. The latent feature vectors each have a reduced dimensionality, with respect to the input vectors. The trainable parameterized quantum processing circuit is configured to receive the latent feature vectors, to encode each latent feature vector into an input quantum state, and to process the input quantum state to produce an output control signal for application to the controlled system.

[0016] The system described above may, in various embodiments, utilize neural-network coefficients and quantum processing circuit parameters that are jointly optimized, e.g., prior to operation of the control system and / or during the control system’s operation. Thus, in some embodiments and / or instances, the neural-network circuit may further comprise a neural-network decoder configured to transform each of the latent feature vectors into a reconstructed vector having the same dimensionality as the input vectors, and the control system may further comprise optimization processing circuitry configured to estimate reconstruction loss metrics based on the input vectors and reconstructed vectors, and train one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics obtained from the controlled system.

[0017] Other embodiments disclosed herein include methods in a control system comprising a neural-network circuit and a parameterized quantum processing circuit. An example method comprises the step of receiving, at a neural-network encoder embodied in the neural-network circuit, a series of input vectors of system state features, where the system state features comprise measurements and / or parameters of a controlled system. The method further comprises transforming, by the neural-network encoder, the series of input vectors into a series of latent feature vectors, using a plurality of trainable coefficients of the neural-network encoder. The latent feature vectors each have a reduced dimensionality, with respect to the input vectors. The method still further comprises: receiving the latent feature vectors at the parameterized quantum processing circuit; encoding each latent feature vector into an input quantum state, in the quantum processing circuit, using one or more trainable parameters; and processing the input quantum state, in the quantum processing circuit, to produce an output control signal for application to the controlled system.

[0018] Also described in detail herein are methods for training quantum agents jointly in the latent space of a set of classical autoencoders representing a network state efficiently for the given control task, e.g., for the dynamic configuration of mobile networks. The joint training may use an additive reconstruction loss made of the reinforcement learning (RL) cost function value, and the reconstruction losses defined in the AEs handling separately categorical and non-categorical feature vectors. Thus, the present disclosure describes an end-to-end hybrid quantum-classical system for training and inference of quantum reinforcement learning in mobile network control tasks, jointly leveraging near-term quantum resources and classical machine learning methods.

[0019] These techniques, apparatuses and systems are described in detail below, along with variations and a discussion of their advantages.

[0020] BRIEF DESCRIPTION OF THE FIGURES

[0021] Fig. 1 depicts an overview of an environment according to an embodiment of the disclosure

[0022] Fig 2. depicts an example system architecture according to the disclosure

[0023] Fig. 3. shows components of an example trained system according to the disclosure

[0024] Fig. 4 shows a benchmark study of a method according to the disclosure

[0025] Fig. 5 is a flow diagram of a method according to the disclosure

[0026] DETAILED DESCRIPTION

[0027] As briefly discussed above, the systems described herein enable the application of near-term quantum circuits in mobile network control problems by introducing autoencoders that are jointly trained with a quantum agent, to reduce feature space dimensionality and extract problem-specific latent feature variables.

[0028] Figure 1 illustrates an example of an environment 100 in which the system and techniques used herein may be implemented. This environment 100 can be a real-world environment, a testbed, or digital twin of a mobile network with some level of observability suitable for the control task, in various embodiments or instances. A state vector can be created to describe the physical system during some time interval by a feature vector. Actions will change its state, and available problem-specific key performance indicators (KPIs) or other performance metrics for the controlled system can be used as a reward score feedback for the training of the agent. In the example shown in Figure 1 , the example environment includes a mobile network 150, which may be regarded as the controlled system. The techniques described herein, however, are not limited to the control of a mobile network.

[0029] As seen in the figure, a Network (NW) & Service Analytics function 130 receives reports and measurements from a network monitoring function 140, which may in turn receive or otherwise collect and organize these measurements and reports from various components of the network, such as user equipments (UE)s, radio access network (RAN) components, core network components, the IP Multimedia System (IMS), etc. A network management system 160 comprising the AEs 110 and QRL agent 120 may adjust one or more parameters or control operations in the mobile network 150, e.g., using various network and / or radio re-configuration operations.

