System and method for selecting optimal actions using quantum computer

Abstract

The disclosure relates to systems and methods for selecting optimal actions with a quantum computer. A quantum computing system for determining an optimal action in a multi-step decision problem based on a current state includes a first computing qubit; a second calculation quantum bit; a first variable component sub-circuit and a second variable component sub-circuit, the first variable component sub-circuit and the second variable component sub-circuit comprise a plurality of quantum gates acting on the first calculation quantum bit and the second calculation quantum bit respectively, each quantum gate comprises a variable component sub-gate and a coding gate used for modifying the state of the calculation quantum bit, and each quantum gate comprises a coding gate used for modifying the state of the calculation quantum bit. The encoding gate is configured to encode the first and second input feature vectors in the first and second computational qubits, respectively, and wherein the quantum gate of the second variable component sub-circuit does not act on the first computational qubit; a coherent interaction quantum circuit for entangling quantum states of the first and second computational qubits; and a measurement section for determining an output feature vector indicative of an optimal action.

Description

Technical Field

[0001] The present invention is in the field of quantum computing. More precisely, the present invention relates to using quantum computing to predict the optimal actions of an agent facing a multi-step decision problem. Background Art

[0002] Natural disasters such as earthquakes can have devastating effects, including loss of life and property. In such scenarios, emergency evacuation procedures are critical, 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 taken by these vehicles are safe and efficient.

[0003] Although reliable algorithms exist for navigating the node graphs encoding maps, the task of finding optimal paths becomes difficult even for state-of-the-art algorithms when dynamically changing conditions are introduced. Specifically, in the case of natural disasters, not only may transportation be affected locally (e.g. due to blocked roads and localized traffic jams), but also the development of traffic jams as part of ongoing evacuation efforts may affect efficient routes.

[0004] Quantum computers provide a platform for controllable quantum mechanical systems whose states and interactions can be controlled to perform computations. Computations are achieved through the deterministic evolution of controllable quantum mechanical systems (e.g., qubits, which are quantum analogs of classical bits), and the states of quantum mechanical systems can be measured to determine the results of the computations.

[0005] The control operations on these qubits are called quantum gates. Quantum gates can act coherently on qubits to induce a change in the state of a single qubit (so-called single-qubit gates) and on multiple qubits (so-called multi-qubit gates) (for example, to entangle the states of multiple qubits) and any combination thereof. For example, a single-qubit gate can induce the spin state of an electron to rotate to a selectable value (for example, π / 2). Multi-qubit gates can act coherently on two or more qubits, such as performing a coherent CNOT operation on the states of two qubits. Multiple quantum gates can be applied to the qubits of a quantum computer in parallel or sequentially to perform calculations. Ultimately, the state of the qubit can be repeatedly measured after applying a series of quantum gates to determine the probability of each possible outcome of the calculation.

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

[0007] Despite these drawbacks, recently available quantum processors, known as noisy intermediate-scale quantum (NISQ) devices, have promising applications, such as variational quantum algorithms. In variational quantum algorithms, the actions of quantum gates are parameterized according to a variational parameter, and the variational parameter can be systematically varied in a manner similar to machine learning with the help of classical computing resources. By varying the variational parameter to maximize a cost function that gives the cost of the variational quantum circuit's output with respect to the optimal solution, the output of the variational quantum circuit can be "trained" to provide optimal solutions to unseen problems. Entanglement between different qubits can allow access to a large internal state space to provide a "quantum advantage."

[0008] Giacomo Nannicini and Leo Liberti. (“Shortest paths on dynamic graphs.” International Transactions in Operational Research, 15(5):551–563, 2008) disclose a general algorithm for determining optimal paths through a graph of nodes and edges. Summary of the invention

[0009] Traditional optimization methods rely on classical algorithms that may not be able to handle the complexity of large-scale problems such as optimization of emergency evacuation plans. In addition, these algorithms usually rely on a comprehensive understanding of the entire problem landscape and dynamics to make accurate predictions.

