System and method for selecting optimal actions using a quantum computer

Abstract

To provide a quantum computation system, a method, and a program for predicting an optimum action in a complex multi-step decision problem.SOLUTION: A quantum computation system 20 for determining an optimum action on the basis of a current state comprises: first computation qubits; second computation qubits; first and second variational quantum circuits 26 and 28 including a plurality of quantum gates acting on the first computation qubits and the second computation qubits, respectively. The plurality of quantum gates each include variational quantum gates and encoding gates for modifying a state of the computation qubits. The encoding gates encode first and second input feature vectors 30 and 32 in the first and second computation qubits, respectively. The quantum gates of the second variational quantum circuit do not act on the first computation qubits. The quantum computation system comprises: a coherent interaction circuit 34 for entangling quantum states of the first and second computation qubits and a measurement portion 36 for determining an output feature vector indicating the optimum action.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention is in the field of quantum computing. More precisely, the present invention relates to the use of quantum computing to predict the optimal behavior of an agent faced with a multi-stage decision problem. [Background technology]

[0002] Natural disasters such as earthquakes can have devastating effects, including loss of life and property damage. Emergency evacuation procedures are critical in such scenarios, and optimizing these procedures is essential to saving lives. One of the most common modes of transportation during emergency evacuations is by car, and it is important to ensure that the routes these vehicles take are safe and efficient.

[0003] While reliable algorithms exist for navigating the graph of nodes that encode a map, the task of finding an optimal path becomes challenging even for state-of-the-art algorithms when dynamically changing conditions are introduced. Specifically, in the case of natural disasters, not only is traffic affected locally through, for example, closed roads and local traffic congestion, but efficient routing may also be affected through the occurrence of traffic congestion as part of ongoing evacuation efforts.

[0004] Quantum computers provide a platform for controllable quantum mechanical systems whose states and interactions can be controlled to perform computations. Computation is realized through the deterministic evolution of controllable quantum mechanical systems, e.g., qubits, as quantum analogs of classical bits, whose states can be measured to determine the outcome of the computation.

[0005] Control operations on these qubits are called quantum gates. Quantum gates can act coherently on qubits, e.g., to cause a change in the state of a single qubit (so-called single-qubit gates) and to act on multiple qubits (so-called multi-qubit gates), e.g., to entangle the states of multiple qubits and any combination thereof. For example, a single-qubit gate may cause a rotation of the electron's spin state by a selectable value, e.g., π / 2. Multi-qubit gates may act coherently on two or more qubits, such as a coherent CNOT operation on the states of two qubits. Multiple quantum gates can be applied to qubits in a quantum computer in parallel or in sequence to perform a computation. Finally, the states of the qubits may be repeatedly measured after applying a sequence of quantum gates to determine the probability for each possible outcome of the computation.

[0006] However, the superposition / entangled states of quantum mechanical systems are inherently volatile (e.g., subject to decoherence), and control and measurement of these systems are subject to fidelity margins that currently limit state-of-the-art quantum computers in both the number of controllable quantum mechanical systems (qubits) and the number of control operations (quantum gates) that can be successively performed.

[0007] Despite these drawbacks, there are promising applications for quantum processors available in the near future, namely noisy intermediate-scale quantum (NISQ) devices, such as variational quantum algorithms. In variational quantum algorithms, the behavior of quantum gates is parameterized in terms of variational parameters, which may be systematically varied with the aid of classical computing resources, similar to machine learning. By varying the variational parameters to extremize a cost function that attributes a cost to the output of a variational quantum circuit relative to the optimal solution, the output of a variational quantum circuit can be "trained" to provide optimal solutions to unseen problems. Quantum entanglement between different qubits may provide access to a large internal state space, providing a "quantum advantage."

[0008] Non-Patent Document 1 discloses a general algorithm for determining an optimal path through a graph of nodes and edges. [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] Giacomo Nannicini and Leo Liberti.(“Shortest paths on dynamic graphs.International Transactions in Operational Research”,15(5):551-563,2008) Summary of the Invention [Problem to be solved by the invention]

[0010] Traditional optimization methods rely on classical algorithms and may not be able to handle the complexity of large-scale problems, such as optimizing emergency evacuation plans. Furthermore, these algorithms generally rely on having complete knowledge of the entire problem landscape and dynamics to make accurate predictions. [Means for solving the problem]

[0011] In view of this state of the art, it is an object of the present invention to provide an improved system for predicting optimal behavior when faced with complex multi-stage decision problems, particularly based on a (local) subset of information about the problem.

[0012] This object is solved by a method and a system according to the independent claims. The dependent claims relate to preferred embodiments.

[0013] According to a first aspect, the present invention relates to a quantum computing system for determining an optimal action in a multi-step decision problem based on a current state. The quantum computing system includes a first qubit register including a first computation qubit, a second qubit register including a second computation qubit, a first variational quantum circuit including a plurality of quantum gates operating on the first computation qubit, and a second variational quantum circuit including a plurality of quantum gates operating on the second computation qubit. The plurality of quantum gates in the first variational quantum circuit and the second variational quantum circuit each include a variational quantum gate and an encoding gate for modifying the states of the first computation qubit and the second computation qubit, respectively, and the parameterized operation of the variational quantum gate on the qubit register qubits is parameterized according to an associated variational parameter. The encoding gate is configured to encode a first input feature vector and a second input feature vector in the quantum states of the first computation qubit and the second computation qubit, respectively, and the quantum gate of the second variational quantum circuit does not operate on the first computation qubit. The system further comprises a coherent interaction quantum circuit, the coherent interaction quantum circuit comprising a plurality of multi-qubit gates for entangling quantum states of a first computation qubit and a second computation qubit acted upon by a first variational quantum circuit and a second variational quantum circuit, respectively; and a measurement portion for determining an output feature vector indicative of optimal operation by measuring the quantum states of one or both of the first computation qubit and the second computation qubit.

[0014] In contrast to current approaches to variational quantum circuits, the first and second variational quantum circuits may operate independently on different sets of qubits, such as to process the first and second computational qubits separately based on their respective variational parameters. A quantum gate in the second variational quantum circuit may not operate on the first computational qubit, and a quantum gate in the first variational quantum circuit may not operate on the second computational qubit. A coherent interaction circuit then entangles the states of the first and second computational qubits, and the resulting entangled quantum state may be processed and measured for decisions and optimal operation. Separation of the first and second variational quantum circuits may enable efficient training and processing of information related to local and global information, with the first and second input feature vectors preferably being used to encode different dynamics of a multi-stage decision problem. For example, the first input feature vector may encode local information into the first computational qubit, while the second input feature vector may encode global information into the second computational qubit.

[0015] In a preferred embodiment, the first input feature vector is based on the current state and the second input feature vector is based on scenario information valid for multiple different states of the multi-stage decision problem.