[0030] Figure 2 shows an example system architecture and data flow for a hybrid quantum- classical system 200, showing the joint training and inference processes of autoencoders (AEs) 110 and quantum reinforcement learning (QRL) agent 120. Each component is explained below. In the figure, inference process steps are depicted as dashed arrows, while the training process also includes the steps shown with solid arrows. Trained machine-language (ML) models of both AEs 110 and QRL agents 120 can be saved into a database for inference and for later use of hot start training or transfer learning between different mobile networks.

[0031] The system includes the following components:

[0032] • Feature separator 210: In some embodiments of the system, categorical and numeric features and are separated, and fed into two separate AEs.

[0033] • Encoders 110: Separate classical neural networks will be used to transform, e.g., the numeric and categorical state feature inputs from a high-dimensional state vector into separate lower-dimensional latent feature vectors. State vectors in this example embodiment are received from a NW & Service Analytics module 220, with these state vectors describing the environment (reports, measurements, etc.).) When trained in a joint training loop with the QRL agent 120, the learned projection of the encoders 110 into their respective latent spaces 230 will create a compressed representation of the network’s state, specifically with regards to the RL task.

[0034] • Decoders 240: Each decoder 240 is a classical neural network which transforms the latent features vector into a reconstructed feature vector of the same dimension as the original feature vector. This is only used in the training phase, but not the inference process.

[0035] • Reconstruction loss calculation 250: a measure of the goodness of input vector reconstruction after decoding of encoded information. For numeric features, this can be implemented as a well-known distance metric like the Euclidean distance of the original and the reconstructed vector, or in case of categorical variables, categorical cross-entropy can be used.

[0036] • RL objective calculation 260: a component to calculate the objective metric that measures the performance of the agent during the training phase. The formula for this metric is dependent on the training algorithm used, e.g., proximal policy optimization (PPO) or deep deterministic policy gradient (DDPG).

[0037] • Quantum Agent 120: a parametric quantum circuit that is running on a quantum computer or a quantum simulator. The architecture of the parametric quantum circuit depends on the specific problem in question and the QPU used. Latent features that come from the encoder are embedded into the initial quantum state in a suitable way, e.g., with angle-embedding or displacement encoding. Running the quantum agent 120 on a QPU or in a simulator, results in a quantum state on which a measurement is applied to obtain the action. When two AEs 110 are used, as in the example shown in Figure 2, both latent variables are encoded into the initial quantum state, with two different suitable encodings, e.g., qubit encodings or qumode encodings, for photonic QPUs. The person skilled in the art may note that the methods of the disclosure may, equally, be implemented in a system comprising a plurality of quantum agents. In a system comprising a plurality of quantum agents, the policy learning may be implemented by either centralized or distributed policy learning.

[0038] • Combined loss calculation 270: A metric is calculated from the RL objective and the reconstruction loss, or losses in case of two AEs. This combined loss is the sum or weighted sum of two or more losses (in case of more than one AE) and is used to calculate updated parameters for each component of the system.

[0039] • Optimizer 280: a classical optimizer which updates all parameters of the encoders, decoders, and quantum agent modules. The new parameters are computed from the combined loss using some common optimizer algorithm like Stochastic Gradient Descent (SGD), (Adam, etc).

[0040] In an additional optional pre-training step, one can replace randomly initialized AE neural networks with ones that were trained for state vector compression separately on a historical dataset. Starting from this compressing representation, the joint training will require fewer training steps for the costly QRL agent but can further compress the state to only keep information necessary for the RL task. This in turn reduces the size requirements for the quantum neural network.

[0041] In some embodiments, for example, the agent performs action on the mobile network for optimal service quality by, e.g., changing configuration settings of antenna tilt. Since the observability of a complex mobile network and the many services run in parallel are not specifically designed for ML tasks, the state information needs to be created by the Network Analytics layer, where raw reports and measurements are collected and correlated or preprocessed otherwise to form a feature vector of dimension of several hundreds or thousands of values. These can be recreated, e.g., every 15 minutes describing the state of the system for a given time interval. Furthermore, the Network Analytics system can provide the Reward feedback for the actions of the previous step in the form of KPIs - e.g., of Downlink throughput - or other performance metrics.