[0010] In view of this prior art, it is an object of the present invention to provide an improved system for predicting an optimal action when faced with a complex multi-step decision problem, in particular based on a (local) subset of information about the problem.

[0011] This object is solved by a method and a system according to the independent claims. The dependent claims relate to preferred embodiments.

[0012] 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 comprises: a first qubit register, the first qubit register comprising a first computational qubit; a second qubit register, the second qubit register comprising a second computational qubit; a first variational quantum circuit, the first variational quantum circuit comprising a plurality of quantum gates acting on the first computational qubit; and a second variational quantum circuit, the second variational quantum circuit comprising a plurality of quantum gates acting on the second computational qubit. The plurality of quantum gates of the first variational quantum circuit and the second variational quantum circuit each comprise a variational quantum gate and an encoding gate for modifying the states of the first computational qubit and the second computational qubit, respectively, and the parameterized action of the variational quantum gate on the qubits of the qubit register 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 computational qubit and the second computational qubit, respectively, and the quantum gate of the second variational quantum circuit does not act on the first computational qubit. The system further includes: a coherently interacting quantum circuit, wherein the coherently interacting quantum circuit includes a plurality of multi-qubit gates for entangling the quantum states of the first computing qubit and the second computing qubit acted upon by the first variational quantum circuit and the second variational quantum circuit, respectively; and a measuring portion for determining an output feature vector indicating the optimal action by measuring the quantum state of one or both of the first computing qubit and the second computing qubit.

[0013] In contrast to current methods for variational quantum circuits, a first variational quantum circuit and a second variational quantum circuit may independently act on different sets of qubits so as to process the first computational qubit and the second computational qubit separately based on corresponding variational parameters. The quantum gate of the second variational quantum circuit does not act on the first computational qubit, and the quantum gate of the first variational quantum circuit may not act on the second computational qubit. Subsequently, the coherent interaction circuit may entangle the states of the first computational qubit and the second computational qubit, and the resulting entangled quantum state may be processed and measured to determine the optimal action. The separation of the first variational quantum circuit and the second variational quantum circuit may allow efficient training and processing of information related to local information as well as global information, wherein the first input feature vector and the second input feature vector are preferably used to encode different dynamics of a multi-step decision problem. For example, the first input feature vector may encode local information into the first computational qubit, and the second input feature vector may encode global information into the second computational qubit.

[0014] In a preferred embodiment, the first input feature vector is based on the current state, and the second input feature vector is based on context information valid for a plurality of different states of the multi-step decision problem.

[0015] The current state may be encoded with local information and may be valid only for a given step of a multi-step decision problem, such as for a node of an interconnected node graph. The context information may be encoded with information that affects multiple states of the multi-step decision problem (particularly multiple nodes of an interconnected node graph under the multi-step decision problem) and / or may be valid for multiple steps of the multi-step decision problem. For example, the context information may be encoded with information related to a disturbance to the multi-step decision problem, such as the root cause and / or origin of the disturbance, such as the spatial origin of an earthquake, the reported location of a terrorist attack, or similar spatial information.

[0016] Information in a first input feature vector and a second input feature vector may be encoded in a variational quantum circuit based on a data re-upload circuit, wherein the first variational quantum circuit and the second variational quantum circuit may each include a layer of variational quantum gates and a layer of encoding gates, and the layers of variational quantum gates and the layers of encoding gates may be applied to corresponding computational qubits in an alternating manner.

[0017] The information in the first input feature vector and / or the second input feature vector can be encoded over multiple layers of encoding gates, wherein pairs of encoding gates can be separated by layers of variational quantum gates, and the encoding of the values ​​of the input feature vectors can be repeated in different layers of encoding gates. The repetition of encoding the values ​​of the input feature vector over multiple layers of encoding gates can simulate data re-uploads, which can increase the order of the internal fitting function of the assumed mechanism of the quantum computing system. Additionally or alternatively, the values ​​of the large input feature vector can be separated into input feature sub-vectors, which can be encoded over multiple layers of encoding gates, wherein a layer of encoding gates can encode one of the input feature sub-vectors.