[0016] The current state may encode local information and may be valid only for a given stage of the multi-stage decision problem, such as valid for one node in a graph of interconnected nodes. Scenario information may encode information that may affect several states of the multi-stage decision problem, particularly information that may affect multiple nodes in the graph of interconnected nodes underlying the multi-stage decision problem and / or be valid for multiple stages of the multi-stage decision problem. For example, scenario information may encode information about a perturbation to the multi-stage decision problem, such as the root cause and / or origin of the perturbation, e.g., the spatial origin of an earthquake, the reported location of a terrorist attack, or similar spatial information.

[0017] The information in the first and second input feature vectors is encoded in a variational quantum circuit based on the data re-upload circuit, the first and second variational quantum circuits each comprising a layer of variational quantum gates and a layer of encoding gates, which may be applied alternately to respective computation qubits.

[0018] Information in the first input feature vector and / or the second input feature vector may be encoded across multiple layers of encoding gates, pairs of encoding gates separated by layers of variational quantum gates, and encoding of values ​​of the input feature vectors may be repeated in different layers of encoding gates. Repeated encoding of values ​​of the input feature vectors across multiple layers of encoding gates may mimic data re-uploading and increase the order of an internal fitting function to the hypothesized mechanism by the quantum computing system. Additionally or alternatively, values ​​of a large input feature vector may be separated into input feature sub-vectors that may be encoded across multiple layers of encoding gates, and a layer of encoding gates may encode one of the input feature sub-vectors.

[0019] In a preferred embodiment, the scenario information is a constant or smooth function over the sequence of stages of the multi-stage decision problem.

[0020] For example, the scenario information may provide spatial information related to the perturbation, e.g., the origin of a traffic perturbation, and may include amplitude information about the perturbation, such as the intensity of the earthquake, the severity of the damage, and / or the size of the affected area.

[0021] In some embodiments, a first variational quantum circuit may process a first computation qubit based on local information encoded in the current state, and a second variational quantum circuit may independently process scenario information encoded in the second computation qubit. The resulting quantum states may be entangled such that measurements of the resulting states may search for optimal behavior based on the current state given perturbations encoded in the scenario information. The decoupling of the first and second variational quantum circuits enables the variational quantum circuits to effectively generalize the scenario information, facilitating convergence of the training algorithm.

[0022] In a preferred embodiment, a multi-stage decision problem is defined on a graph of interconnected nodes, and the multi-stage decision problem is based on selecting a next node based on a current node.

[0023] The multi-step decision problem may be navigation to a target destination node based on a node-by-node progression of current states. The current state may be based on the current node, adjacent edge information, and / or properties of adjacent nodes. Additionally, the current state may include contextual information for the current state, which may relate to real-world properties that may not be represented by a graph of interconnected nodes. For example, the contextual information may include spatial coordinates of the agent and / or task context, such as the coordinates of the start and end nodes of a navigation task.

[0024] In a preferred embodiment, the current state includes information about the current node, and the scenario information is independent of the current node.

[0025] The current state may encode local information of the current node, such as neighboring nodes, edge weights, centrality information, and spatial information about the current position, start position, and target position. The scenario information may be the location of an earthquake.

[0026] In a preferred embodiment, the current state and / or scenario information changes based on the amount of time elapsed and / or the number of steps taken to solve a multi-step decision problem.

[0027] For example, the current state may be based on dynamic information, such as edge weights that are dynamically updated based on elapsed time and / or number of steps taken. In some embodiments, the dynamic information that drives changes in the current state based on elapsed time and / or number of steps taken affects multiple nodes, which may cause the current state to be underestimated as the current node. In some embodiments, the elapsed time from the start of the perturbation is part of the input data. The system may be trained to take dynamic information into account based on a training set of optimal routes in a dynamically changing problem environment. For example, the evolution of conditions in a multi-step decision problem, such as graph edge weights in a graph navigation problem, may be updated according to a simulation of the perturbation.

[0028] In a preferred embodiment, the multi-stage decision problem is a navigation problem, where the optimal action is the optimal direction of travel on a map characterized by intersections interconnected by edges.

[0029] In an earthquake evacuation scenario, edge weights may increase near the epicenter and near potential exits where traffic congestion naturally converges (e.g., based on the occurrence of traffic congestion as part of ongoing evacuation dynamics), and a corresponding dynamic graph may be simulated. For training purposes, multiple dynamic evacuation scenarios may be simulated, e.g., based on different starting nodes, epicenters, and exit conditions to generate a training set. The system may then be trained on multiple evacuation scenarios. For example, a modified navigation algorithm may be responsible for node-by-node navigation, and graph information (e.g., edge weights) may be updated after each stage determined by the navigation algorithm based on earthquake simulations by the simulation algorithm. The system may then be trained to select the optimal node based on the current state of the multi-stage decision problem for evacuation in the dynamic scenario, with a classical heuristic routing algorithm acting as a supervisor in a supervised learning scheme.

[0030] In a preferred embodiment, the scenario information encodes information about traffic perturbations, in particular about the spatial origin of the traffic perturbations, and the multi-stage decision problem relates to evacuation routing taking the traffic perturbations into account.

[0031] The scenario information may encode earthquake epicenter coordinates and / or earthquake intensity that may modify the optimal action taken by the agent in a dynamically changing evacuation scenario. The scenario information may be smaller than the information related to the current state, and therefore the number of second computational qubits may be smaller than the number of first computational qubits.

[0032] In a preferred embodiment, the quantum computing system includes a first number of first computation qubits and a second number of second computation qubits, the first and second numbers being different.

[0033] For example, the second number may be less than the first number.

[0034] The coherent interaction circuit can entangle the quantum state of the first computation qubit, such as to increase the quantum state space available for any further computations of the first computation qubit, based on the action of the second variational quantum circuit on the second computation qubit.

[0035] In a preferred embodiment, the system further comprises a third variational quantum circuit, which operates on the output quantum state of the coherent interaction quantum circuit.

[0036] The third variational quantum circuit may process the entangled states of the first and second computation qubits to generate an output state for determining an optimal operation. The third variational quantum circuit may operate on all or a portion of the first and second computation qubits. In some embodiments, the number of qubits operated on by the quantum gates of the third variational quantum circuit is less than the sum of the first and second numbers. When the third variational quantum circuit operates on a subset of the first and second computation qubits, the information in the quantum states produced by the first and second variational quantum circuits is further condensed, which may improve the convergence of the variational quantum circuit towards an optimal combination of variational parameters for the task of ascribing optimal labels to inputs provided as the first and second input feature vectors to different sets of computation qubits.

[0037] In a preferred embodiment, the variational parameters are trained based on a training algorithm for predicting a selected action of a multi-stage decision-making algorithm based on a current state, and the variational parameters are trained based in particular on a navigation algorithm for navigating a graph of nodes, and the optimal action is based on a predicted next node for optimally navigating the graph of nodes.