[0042] Figure 3 shows components of an example trained system during inference. When the trained system is used in inference mode, the decoder parts of the AEs are not needed, and only the encoder networks are used together with the quantum agent. The best set of parameters is chosen both for the encoder neural networks and for the agent quantum circuit.

[0043] A comparative analysis has been performed to validate the feasibility and demonstrate the advantages of the systems and methods described herein. In this study, the proposed method was validated through the OpenAI Gym Cart-Pole problem, a standard benchmark for continuous control tasks. A manual feature selection training scenario and the AE-enhanced method described above was implemented. In the case of the Cart-Pole problem, a manual feature selection is possible, since the feature space is only four-dimensional. Furthermore, in the case of Cart-Pole, it is known that a two-dimensional manually selected feature space is suitable for training an agent.

[0044] The method was tested by first training a quantum agent on the manually selected two- dimensional feature space and then training another quantum agent of the same type but with an AE and the full four-dimensional feature input. The latter joint training extracts a two-dimensional latent space for the agent. For training the agents in the OpenAI test environment, the PPO algorithm was used in both cases, and while testing the proposed method, mean-squared error loss was used as reconstruction loss for the AE, which is suitable for numeric feature vectors.

[0045] In Figure 4, the reward score reached by the training of the two scenarios running for 4000 training episodes is shown. The evolution of reward score curves clearly demonstrates that the proposed method outperforms the manual features selection and shows a much faster convergence with less fluctuation. In the proof-of-concept baseline, a reward score of 100 is considered a perfect solution.

[0046] Figure 5 is a process flow diagram illustrating, in general terms, a method for controlling a system using the techniques described herein. It should be understood that the illustrated process is intended to be a generalization of the techniques described above. Accordingly, where there are differences in terminology used to describe these techniques, the terminology used with respect to Figure 5 should be understood, wherever reasonably possible, to at least encompass similar or related terminology used above.

[0047] The illustrated method is implemented in a control system comprising a neural-network circuit and a parameterized quantum processing circuit, and comprises the step of receiving, at a neural-network encoder embodied in the neural-network circuit, a series of input vectors of system state features, where these system state features comprise measurements and / or parameters of a controlled system. This step is shown at block 510. Block 520 illustrates the step of transforming, by the neural-network encoder, the series of input vectors into a series of latent feature vectors. This transforming uses a plurality of trainable coefficients of the neural-network encoder, and the resulting latent feature vectors each have a reduced dimensionality, with respect to the input vectors.

[0048] As shown at blocks 530 and 540, the illustrated method further comprises receiving the latent feature vectors at the parameterized quantum processing circuit and encoding each latent feature vector into an input quantum state, in the quantum processing circuit, using one or more trainable parameters. As shown at block 550, the method still further comprises processing the input quantum state, in the quantum processing circuit, to produce an output control signal for application to the controlled system.

[0049] The illustrated method may be repeated, e.g., at regular intervals and / or as triggered by events in the controlled system and / or changes to the system state features, such that changes in the system state features drive optimized responses by the control system.

[0050] As discussed above, the control system described here may be pre-trained, such that the control system carries out the steps shown at block 510-550 while operating in a so- called inference mode. In some embodiments or instances, the method shown may form part of or be carried out in conjunction with a “training” of the system, i.e., an optimization of the adjustments made by the system. In such embodiments or instances, the neural-network circuit may further comprise a neural-network decoder and optimization processing circuitry, and the method may comprise transforming, in the neural-network decoder, each of the latent feature vectors into a reconstructed vector having the same dimensionality as the input vectors. This is shown at block 560. This is followed, in the optimization circuitry, with the steps of estimating reconstruction loss metrics based on the input vectors and reconstructed vectors and training one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics obtained from the controlled system. This is shown in Figure 5 at block 570. The entire process may be repeated many times to optimize the training of the conventional neural network and the quantum processing circuit. The training may comprise jointly optimizing one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit, based on the reconstruction loss metrics and performance metrics obtained from the controlled system. Note that the controlled system may be a live system or an offline simulation, in various instances and embodiments.