[0018] In a preferred embodiment, the context information is either constant or a smooth function over the sequence of steps in the multi-step decision problem.

[0019] For example, scene information may provide spatial information related to the disturbance, such as the origin of a traffic disturbance, and may include information about the magnitude of the disturbance, such as the intensity of the earthquake, the severity of the damage, and / or the size of the affected area.

[0020] In some embodiments, a first variational quantum circuit may process a first computational qubit based on local information encoded in a current state, and a second variational quantum circuit may independently process scene information encoded in a second computational qubit. The resulting quantum state may be entangled, such that a measurement of the resulting state may take an optimal action based on the current state according to a perturbation encoded in the scene information. The separation of the first variational quantum circuit and the second variational quantum circuit may enable the variational quantum circuit to effectively generalize scene information and promote convergence of the training algorithm.

[0021] In a preferred embodiment, a multi-step decision problem is defined on a graph of interconnected nodes, wherein the multi-step decision problem is based on the selection of a next node based on a current node.

[0022] The multi-step decision problem may be a node-by-node navigation toward a target destination node based on a current state. The current state may be based on a current node, and may be based on neighboring edge information and / or properties of neighboring nodes. Further, the current state may include contextual information of the current state, which may be associated with real-world properties that may not be represented in the interconnected node graph. For example, the contextual information may include spatial coordinates of an agent and / or task context, such as a start node coordinate and an end node coordinate of a navigation task.

[0023] In a preferred embodiment, the current state includes information about the current node, and wherein the scene information is independent of the current node.

[0024] The current state can encode local information of the current node, such as neighboring nodes, edge weights, centrality information, and spatial information about the current position, starting position, and target position. The scene information can be the location of an earthquake.

[0025] In a preferred embodiment, the current state and / or scene information changes based on the elapsed time and / or the number of steps taken to solve the multi-step decision problem.

[0026] For example, the current state can be based on dynamic information, such as edge weights that are dynamically updated based on the time elapsed and / or the number of steps taken. In some embodiments, the dynamic information that promotes the change of the current state based on the time elapsed and / or the number of steps taken affects multiple nodes, which can be used as the current node is at the current state. In some embodiments, the time elapsed since the disturbance began is part of the input data. The system can be trained to account for dynamic information based on a training set of optimal routes in a dynamically changing problem environment. For example, the development of the conditions of a multi-step decision problem can be updated based on a simulation of a disturbance, such as the edge weights of the graph in the navigation problem shown in the figure.

[0027] In a preferred embodiment, the multi-step decision problem is a navigation problem, and the optimal action indicates an optimal direction of travel on a map featuring intersections interconnected by edges.

[0028] For earthquake evacuation scenarios, edge weights near the epicenter and near potential exits where traffic naturally converges may be increased (e.g., based on the development of traffic congestion as part of the ongoing evacuation dynamics), and corresponding dynamic graphs can be simulated. For training purposes, multiple dynamic evacuation scenarios can be simulated, for example, based on different starting nodes, epicenters, and exit conditions used to generate training sets. The system can then be trained on multiple evacuation scenarios. For example, a modified navigation algorithm can be assigned the task of node-by-node navigation, where graph information (e.g., edge weights) can be updated after each step determined by the navigation algorithm based on the simulation algorithm's simulation of the earthquake. The system can then be trained to select the optimal node based on the current state of the multi-step decision problem for evacuation in a dynamic scenario, where a classical heuristic routing algorithm can act as a supervisor in a supervised learning scheme.

[0029] In a preferred embodiment, the scene information encodes information about traffic disturbances, in particular about the spatial origin of the traffic disturbances, and wherein the multi-step decision problem involves evacuation routes taking into account the traffic disturbances.

[0030] The scenario information may be encoded with epicenter coordinates and / or earthquake intensity, which may modify the optimal actions 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 the number of second computational qubits may be correspondingly smaller than the number of first computational qubits.

[0031] In a preferred embodiment, the quantum computing system includes a first number of first computing qubits and a second number of second computing qubits, wherein the first number and the second number are different.