[0038] The first input feature vector may encode information about the current state, such as a current node corresponding to the agent's current state. The second input feature vector may encode perturbation information indicating edge weight variations for multiple nodes in the graph of nodes. The optimal action may be a label indicating a predicted next node for navigating to a target (destination) node, and the target node may be indicated in the first input feature vector or the second input feature vector.

[0039] In a preferred embodiment, the current state includes neighboring node information for each neighboring node, the neighboring node information including one or more information fields selected from the group of: current node coordinates, destination node coordinates, start node coordinates, edge weight information indicating travel time between the current node and the neighboring node, distance information regarding the Euclidean distance between the neighboring node and the current node, edge centrality information regarding the neighboring node, and cosine norm information based on the coordinates of the current node, the neighboring node, and the destination node.

[0040] The current node coordinates may encode the spatial location of the node on a map that may be abstracted by a graph of nodes. The destination node coordinates may encode the spatial location of each neighboring node on the map, and the start and end node coordinates may encode the spatial location of the start and target navigation goal, respectively. Edge weight information may be provided for each neighboring node to indicate, for example, the travel time to each node option of the neighboring node, and edge centrality information may encode the number of edges connected to each neighboring node. The cosine norm information may indicate directional information related to whether a change from the current node to one of the neighboring nodes is associated with a movement away from the target navigation goal or tangentially toward the target navigation goal. For example, the directional information may be based on the angle between and / or the scalar product between the vector between the current node and the neighboring node and the vector between the current node and the end node associated with the target navigation goal. Specifically, the cosine distance may be defined as follows:

[0041]

number

[0042] Here, for node p, exit, and adjacent node q, A and B are A=(q x -p x ,q y -p y ), and B=(exit x -p x ,exit y -p y ) can be defined as

[0043] The Euclidean distance information may be based on the separation distance between the current node and the neighboring nodes.

[0044] The information about neighboring nodes may further include betweenness centrality information. Betweenness centrality is a measure of graph centrality based on shortest paths, and represents, for each node, the number of these shortest paths that pass through the edges. A node with high betweenness centrality means that it is strategically placed along the shortest paths between other nodes and has a significant impact on the connectivity of the graph.

[0045] In the training data, information about neighboring nodes may be strengthened by switching the order of neighboring nodes in each input feature vector, e.g., to promote corresponding symmetries in handling information about multiple neighboring nodes to the variational quantum circuit.

[0046] According to a second aspect, the present invention relates to a hybrid quantum computing system comprising the quantum computing system according to the first aspect. The system further comprises a first machine learning model implemented on classical hardware, the first machine learning model configured to process a first input feature vector and / or a second input feature vector to obtain an output feature vector. The hybrid quantum computing system further comprises a combination module configured to combine the output feature vector of the first machine learning model with the output feature vector of the measurement portion and determine an output state indicative of optimal operation based on the combination parameters. The variational parameters, the machine learning parameters, and the combination parameters are obtained based on a common training algorithm, and the variational parameters, the machine learning parameters, and the combination parameters are iteratively updated together to improve prediction of optimal operation.

[0047] The inventors have found that combining a classical machine learning model implemented on classical hardware, which may process input feature vectors based on binary values ​​of 0 and 1, with a quantum computing system according to a first aspect improves labeling of input feature vectors for a trained task, and that the quantum variational circuit configuration conforms to a global aspect of optimal selection of optimal behavior, and that the first machine learning model may be susceptible to deviations from the global aspect of optimal selection as part of optimally solving a multi-stage decision problem. The joint solution of the multi-stage decision problem relies on joint training of the first machine learning model and the quantum computing system, and although the individual outputs of the quantum computing system and the machine learning model may not exhibit optimal behavior by themselves, trained combinations of their respective output feature vectors may be derived from intermediate results to predict optimal behavior. The combination of output feature vectors may be a linear combination of output feature vectors or a nonlinear combination of output feature vectors, for example, based on the first machine learning model and the second machine learning model processing the concatenated output feature vectors of the quantum computing system.

[0048] In a preferred embodiment, the combination module comprises a second machine learning module for combining the output feature vector of the first machine learning model with the measurement portion of the quantum computing system.

[0049] Before combining the outputs of the first sub-model and the second sub-model to obtain an output feature vector of the first machine learning model, the first machine learning model may mimic the structure of a quantum computing system based on providing the first and second sub-models for processing the first and second feature vectors individually, respectively.

[0050] In a preferred embodiment, the first machine learning model comprises a first sub-model and a second sub-model for processing the first feature vector and the second feature vector, respectively, and further comprises a feature-based modulation layer, wherein the feature-based modulation layer operates on the output of the first sub-model, and the weights and / or biases of the feature-based modulation layer are modulated based on the output of the second sub-model.

[0051] The outputs of the first sub-model and the second sub-model may be combined using a third sub-model, for example using an artificial neural network that receives the combined output of the first sub-model and the second sub-model, for example the output of a modulation layer of feature units, which may be a layer of artificial neurons.

[0052] In a preferred embodiment, the machine learning model further comprises a third sub-model configured to process the output of the modulation layer for each feature.

[0053] In a preferred embodiment, the system is obtained based on training with training hyperparameters selected to promote balanced contributions to optimal operation of the first machine learning model and the quantum computing system, in particular based on training with varying learning rates for updating the parameters of the machine learning model and for updating the variational parameters of the quantum computing system.

[0054] For example, the learning rate for the variational parameters may be greater than, or in some embodiments less than, the learning rate for updating the parameters of the first machine learning model, e.g., the weights and biases.

[0055] The system according to the second aspect may also benefit from any of the features of the preferred embodiments of the first aspect.

[0056] According to a third aspect, the invention relates to a navigation system comprising a system according to the first or second aspect.

[0057] The system according to the second aspect may also benefit from any feature of the first aspect or preferred embodiments of the second aspect.

[0058] According to a fourth aspect, the present invention relates to a method for training a system according to any one of the systems according to the first, second, or third aspects to predict an optimal behavior in a multi-stage decision problem based on a current state, where the conditions of the multi-stage decision problem evolve over time. The method includes iteratively determining candidate solutions to the multi-stage decision problem by determining scenario information and current state information for the multi-stage decision problem, predicting an optimal stage based on a supervisor algorithm, obtaining the prediction of the optimal stage by the system, and updating the current state and conditions of the multi-stage decision problem. The method further includes updating variational parameters of the quantum computing system based on an optimization algorithm so that the prediction of the optimal stage predicted by the system approaches the optimal stage predicted by the supervisor algorithm.

[0059] In some embodiments, the method further includes selecting another multi-stage decision problem having associated scenario information.

[0060] In a preferred embodiment, the supervisor algorithm determines the optimal step based on a complete solution of a multi-step decision problem starting from the current state.