[0051] It will be appreciated that this training process may result in many, a few, or no changes to the coefficients of the neural-network encoder and parameters of the quantum processing circuit, at any given training instance, or “episode,” depending on the state of the controlled system, changes to that state, etc. Thus, it should be understand that “training” one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit may mean selectively adjusting one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, at a plurality of training instances, in such a way that adjustments are made at fewer than all of the training instances, in dependence on the reconstruction loss metrics and performance metrics.

[0052] The illustrated method may be implemented using a combination of continuous-valued and categorical features of the system. Thus, in some embodiments or instances, the neural network circuit may comprise first and second neural-network encoders, with the method comprising transforming, by the first neural-network encoder, vectors of continuous features extracted from system state features into a first series of latent feature vectors and transforming, by the second neural-network encoder, vectors of categorical features extracted from system state features into a second series of latent feature vectors. In some of these embodiments or instances, the method may still further comprise receiving the first and second series of latent feature vectors at the quantum processing circuit and encoding, in the quantum processing circuit, a latent feature vector from each of the first and second series of latent feature vectors to obtain each input quantum state, i.e. , a latent feature vector for the continuous-valued features and another for the categorical features. In some of these embodiments or instances, estimating the reconstruction loss metrics may computing one or more distance metrics and / or one or more categorical distance metrics, such as a categorical cross-entropy metric, based on the input vectors and corresponding reconstructed vectors.

[0053] Any of various optimization algorithms, such as the SGD and Adam optimization algorithms, may be used to jointly optimize the one or more coefficients of the neural- network encoder and / or one more parameters of the quantum processing circuit, in instances or embodiments of the above-described methods. Likewise, while the controlled system may be all or part of a mobile network, in some embodiments or instances, the techniques shown and described here are by no means limited to this application, but may instead be applied to any of a wide variety of complex systems, where system state features of continuous-valued and / or categorical types are available and where performance metrics, such as KPIs, can be obtained.

[0054] Physical embodiments of the techniques described herein may be understood as being control systems, where an example control system according to these embodiments comprises a neural-network circuit, which in turn comprises a neural-network encoder configured to receive a series of input vectors of system state features, the system state features comprising measurements and / or parameters of a controlled system, and to output a series of latent feature vectors, based on the series of input vectors and based on trainable coefficients of the neural-network encoder. As discussed above, the latent feature vectors each have a reduced dimensionality, with respect to the input vectors. The control system further comprises a trainable parameterized quantum processing circuit configured to receive the latent feature vectors, to encode each latent feature vector into an input quantum state, and to process the input quantum state to produce an output control signal for application to the controlled system.

[0055] The neural network circuit may be implemented using any combination of digital hardware and microprocessors, microcontrollers, etc., using, at least in some embodiments, program code stored in memory and retrieved by the microprocessors and / or microcontroller for execution, where the memory may be any one of or combination of random access memory, read-only memory, Flash, etc. Various sorts of quantum processing units or quantum processing circuits have been demonstrated, with variations and improvements of these under continuous development, along with new architectures and implementations. Any of these, or combinations of these, might be used for the quantum processing circuit that forms part of the control systems described herein.

[0056] Referring back to the neural-network circuit, this circuit may in some embodiments or instances implement a neural-network decoder configured to transform each of the latent feature vectors into a reconstructed vector having the same dimensionality as the input vectors. In these embodiments or instances, the control system may further comprise optimization processing circuitry configured to estimate reconstruction loss metrics based on the input vectors and reconstructed vectors, and train one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics obtained from the controlled system. This optimization processing circuitry may again comprise any combination of digital hardware and microprocessors, microcontrollers, etc., using, at least in some embodiments, program code stored in memory and retrieved by the microprocessors and / or microcontroller for execution, where the memory may be any one of or combination of random access memory, readonly memory, Flash, etc. The optimization processing circuitry may share hardware with the neural-network circuitry, in some embodiments, or be distinct, in others.