[0032] For example, the second number may be smaller than the first number.

[0033] The coherent interaction circuit may entangle the quantum state of the first computational qubit to increase the quantum state space available for any further computation of the first computational qubit based on the action of the second variational quantum circuit on the second computational qubit.

[0034] In a preferred embodiment, the system further comprises a third variational quantum circuit, wherein the third variational quantum circuit acts on the output quantum state of the coherent interaction quantum circuit.

[0035] The third variational quantum circuit can process the entangled state of the first computational qubit and the second computational qubit to generate an output state for determining an optimal action. The third variational quantum circuit can act on all or part of the first computational qubit and the second computational qubit. In some embodiments, the number of qubits acted on by the quantum gates of the third variational quantum circuit is less than the sum of the first number and the second number. When the third variational quantum circuit acts on a subset of the first computational qubit and the second computational qubit, the concentration of information of the quantum states generated by the first variational quantum circuit and the second variational quantum circuit can be promoted, which can improve the convergence of the variational quantum circuit toward the optimal combination of variational parameters, which is used to attribute the optimal labels of the inputs provided as the first input feature vector and the second input feature vector to the task of different sets of computational qubits.

[0036] In a preferred embodiment, the variational parameters are trained based on a training algorithm to predict a selected action of a multi-step decision making algorithm based on a current state, wherein the variational parameters are specifically trained based on a navigation algorithm for navigating a node graph, wherein the optimal action is based on a predicted next node for optimally navigating the node graph.

[0037] The first input feature vector may be encoded with information related to the current state, such as a current node corresponding to the current state of the agent. The second input feature vector may be encoded with perturbation information indicating changes in edge weights of multiple nodes of the node graph. The optimal action may be a label indicating a predicted next node for navigating to a target (destination) node, where the target node may be indicated in the first input feature vector or the second input feature vector.

[0038] In a preferred embodiment, the current state includes neighbor node information for each neighbor node. The neighbor node information includes one or more information fields selected from the group consisting of: current node coordinates, destination node coordinates, start node coordinates, edge weight information indicating travel time between the current node and the neighbor node, distance information about the Euclidean distance between the neighbor node and the current node, edge centrality information about the neighbor node, and cosine norm information based on the coordinates of the current node, the neighbor node, and the destination node.

[0039] The current node coordinates may be encoded with the spatial position of the node on a map that may be abstracted by a node graph. The destination node coordinates may be encoded with the spatial position of each adjacent node on the map, and the start node coordinates and the end node coordinates may be encoded with the spatial positions of the start position and the target navigation endpoint, respectively. Edge weight information may be provided for each adjacent node to indicate the travel time of each node option to the adjacent node, and the edge centrality information may be encoded with a plurality of edges connected to each adjacent node. The cosine norm information may indicate directional information related to the question of whether a change from the current node to one of the adjacent nodes belongs to a movement toward, away from, or tangential to the target navigation endpoint. For example, the directional information may be based on the angle and / or scalar product between the vector between the current node and the adjacent node and the vector between the current node and the end node associated with the target navigation endpoint. Specifically, the cosine distance may be defined as

[0040]

[0041] Wherein, for node p and exit “exit” and adjacent node q, A and B can be defined as A=(q x -p x ,q y -p y ) and B=(exit x -p x ,exit y -p y ).

[0042] The Euclidean distance information may be based on a separation distance between a current node and a neighboring node.

[0043] The information about neighboring nodes can further include betweenness centrality information. Betweenness centrality is a measure of centrality in a shortest path-based graph, which describes the number of shortest paths through edges for each node. Nodes with high betweenness centrality are strategically located along the shortest paths between other nodes, which means they have a significant impact on the connectivity of the graph.

[0044] In the training data, information about neighboring nodes can be enhanced, for example, by switching the order of neighboring nodes in the corresponding input feature vector, so as to promote corresponding symmetry of processing of information about multiple neighboring nodes to the variational quantum circuit.