[0061] The supervisor algorithm may calculate an optimal sequence of steps for solving the multi-step decision problem and predict a next optimal action based on the optimal sequence. The current state may then be updated based on the next optimal action, and the conditions may be updated after the next optimal action is executed. The algorithm may then continue to determine the next optimal sequence of steps for solving the multi-step decision problem.

[0062] In a preferred embodiment, the conditions are fixed to determine the complete solution.

[0063] The conditions may be updated after taking a predicted optimal action, and the conditions may only be updated from an updated current state. The sequence of optimal actions may be recorded to determine a training set of data, and the quantum computing system and / or hybrid quantum computing system may be trained based on the training set of data. For example, for each stage of the solution of a multi-stage decision problem by a supervisor algorithm, current state information may be recorded, and the quantum computing system and / or hybrid quantum computing system may be trained to predict a predicted optimal stage based on the current state.

[0064] According to a fifth aspect, the present invention relates to a non-transitory medium comprising machine-readable instructions which, when executed by a processing system, cause the processing system to implement a system according to any one of the first, second or third aspects and / or to implement a method according to the fourth aspect.

[0065] Although the present invention is primarily described with respect to embodiments in the field of navigation problems considering perturbations, quantum computing systems and / or hybrid quantum computing systems may also be used to solve other multi-stage decision problems, such as robotics control problems and / or maze problems. Furthermore, quantum computing systems and / or hybrid quantum computing system structures may also be used to determine optimal labels based on a first input feature vector and a second feature vector for problems based on various information types, such as query-driven image analysis, where the first input feature vector may be based on an ordered sequence of features and the second input feature vector may be based on a two-dimensional map of features, or vice versa.

[0066] The systems according to the first, second and / or third aspects may be controlled using a processing system, which may comprise a single processing unit or may comprise multiple processing units that may be operatively connected. The processing unit may comprise a microcontroller, an ASIC, a PLA (CPLA), an FPGA, or other processing device, including processing devices operating based on software, hardware, firmware, or a combination thereof. The processing device may include integrated memory or communicate with external memory, or both, and may further comprise interfaces for connecting to sensors, devices, instruments, integrated logic circuits, other controllers, etc., which may be configured to receive or transmit signals, such as electrical signals, optical signals, radio signals, acoustic signals, etc.

[0067] The quantum computing system may be implemented in quantum hardware, and the control system may determine, based on the specifications of the quantum computing system, control signals for controlling the quantum hardware, e.g., by initializing qubits, performing gate rotations, and applying multi-qubit gates to some qubits implemented in the quantum hardware. The machine learning model may be implemented in classical hardware, e.g., as a neural network in a processing system such as a computer or dedicated classical hardware for implementing neural networks. [Brief explanation of the drawings]

[0068] The features and many advantages of the method and system according to the present invention will be best understood from the detailed description of the preferred embodiment, when read in conjunction with the accompanying drawings. [Figure 1] FIG. 1 is a schematic diagram illustrating an abstracted map based on a graph of nodes interconnected by edges according to one embodiment. [Figure 2] FIG. 1 illustrates one embodiment of a quantum computing system for determining an optimal action based on the current state of a multi-step decision problem. [Figure 3]FIG. 1 is a schematic diagram of another embodiment of a quantum computing system. [Figure 4] FIG. 4 is a diagram illustrating an embodiment of a hybrid quantum-classical computing system that combines the quantum computing system illustrated in FIG. 3 with a machine learning model. [Figure 5] FIG. 5 illustrates an embodiment of a flowchart for a method of generating a training data set for the system of FIGS. [Figure 6] FIG. 5 illustrates an example embodiment of a method for training the hybrid quantum-classical computing system shown in FIG. 4. DETAILED DESCRIPTION OF THE INVENTION

[0069] FIG. 1 schematically illustrates an abstract map 10 based on a graph of nodes interconnected by edges according to one embodiment. The edges of the graph correspond to streets in the map 10, and the nodes may correspond to intersections in a road system. In the map 10, a starting location 12 is shown as a hollow circle, which may correspond to, for example, a starting state associated with an edge or node. Note that an edge can be decomposed into a node and two edges, such that the starting location 12 on an edge can be translated to a starting node, and vice versa. A navigation system may be responsible for finding a path through a graph of nodes and edges toward a selected exit 14 from multiple potential exits 14 as shown in the exemplary map 10. For the corresponding navigation problem, several algorithms, such as the Dijkstra algorithm or the A* algorithm, are known for determining an optimal path, which may indicate an optimal sequence of nodes and / or edges to traverse from the starting location 12 to a target destination, one of the exits 14. An edge is associated with an edge weight, which may relate to the travel distance and / or travel time for traversing the edge toward the next node.

[0070] However, in the illustrated example, the navigation problem is perturbed by a traffic perturbation in the form of an earthquake 16, which may directly affect a given area of ​​the map 10, as indicated by the associated solid open circle. The earthquake 16 may be associated with an epicenter 18, which may indicate the (estimated) spatial origin of the perturbation.

[0071] In such cases, traffic in the area surrounding the epicenter 18 may be directly affected by the effects of the earthquake 16, for example, based on closed roads and local traffic congestion. Furthermore, ongoing evacuations, particularly along common evacuation routes near exits 14, may increase traffic volume and dynamically evolve after the occurrence of the earthquake 16, which may adversely affect the navigation system's ability to find optimal evacuation paths. Specifically, in such dynamically changing environments, the determination of the optimal next edge based on the current location may need to be periodically reevaluated as part of a multi-stage decision problem for optimal navigation on a graph of nodes and edges.

[0072] 2 shows one embodiment of a quantum computing system 20 for determining an optimal action based on the current state of a multi-step decision problem. The system includes a first qubit register 22 for a first computation qubit and a second qubit register 24 for a second computation qubit, which are processed by a first variational quantum circuit 26 and a second variational quantum circuit 28, respectively. First variational quantum circuit 26 and second variational quantum circuit 28 each include an encoding gate for modifying the state of the first computation qubit and the second computation qubit, respectively, and each further include a variational quantum gate whose action on the qubit is parameterized by a variational parameter.

[0073] First variational quantum circuit 26 and second variational quantum circuit 28 may each comprise multiple layers of variational quantum gates, each layer of variational quantum gates comprising a multi-qubit gate for operating on each qubit of a respective qubit and entangling the state of the respective qubit.

[0074] The encoding gates of the first variational quantum circuit 26 and the second variational quantum circuit 28 may encode the first input feature vector 30 and the second input feature vector 32 in the states of the first computation qubit and the second computation qubit, respectively.

[0075] The first input feature vector 30 may encode current state information based on the respective multi-stage decision problem, such as information related to the current node, neighboring nodes, and location information on the map, e.g., the current location, the starting location 12, and / or the location information of the selected or multiple exits 14. The second input feature vector 32 may encode perturbation information related to the earthquake 16, such as the location of the epicenter 18 and / or the severity of the earthquake 16.