[0057] As was discussed above, in some embodiments or instances the optimization processing circuitry is configured to jointly optimize one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit, based on the reconstruction loss metrics and performance metrics obtained from the controlled system. More particularly, the optimization processing circuitry may be configured to train one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit by selectively adjusting one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, at a plurality of training instances, in such a way that adjustments are made at fewer than all of the training instances, in dependence on the reconstruction loss metrics and performance metrics.

[0058] As was also discussed above, the optimization processing circuitry may be configured to estimate reconstruction loss metrics by computing one or more distance metrics and / or one or more categorical distance metrics, based on the input vectors and corresponding reconstructed vectors. The one or more categorical distance metrics may comprise at least one categorical cross-entropy metric, for example.

[0059] Again, any of a variety of optimization algorithms may be used, such as the SGD and / or Adam optimization algorithms, to jointly optimize the one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit.

[0060] Control systems may use combinations of continuous-valued and categorical features, in some embodiments. Thus, the neural network circuit may comprise first and second neural-network encoders, the first neural-network encoder being configured to operate on a first vector of continuous features extracted from system state features and output a first series of latent feature vectors, and the second neural-network encoder being configured to operate on categorical features extracted from system state features and output a second series of latent feature vectors. The quantum processing circuit in these embodiments is configured to receive the first and second series of latent feature vectors and to encode a latent feature vector from each of the first and second series of latent feature vectors to obtain each input quantum state, before processing the input quantum states to create or update a control output.

[0061] Note that by saying that the neural network circuit “comprises” certain operational features is meant that the neural network circuit implements these features, e.g., with appropriate programming. A similar meaning applies to discussions of the quantum processing circuit, with the understanding that there are several known hardware implementations today and more under development.

[0062] The techniques, apparatuses, and systems described herein provide several advantages. They can be applied to various types of control tasks and leverage different types of quantum neural network network (QNN) Ansatz or QPU. The application of a classical autoencoder enables the use of quantum circuit-based agents in cases where the dimensionality of feature vectors is beyond the capabilities of quantum devices. By this, the system brings forwards the practical training and inference of RL models on real QPUs - as scaling roadmaps of technology providers plan for slow progress, this can translate into years of practical advantage.

[0063] The proposed joint training of the hybrid system leads to better optimization (i.e. , in control decisions leading to higher KPIs) than other RL models using manual selection of a feature subspace.

[0064] For shorter training processes, an option is available to use pre-trained AEs via transfer learning to be fine-tuned for the given control task rather than implementing cold training. If a pre-trained AE does not exist, but historical data is available in a database, pre-training for compression task of the state vector can create the initial AE with only fine tuning needed in the hybrid training loop.

[0065] For complex feature vectors composed of different data types, such as numeric and categorical data, separate AEs may be used for each specific datatype, with their corresponding cost functions contributing to the joint optimization.

Claims

CLAIMSWhat is claimed is:

1. A control system, comprising: a neural-network circuit comprising a neural-network encoder configured to receive a series of input vectors of system state features, the system state features comprising measurements and / or parameters of a controlled system, and to output a series of latent feature vectors, based on the series of input vectors and based on trainable coefficients of the neural- network encoder, the latent feature vectors each having a reduced dimensionality, with respect to the input vectors; and a trainable parameterized quantum processing circuit configured to receive the latent feature vectors, to encode each latent feature vector into an input quantum state, and to process the input quantum state to produce an output control signal for application to the controlled system.

2. The control system of any one of claims 1-3, wherein the neural-network circuit further comprises a neural-network decoder configured to transform each of the latent feature vectors into a reconstructed vector having the same dimensionality as the input vectors, and wherein the control system further comprises optimization processing circuitry configured to: estimate reconstruction loss metrics based on the input vectors and reconstructed vectors; and train one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics obtained from the controlled system.

3. The control system of claim 2, wherein the optimization processing circuitry is configured to jointly optimize one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit, based on thereconstruction loss metrics and performance metrics obtained from the controlled system.

4. The control system of claim 2 or 3, wherein the optimization processing circuitry is configured to train one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit by selectively adjusting one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, at a plurality of training instances, in such a way that adjustments are made at fewer than all of the training instances, in dependence on the reconstruction loss metrics and performance metrics.