[0045] According to a second aspect, the present invention relates to a hybrid quantum computing system, which comprises a quantum computing system according to the first aspect. The system further comprises a first machine learning model implemented on classical hardware, wherein the first machine learning model is 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, wherein the combination module is configured to combine the output feature vector of the first machine learning model and the output feature vector of the measurement part and determine an output state indicating an optimal action based on a combination parameter. The variational parameters, the machine learning parameters and the combination parameters are obtained based on a common training algorithm, wherein the variational parameters, the machine learning parameters and the combination parameters are jointly updated in an iterative manner to improve the prediction of the optimal action.

[0046] The inventors have found that a combination of a classical machine learning model that can be implemented on classical hardware and that can process input feature vectors based on binary values ​​zero and one and a quantum computing system according to the first aspect can improve the labeling of the input feature vector relative to the trained task, wherein the quantum variational circuit arrangement can be adapted to the global aspects of the optimal selection of the optimal action, and wherein, as part of optimally solving the multi-step decision problem, the first machine learning model can be sensitive to deviations from the global aspects of the optimal selection. The joint solution of the multi-step decision problem can rely on the joint training of the first machine learning model and the quantum computing system, wherein the respective outputs of the quantum computing system and the machine learning model may not indicate the optimal action by themselves, but the trained combination of their corresponding output feature vectors can be obtained from the intermediate results for predicting the optimal action. For example, based on the second machine learning model that processes the cascaded output feature vectors of the quantum computing system and the first machine learning model, the combination of the output feature vectors can be a linear combination of the output feature vectors or can be a nonlinear combination of the output feature vectors.

[0047] In a preferred embodiment, the combining module includes a second machine learning module for combining the first machine learning model and the output feature vector of the measurement part of the quantum computing system.

[0048] Before the outputs of the first sub-model and the second sub-model for respectively processing the first eigenvector and the second eigenvector can be combined to obtain the output eigenvector of the first machine learning model, the first machine learning model can simulate the structure of the quantum computing system based on providing the first sub-model and the second sub-model.

[0049] In a preferred embodiment, the first machine learning model includes a first sub-model and a second sub-model for processing the first feature vector and the second feature vector, respectively, and further includes a feature-by-feature modulation layer, wherein the feature-by-feature modulation layer acts on the output of the first sub-model, and wherein the weights and / or biases of the feature-by-feature modulation layer are modulated based on the output of the second sub-model.

[0050] The outputs of the first sub-model and the second sub-model can be combined using a third sub-model (e.g., an artificial neural network that receives the combined output of the first sub-model and the second sub-model (e.g., which can be the output of a feature-by-feature modulation layer of an artificial neuron layer)).

[0051] In a preferred embodiment, the machine learning model further includes a third sub-model configured to process the output of the feature-by-feature modulation layer.

[0052] In a preferred embodiment, the system is obtained based on training with training hyperparameters selected to promote balanced contributions of the first machine learning model and the quantum computing system to the optimal action, and in particular based on training with different learning rates for updating the parameters of the machine learning model and for updating the variational parameters of the quantum computing system.

[0053] For example, the learning rate for the variational parameters can be greater than, or in some embodiments, less than, the learning rate used to update the parameters (e.g., weights and biases) of the first machine learning model.

[0054] The system according to the second aspect may also benefit from any features of the preferred embodiments of the first aspect.

[0055] According to a third aspect, the invention relates to a navigation system comprising the system according to the first aspect or the second aspect.

[0056] The system according to the second aspect may also benefit from any features of the preferred embodiments of the first aspect or the second aspect.

[0057] According to a fourth aspect, the present invention relates to a method for training a system based on a system according to any one of the first, second or third aspects to predict the optimal action in a multi-step decision problem based on a current state, wherein the conditions of the multi-step decision problem evolve over time. The method comprises: determining scene information and current state information of the multi-step decision problem, and iteratively determining candidate solutions to the multi-step decision problem by: predicting the optimal step based on a supervisor algorithm; obtaining a prediction of the optimal step through the system; and updating the current state and conditions of the multi-step decision problem. The method further comprises updating the variational parameters of the quantum computing system based on an optimization algorithm so that the prediction of the optimal step predicted by the system is close to the optimal step predicted by the supervisor algorithm.