[0076] After first variational quantum circuit 26 and second variational quantum circuit 28 operate on the first and second computation qubits, coherent interaction circuit 34 may entangle the resulting quantum states of the first and second computation qubits. For example, coherent interaction circuit 34 may include a multi-qubit gate that may prepare a coherent superposition state of the first and second computation qubits and manipulate the superposition state, for example, according to further variational parameters.

[0077] The resulting quantum states of the first computation qubit and / or the second computation qubit may be measured in measurement portion 36, for example, based on projective measurements of the qubits by a suitable qubit state detector.

[0078] The resulting output feature vector 38, which may be determined based on the measurement state of the measurement portion 36, indicates the optimal operation and may indicate, for example, the next node selected from multiple adjacent nodes on the map 10.

[0079] 3 schematically illustrates another embodiment of a quantum computing system 20. The quantum computing system 20 includes a first qubit register 22 for a first computation qubit and a second qubit register 24 for a second computation qubit, which are independently processed by a first variational quantum circuit 26 and a second variational quantum circuit 28, respectively. After the first variational quantum circuit 26 and the second variational quantum circuit 28 operate on the first computation qubit and the second computation qubit, a coherent interaction circuit 34 may entangle the resulting quantum states of the first computation qubit and the second computation qubit based on pairwise CNOT operations of the first computation qubit and the second computation qubit, for example, as shown in FIG. 3. After the coherent interaction circuit 34 entangles the state of the first computation qubit with the state of the second computation qubit, a third variational quantum circuit 40 processes the first computation qubit, and the resulting quantum state may be measured by a measurement portion 36.

[0080] Both the first variational quantum circuit 26 and the second variational quantum circuit 28 comprise a layer of variational quantum gates 26a, 28a and a layer of encoding gates 26b, 28b, denoted as units U(θ) and V(x), respectively. A unit U(θ) may comprise multiple quantum gates that can rotate the state of a qubit around a given axis by an angle θ based on corresponding variational parameters. For example, each unit U(θ) comprises a single-qubit rotation gate, per computation qubit, that, for n computation qubits, rotates the quantum state of each qubit around an associated angle, e.g., θ1, θ2, ..., θ n Each of the angles may be based on a corresponding variational parameter, and the variational parameters for each layer 26a, 28a may be different for different layers of the variational quantum gate 26a, 28a.

[0081] Similarly, each layer of encoding gates 26b, 28b may comprise multiple quantum gates for encoding the values ​​of the first and second input feature vectors 30, 32. The operation of the encoding gates may be based on the value of the first input feature vector 30 for one of the encoding gates of the first variational quantum circuit 26, and may be based on the value of the second input feature vector 32 for one of the encoding gates of the second variational quantum circuit 28. For example, the current state may be associated with a vector of 30 values ​​that may be encoded across six layers of encoding gates 26b, 28b, i.e., each layer of encoding gates 26b, 28b encodes five values ​​of the input feature vector by rotating the quantum states of five qubits in the first qubit register based on the respective values.

[0082] The application of a particular layer of encoding gates 26b, 28b may be repeated as part of the first variational quantum circuit 26 and / or the second variational quantum circuit 28, for example, to re-upload the second feature vector 32 multiple times through multiple layers of encoding gates 28b, which modifies the quantum state of the second computational qubit according to the same rotation between applications of layers of variational quantum gates 28a.

[0083] The layers of variational quantum gates 26a, 28a and the layers of encoding gates 26b, 28b may alternately operate on the states of the computation qubits, such as to improve the encoding of features of the input feature vectors 30, 32 in the quantum states of the computation qubits.

[0084] As an example, the second input feature vector 32 includes the coordinates of the earthquake source 18 and the first input feature vector 30 includes information about the current state of the navigation problem, such that the quantum state of the second computational quantum bit may be affected based on the location of the earthquake 16 and the state of the first computational quantum bit may be affected based on locally available navigation information.

[0085] The entangled state produced by the coherent interaction circuit 34 is processed according to a third variational quantum circuit 40 that can affect the quantum state based on corresponding variational parameters, which may again be implemented as a plurality of single-qubit rotations based on corresponding angles θ, and multi-qubit gates to entangle the qubits. The third variational quantum circuit 40 may also comprise multiple layers of variational quantum gates, each layer of variational quantum gates comprising a variational quantum gate that operates on a qubit based on an associated variational parameter, and a multi-qubit gate that induces entanglement between some or all of the computational qubits processed by the third variational quantum circuit 40 (multi-qubit gates may generally be associated with variable operations).

[0086] The quantum computing circuit is trained based on a training set of data, the training set of data including multiple optimal routes for relevant evacuation scenarios, each optimal route may include multiple decision steps, for example, based on selecting an optimal next node.

[0087] The variational parameters may be optimized based on multiple decision steps so that the quantum computing system 20 can predict the optimal behavior predicted by the supervisor algorithm that created the optimal route for the training set of data. For example, the gradient of a cost function that attributes cost to a predicted node by the system 20 with respect to the optimal node may be determined, e.g., based on measurements of partial derivatives of the quantum computing system 20, and the variational parameters may be updated to minimize the cost. The variational parameters of the first, second, and third variational quantum circuits 26, 28, 40 should be updated together, and so on, to result in the quantum computing system 20 efficiently determining the next optimal behavior.

[0088] It has been found that separating the input features into a first input feature vector 30 and a second input feature vector 32 and their independent processing by the first variational quantum circuit 26 and the second variational quantum circuit 28 can improve the handling of perturbation information by the quantum computing system 20, improve convergence to optimal extrema of the variational parameters, and thereby improve the quality of optimal operation for corresponding multi-stage decision problems with dynamically evolving conditions and perturbations, for example, in the case of a map navigation problem taking into account earthquakes 16, as perturbations affecting multiple different possible states.

[0089] As a result, based substantially on local information about the current state, which may be encoded in the first input feature vector 30, and scenario information about traffic perturbations, which may be encoded in the second input feature vector 32, the quantum computing system 20 may be used in a multi-stage decision problem to predict the next optimal state.

[0090] FIG. 4 illustrates one embodiment of a hybrid quantum-classical computing system 42 that combines the quantum computing system 20 shown in FIG. 3 with a machine learning model 44 to improve prediction of optimal behavior.

[0091] The machine learning model 44 is implemented as a neural network of artificial neurons, including a first sub-model 46 and a second sub-model 48 for processing the first input feature vector 30 and the second input feature vector 32, respectively. The output feature vector of the second sub-model 48 modifies the weights and / or biases of the hidden layers of the artificial neurons 50 of the first sub-model 46, such as by introducing an interaction between features based on the perturbation (encoded as the second input feature vector 32) and features based on locally available current state information processed by the first sub-model 46. The resulting features are processed by a third sub-model 52 to determine the output feature vector of the machine learning model 44.