5. The control system of claim 4, wherein the optimization processing circuitry is configured to estimate reconstruction loss metrics by computing one or more distance metrics and / or one or more categorical distance metrics, based on the input vectors and corresponding reconstructed vectors.

6. The control system of claim 5, wherein the one or more categorical distance metrics comprise at least one categorical cross-entropy metric.

7. The control system of any one of claims 2-6, wherein the optimization processing circuitry is configured to use an SGD and / or Adam optimization algorithm to jointly optimize the one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit.

8. The control system of any one claims 1-7, wherein the neural network circuit comprises first and second neural-network encoders, the first neural-network encoder being configured to operate on a first vector of continuous features extracted from system state features and output a first series of latent feature vectors, and the second neural-network encoder being configured to operate on categorical features extracted from system state features and output a second series of latent feature vectors.

9. The control system of claim 8, wherein the quantum processing circuit is configured to receive the first and second series of latent feature vectors and to encode a latent feature vector from each of the first and second series of latent feature vectors to obtain each input quantum state.

10. The control system of any one of claims 1-9, wherein the controlled system comprises at least a portion of a mobile network.11 . A method, in a control system comprising a neural-network circuit and a parameterized quantum processing circuit, the method comprising: receiving, at a neural-network encoder embodied in the neural-network circuit, a series of input vectors of system state features, the system state features comprising measurements and / or parameters of a controlled system; transforming, by the neural-network encoder, the series of input vectors into a series of latent feature vectors, using a plurality of trainable coefficients of the neural-network encoder, the latent feature vectors each having a reduced dimensionality, with respect to the input vectors; receiving the latent feature vectors at the parameterized quantum processing circuit; encoding each latent feature vector into an input quantum state, in the quantum processing circuit, using one or more trainable parameters; and processing the input quantum state, in the quantum processing circuit, to produce an output control signal for application to the controlled system.

12. The method of claim 11 , wherein the neural-network circuit further comprises a neural-network decoder and optimization processing circuitry, and wherein the method comprises: transforming, in the neural-network decoder, each of the latent feature vectors into a reconstructed vector having the same dimensionality as the input vectors; and,in the optimization processing circuitry, estimating reconstruction loss metrics based on the input vectors and reconstructed vectors and training one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, based on the reconstruction loss metrics and based on performance metrics obtained from the controlled system.

13. The method of claim 12, wherein the method comprises, in the optimization circuitry, jointly optimizing one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit, based on the reconstruction loss metrics and performance metrics obtained from the controlled system.

14. The method of claim 12 or 13, wherein said training one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit comprises selectively adjusting one or more coefficients of the neural-network encoder and / or one or more parameters of the quantum processing circuit, at a plurality of training instances, in such a way that adjustments are made at fewer than all of the training instances, in dependence on the reconstruction loss metrics and performance metrics.

15. The method of any one of claims 11-14, wherein the neural network circuit comprises first and second neural-network encoders, and wherein the method comprises: transforming, by the first neural-network encoder, vectors of continuous features extracted from system state features into a first series of latent feature vectors; transforming, by the second neural-network encoder, vectors of categorical features extracted from system state features into a second series of latent feature vectors.

16. The method of claim 15, wherein the method comprises receiving the first and second series of latent feature vectors at the quantum processing circuit and encoding, in the quantum processing circuit, a latent feature vector from each of the first and second series of latent feature vectors to obtain each input quantum state.

17. The method of claim 16, wherein estimating the reconstruction loss metrics comprises computing one or more distance metrics and / or one or more categorical distance metrics, based on the input vectors and corresponding reconstructed vectors.

18. The method of claim 17, wherein the one or more categorical distance metrics comprise at least one categorical cross-entropy metric.

19. The method of claim any one of claims 11-18, wherein the method comprises using an SGD and / or Adam optimization algorithm to jointly optimize the one or more coefficients of the neural-network encoder and / or one more parameters of the quantum processing circuit.

20. The method of any one of claims 11-19, wherein the controlled system comprises at least a portion of a mobile network.

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