[0092] The resulting output feature vector of machine learning model 44 may be concatenated with an output feature vector based on the measurement output of quantum computing system 20 to obtain a concatenated output feature vector. The concatenated output feature vector may then be processed by combination module 54 to combine the output features of machine learning model 44 and quantum computing system 20, which may be implemented as a second machine learning model based on another neural network of artificial neurons.

[0093] The output 56 of the hybrid quantum-classical computation system 42 indicates the optimal behavior of a multi-stage decision problem based on the corresponding training of the system 42, such as indicating the next optimal node for solving a navigation problem, e.g., an agent directing the behavior of a car can select the next node / edge at every intermediate stage traversing a graph of nodes interconnected by edges.

[0094] The inventors have discovered that the hybrid quantum-classical computing system 42 can produce improved output 56 with respect to individual components of the hybrid quantum-classical computing system 42, i.e., the machine learning model 44 or the quantum computing system 20 itself.

[0095] The parameters (e.g., weights and / or biases) of the machine learning model 44 and the second machine learning model 54, as well as the variational parameters of the quantum computing system 20, may be trained within a joint training algorithm as a joint set of trainable parameters, and the algorithm iteratively updates the trainable parameters, such as to optimize a prediction of optimal behavior, given the current state and scenario information that acts as perturbations to the multi-stage decision problem being solved.

[0096] The algorithm may iteratively provide first and second input feature vectors 30, 32 to the quantum computing system 20 and the machine learning model 44, and the respective output feature vectors may be provided to the second machine learning model 54. The algorithm may then determine parameter updates for the variational parameters and the parameters of the machine learning models 44, 54 based on the value of the cost function for optimal performance of the input feature vectors 30, 32. The trainable parameters are generally iteratively updated together to extremize the cost function associated with the output 56 of the hybrid quantum-classical computing system 42.

[0097] Typically, gradients of multiple predicted optimal actions are determined, and trainable parameters may be updated based on multiple optimal sequences of optimal actions, e.g., based on multiple routes. The cost attributed to each optimal action may be based on an optimal solution determined by a supervisor algorithm in a supervised learning approach, or in reinforcement learning, for example, based on the cost attributed to the solution of a navigation problem, e.g., the time required to navigate map 10 from start location 12 to exit 14, where the time may be calculated based on the time required to traverse each edge of the graph when following the predicted sequence.

[0098] In the training algorithm, the variational parameters and the learning rates for updating the parameters of the machine learning model 44 may be different, such as to adjust the convergence time of each model during training to obtain a balanced contribution of the quantum computing system 20 and the machine learning model 44 to the solution.

[0099] While the following describes a particular application of the hybrid quantum-classical computing system 42 and the corresponding training process, those skilled in the art will understand that individual aspects of the embodiments may be applied to other problems and scenarios.

[0100] FIG. 5 shows an example flowchart of a method for generating a training dataset. The method may begin by initializing a map 10, such as a city, as a weighted computational graph (S10), associating interconnected node edges with weights that indicate the travel time to traverse the edge. The method is performed for a predetermined dataset size, which may be determined based on the number of m earthquake source 18 locations on the map 10 and the number of n paths to be generated for each earthquake scenario (S12). The algorithm then randomly generates coordinates for each earthquake 16, and the coordinates of the earthquake source 18 may be stored as part of the dataset generation (S16). For each earthquake 16, the algorithm randomly selects n start nodes and corresponding exit nodes, which may be selected from a list of specified exits 14 (S16, S18), and the start and exit nodes may be stored within the dataset.

[0101] Thereafter, for each pair of start and exit nodes, edge weights in the map 10 may be initialized based on the coordinates of the epicenter 18 (S20). Next, Dijkstra's algorithm is run from the current node to the designated exit node to determine the optimal next node, and the next node is saved in the dataset as part of the currently generated path between the selected start and exit node pair (S22). The current node is then updated according to the predicted optimal next node of the previous step (S24), the conditions of the map 10 are updated according to the dynamic evolution of the evacuation / earthquake scenario, and steps S22 and S24 are repeated until the current node is equal to the exit node that generated one of the n paths for the earthquake scenario.

[0102] As an illustrative example, an earthquake scenario may be modeled based on the effects of earthquake 16 around epicenter 18 and based on dynamic effects based on increased traffic around exit 14 .

[0103] The static effect of an earthquake can be modeled by increasing edge weights at the beginning of the simulation. The earthquake then has a continuing dynamic effect, increasing nearby edge weights while the area of ​​effect can also increase over time. Travel flow near an exit node may dynamically increase edge weights as cars move from node to node.

[0104] To simulate these three mechanisms, three active and independent models are used simultaneously. The first two models simulate the effect of the earthquake on the travel time between nodes. The source is considered to have a circular area of ​​effect that increases with time. Its radius is denoted as the damage radius, which is r epi = 0.5 + √(0.0002t), where t is the number of nodes traveled to reach the current node. The first model simulates the initial effect and increases the edge weight once, i.e., at time t = 0. The second model covers the ongoing effect of the earthquake and increases the edge weight in the area of ​​effect over time.

[0105] For both of these models, the increase in edge weight is calculated by the epi The smaller this distance, the larger the increase.

[0106] In the experiments conducted by the inventors, the update function for each edge weight w for the first model was defined as follows:

[0107]

number

[0108] The second model updated the edge weights as follows:

[0109]

number

[0110] To simulate traffic flow, we chose the third model, which dynamically increases the edge weight near the exit node while moving from the start node to the exit node. For the earthquake simulation, the exit point is a point with a radius r exit The radius of the effect increases over time. Within the effect area, all edge weights are increased. The increase in each edge is d exit The corresponding update function for each edge weight w is defined as:

[0111]

number

[0112] where:

number

[0113] Thus, each time any data point in the dataset is generated, the node weights are updated, and the supervisor algorithm may determine a new optimal path based on the map 10 with the updated weights from the next node. Multiple earthquake scenarios may be processed in this manner to generate a dataset for training the quantum computing system 20 and / or hybrid quantum-classical computing system 42. Each earthquake scenario is associated with a fixed earthquake source 18 location, and multiple navigation paths may be generated for the same earthquake source 18 location, for example, based on different pairs of start locations 12 and exits 14.

[0114] 6 illustrates one embodiment of a method for training a hybrid quantum-classical computing system 42. In the training algorithm, the coordinates of the epicenter 18 are encoded into a second input feature vector 32 for processing by a second portion of the hybrid quantum-classical computing system 42, i.e., the second variational quantum circuit 28 and the second submodel 48 of the machine learning model 44. Additionally, current state information is encoded into a first input feature vector 30 for processing by a first portion of the hybrid quantum-classical computing system 42, i.e., the first variational quantum circuit 26 and the first submodel 46 of the machine learning model 44.

[0115] The algorithm may then configure the quantum circuits 26, 28, 34, 40 to process the first and second input feature vectors 30, 32 and obtain a corresponding output feature vector 38 from the measurement portion 36. Additionally, the algorithm may forward propagate through a classical machine learning model 44 to obtain a corresponding output feature vector, and the output feature vectors of the quantum computing system 20 and the machine learning model 44 may be combined using a combination layer. The combination layer may be a linear combination of the respective output feature vectors based on combination parameters that assign weights to the respective outputs of the quantum computing system 20 and the machine learning model 44, or may be a machine learning model that may generate an output of the hybrid quantum-classical computing system 42 based on trainable parameters, such as the weights and biases of an underlying artificial neuron network. Based on the output 56 of the hybrid quantum-classical computing system 42, a label prediction is obtained, which may indicate a prediction for the next node among multiple neighboring nodes.

[0116] The predicted labels and the optimal labels in the dataset may be compared, and a loss function and its gradient may be calculated based on the difference between the prediction and the stored optimal label.

[0117] The above steps may be repeated for all data points in the dataset, and an average gradient may be calculated across all data points. Based on the calculated gradients, all trainable parameters of the quantum computing system 20 (i.e., the variational parameters), the machine learning model 44, and the combinational layer may be updated, for example, based on an optimization algorithm, such as adaptive moment estimation, gradient descent, or momentum-based gradient descent.

[0118] The training algorithm may be repeated until a predetermined number of iterations is achieved, or until the quality of the predicted labels meets or exceeds (or is below) a predetermined quality threshold.

[0119] A hybrid quantum-classical computing system 42 was implemented based on quantum computing system 20 implemented on a hybrid quantum cloud, and system 42 was trained to navigate a graph of 357 nodes interconnected by 549 edges and representing the town of Furubira, Japan. The minimum and maximum connectivity of map 10 are 2 and 5. Having a minimum connectivity greater than 1 ensures that the graph is fully connected. Each edge in the graph has a weight proportional to the travel time along the road.

[0120] The output 56 of this architecture is five numbers that act as a logit layer of a node classifier, with the number of five output numbers selected in the example based on the maximum connectivity of the five maps 10. The neighboring node corresponding to the maximum number was selected as the next node. The coordinates of the epicenter 18 are encoded as a second input feature vector 28, with the x and y coordinates encoded into the first and second qubits of the second qubit register 24, respectively, and a corresponding encoding gate applied five times to each of the two "epicenter qubits," with the encoding gates alternating with layers of variational quantum gates 28a.

[0121] In parallel, the five first computational qubits in the first qubit register 22 are processed based on the operation of the first variational quantum circuit 26, and layers of encoding gates 26b and layers of variational quantum gates 26a are alternately applied to the first computational qubits, with the layer of encoding gates 26b encoding the first input feature vector based on the current state information, and different layers of encoding gates 26b encoding different sub-vectors of the first input feature vector 30.

[0122] In this example implementation, two "seismic qubits" are entangled with the current-state-based portion of quantum computing system 20 using a CNOT gate 34 controlled using a NOT applied to the two qubits and all of the first computation qubits. Finally, another variational basis entangler layer 40 is applied to the first computation qubit in first qubit register 22, and the first computation qubit is measured in a Pauli-Z basis. The output of measurement portion 36 is concatenated with the output of a classical machine learning model 44 through a fully connected layer of artificial neurons.

[0123] Additionally, a classical machine learning model 44 was itself trained to predict the next node based on the same dataset and used as a comparison for the hybrid quantum-classical computing system 42.

[0124] Classical machine learning models44 have demonstrated by themselves the ability to mimic Dijkstra's algorithm used to generate the training dataset, reaching an average accuracy of 87% in predicting the optimal next node and an arrival rate of 95% at the exit node. Accuracy can be calculated, for example, as accuracy = |Σ weight path Dij -Σ weight path model |Σ weight path Dij According to the Dijkstra algorithm (path Dij ) may be determined based on the cumulative edge weight difference for the solution by

[0125] Furthermore, the classical model itself was found to be twice as fast in terms of runtime when compared to a node-by-node Dijkstra algorithm that recalculates the optimal path to the next node after each stage based on the updated conditions of the evacuation scenario. This runtime advantage refers to the time it takes the model to predict the next node compared to Dijkstra's algorithm. The average running time of Dijkstra with each variance is μ Dij =1.3×10 -3 s, σ Dij =4.2×10 -4 s, while the classical model is μ NN =4.9×10 -4 s and σ NN =5.7×10 -5 Achieve s.

[0126] The hybrid quantum computing system 42 was found to significantly improve on the classical machine learning model 44, achieving an average accuracy of 94%. This means that, on average, the hybrid quantum computing system 42 predicted 7% of paths that were close to Dijkstra's predicted paths on a node-by-node basis. Furthermore, the hybrid quantum computing system 42 was found to predict more successful paths than the classical machine learning model 44 on its own, and furthermore, when considering the entire trajectory, was found to discover many paths that were faster than or equal to Dijkstra's algorithm.

[0127] Thus, hybrid quantum-classical computing system 42 may improve over classical approaches for complex multi-step decision problems, taking into account foreseeable developments in quantum circuit technology. Furthermore, hybrid quantum-classical computing system 42 may be trained based on a reinforcement learning algorithm, which may further train hybrid quantum-classical computing system 42 to outperform the supervisor algorithm used in the above examples.

[0128] The description of the preferred embodiment and the drawings merely serve to illustrate the invention and its associated beneficial effects and should not be understood as implying any limitation, the scope of which should be determined solely by the appended claims. [Explanation of symbols]

[0129] 10. Map 12 Starting position 14 Exit 16 Earthquake 18. Epicenter 20 Quantum Computing System 22 First qubit register 24 Second qubit register 26 The first variational quantum circuit 28 Second variational quantum circuit 30 First input feature vector 32 Second input feature vector 34 Coherent Interaction Circuit 36 Measuring part 38 Output feature vector of quantum computing system 40 The third quantum computing circuit 42 Hybrid quantum-classical computing system 44 Machine Learning Models 46 First submodel 48 Second Submodel 50 Hidden Layers of Artificial Neurons 52 Third submodel 54 Second Machine Learning Model 56 Output of hybrid quantum-classical computing system

Claims

1. A quantum computing system (20) for determining an optimal action in a multi-stage decision problem based on a current state, the quantum computing system (20) comprising: a first qubit register (22) comprising a first computation qubit; a second qubit register (24) comprising a second computation qubit; a first variational quantum circuit (26) comprising a plurality of quantum gates operating on the first computation qubit; a second variational quantum circuit (28) comprising a plurality of quantum gates operating on the second computation qubit; Equipped with the plurality of quantum gates of the first variational quantum circuit (26) and the second variational quantum circuit (28) each comprise a variational quantum gate (26a, 28a) and an encoding gate (26b, 28b) for modifying the quantum states of the first computation qubit and the second computation qubit, respectively; the parameterized operations of the variational quantum gates (26 a, 28 a) on the first and second computation qubits of the first and second qubit registers (22, 24) are parameterized according to associated variational parameters; the encoding gates (26b, 28b) are configured to encode a first input feature vector (30) and a second input feature vector (32) in the quantum states of the first computation qubit and the second computation qubit, respectively; the quantum gate of the second variational quantum circuit (28) does not operate on the first computation qubit; The quantum computing system (20) a coherent interaction quantum circuit (34) comprising a plurality of multi-qubit gates for entangling the quantum states of the first computation qubit and the second computation qubit acted upon by the first variational quantum circuit (26) and the second variational quantum circuit (28), respectively; a measurement portion (36) for determining an output feature vector (38) indicative of the optimal operation by measuring the quantum states of one or both of the first computation qubit and the second computation qubit; Quantum computing system (20).

2. the first input feature vector (30) is based on the current state and the second input feature vector (32) is based on scenario information valid for a plurality of different states of the multi-stage decision problem; the scenario information is a particularly constant or smooth function over the sequence of stages of the multi-stage decision problem; The quantum computing system (20) of claim 1.

3. the multi-stage decision problem is defined on a graph of interconnected nodes, the multi-stage decision problem being based on selecting a next node based on a current node; the current state includes, inter alia, information about the current node, and the scenario information is independent of the current node; and / or the current state and / or the scenario information changes based on elapsed time and / or the number of steps taken to solve the multi-step decision problem; The quantum computing system (20) of claim 2.

4. the multi-stage decision problem is a navigation problem, and the optimal action indicates an optimal direction of travel on a map characterized by intersections interconnected by edges; the scenario information in particular encodes information about traffic perturbations, preferably about the spatial origin of the traffic perturbations, and the multi-stage decision problem relates to evacuation routing taking into account the traffic perturbations. The quantum computing system (20) of claim 2.

5. the quantum computing system (20) includes a first number of first computation qubits and a second number of second computation qubits, the first number and the second number being different; The quantum computing system (20) of claim 1.

6. the quantum computing system (20) further comprises a third variational quantum circuit (40), the third variational quantum circuit (40) operating on the output quantum state of the coherent interaction quantum circuit (34); The quantum computing system (20) of claim 1.

7. the variational parameters are trained based on a training algorithm for predicting a selected action of a multi-stage decision-making algorithm based on the current state, the variational parameters are trained based on a navigation algorithm for navigating a graph of nodes, in particular, and the optimal action is based on a predicted next node for optimally navigating the graph of nodes; The current state includes, in particular, neighboring node information for each neighboring node, and the neighboring node information preferably includes: The current node coordinates, destination node coordinates; The starting node coordinates, edge weight information indicating the travel time between the current node and the adjacent node; distance information regarding the Euclidean distance between the neighboring node and the current node; edge centrality information about the neighboring nodes; Cosine norm information based on the coordinates of the current node, the adjacent node, and the destination node; including one or more information fields selected from the group The quantum computing system (20) of claim 1.

8. A hybrid quantum computing system (42) comprising the quantum computing system (20) of claim 1, the hybrid quantum computing system (42) further comprises a first machine learning model (44) implemented on classical hardware; the first machine learning model (44) is configured to process the first input feature vector (30) and / or the second input feature vector (32) to obtain an output feature vector (38); the hybrid quantum computing system (42) further comprises a combination module (54), the combination module (54) configured to combine the output feature vector (38) of the first machine learning model (44) with the output feature vector (38) of the measurement portion (36) and determine an output state indicative of the optimal operation based on a combination parameter; the variational parameters, the machine learning parameters, and the combined parameters are obtained based on a common training algorithm, and the variational parameters, the machine learning parameters, and the combined parameters are iteratively updated together to improve prediction of the optimal behavior. Hybrid quantum computing system (42).

9. the combination module (54) comprises a second machine learning module (54) for combining the output feature vector (38) of the first machine learning model with the measurement portion (36) of the quantum computing system (20); The hybrid quantum computing system (42) of claim 8.

10. the first machine learning model (44) comprises a first sub-model (46) and a second sub-model (48, 50) for processing the first input feature vector (30) and the second input feature vector (32), respectively, and further comprises a feature unit modulation layer (50), the feature unit modulation layer (50) operates on an output (56) of the first sub-model (46), and weights and / or biases of the feature unit modulation layer (50) are modulated based on the output (56) of the second sub-model (48, 50); the machine learning model (44, 54) further comprises a third sub-model (52) configured to process, in particular, the output (56) of the feature unit modulation layer (50); The hybrid quantum computing system (42) of claim 8.

11. The hybrid quantum computing system (42) is obtained based on training with training hyperparameters selected to promote balanced contributions to the optimal operation of the first machine learning model (44) and the quantum computing system (20), in particular based on training with different learning rates for updating the parameters of the machine learning models (44, 54) and for updating the variational parameters of the quantum computing system (20). The hybrid quantum computing system (42) of claim 8.

12. A quantum computing system (20) according to any one of claims 1 to 7 or a hybrid quantum computing system (42) according to any one of claims 8 to 11. Navigation system.

13. 12. A method for training a quantum computing system (20) according to any one of claims 1 to 7 or a hybrid quantum computing system (42) according to any one of claims 8 to 11 to predict optimal behavior in a multi-stage decision problem based on a current state, the method comprising: determining scenario information and current state information for the multi-stage decision problem; predicting an optimal stage based on a supervisor algorithm; obtaining a prediction of the optimal stage by the quantum computing system (20) or the hybrid quantum computing system (42); updating the current state and the conditions of the multi-stage decision problem; iteratively determining candidate solutions to the multi-stage decision problem by updating the variational parameters of the quantum computing system (20) based on an optimization algorithm such that the prediction of the optimal phase predicted by the quantum computing system (20) or the hybrid quantum computing system (42) approaches the optimal phase predicted by the supervisor algorithm; method.

14. the supervisor algorithm determines the optimal step based on a complete solution of the multi-step decision problem starting from the current state; the conditions are specifically fixed to determine the complete solution; The method of claim 13.

15. 12. A computer program comprising machine-readable instructions, which, when executed by a processing unit, causes the processing unit to implement a quantum computing system (20) according to any one of claims 1 to 7 or a hybrid quantum computing system (42) according to any one of claims 8 to 11. Computer program.

16. 13. A computer program comprising machine-readable instructions, which when executed by a processing unit causes the processing unit to implement the navigation system of claim 12. Computer program.

17. A computer program comprising machine-readable instructions, which when executed by a processing unit, causes the processing unit to perform the method of claim 13. Computer program.

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