[0058] In some embodiments, the method further includes selecting another multi-step decision problem having associated context information.

[0059] In a preferred embodiment, a supervisor algorithm determines the optimal step based on a complete solution to the multi-step problem starting from the current state.

[0060] The supervisor algorithm can calculate the optimal sequence of steps for solving the multi-step decision problem, and can predict the next optimal action based on the optimal sequence. The current state can then be updated based on the next optimal action, and the condition can be updated after the next optimal action is performed. The algorithm can then continue to determine the next optimal sequence of steps for solving the multi-step decision problem.

[0061] In a preferred embodiment, the conditions are fixed for determining the complete solution.

[0062] The condition may be updated after taking the predicted optimal action, and the condition may be updated only from the updated current state. The optimal action sequence may be recorded to determine a training data set, and the quantum computing system and / or hybrid quantum computing system may be trained based on the training data set. For example, for each step of solving a multi-step decision problem by a supervisor algorithm, the current state information may be recorded, and the quantum computing system and / or hybrid quantum computing system may be trained to predict the predicted optimal step based on the current state.

[0063] According to a fifth aspect, the present invention relates to a non-transitory medium, which includes machine-readable instructions, which, when executed by a processing system, enable the processing system to implement a system according to any one of the first aspect, the second aspect or the third aspect and / or implement a method according to the fourth aspect.

[0064] Although the present invention is mainly described with respect to examples in the field of navigation problems in the context of perturbations, the quantum computing system and / or hybrid quantum computing system can be used to solve other multi-step decision problems, such as robot control problems and / or maze problems. Further, the structure of the quantum computing system and / or hybrid quantum computing system can also be used to determine the optimal label for problems based on different information types such as query-driven image analysis based on a first input feature vector and a second feature vector, wherein the first input feature vector can be based on an ordered feature sequence and the second input feature vector can be based on a two-dimensional feature map, or vice versa.

[0065] A processing system may be used to control the system according to the first aspect, the second aspect and / or the third aspect, and the processing system may include a single processing unit or may include multiple processing units that can be functionally connected. The processing unit may include a microcontroller, an ASIC, a PLA (CPLA), an FPGA, or other processing devices (including processing devices that operate based on software, hardware, firmware, or a combination thereof). The processing device may include an integrated memory, or communicate with an external memory, or both, and may further include an interface for connecting to a sensor, device, apparatus, integrated logic circuit, other controller, etc., wherein these interfaces may be configured to receive or send signals such as electrical signals, optical signals, wireless signals, acoustic signals, etc.

[0066] The quantum computing system can be implemented in quantum hardware, where the control system can determine control signals for controlling the quantum hardware based on the details of the quantum computing system, such as by initializing qubits, performing gate rotations, and applying multi-qubit gates to several qubits implemented in the quantum hardware. The machine learning model can be implemented as a neural network in classical hardware (e.g., a processing system such as a computer or dedicated classical hardware for implementing a neural network). DETAILED DESCRIPTION

[0067] The features and numerous advantages of the method and system according to the present invention will be best understood from the detailed description of the preferred embodiments with reference to the accompanying drawings, in which:

[0068] Figure 1 schematically illustrates a map abstracted based on a graph of nodes interconnected by edges according to an example;

[0069] Figure 2 An example of a quantum computing system for determining an optimal action based on a current state of a multi-step decision problem is illustrated;

[0070] Figure 3 Another example of a quantum computing system is schematically illustrated;

[0071] Figure 4 An example of a hybrid quantum-classical computing system is shown. Figure 3 The combination of a quantum computing system and a machine learning model is shown in Figure 2.

[0072] Figure 5 The diagram shows Figures 1 to 4 An example of a flowchart of a method for a system to generate a training data set; and

[0073] Figure 6 The diagram shows the Figure 4 An example of a method for a hybrid quantum-classical computing system is shown in FIG.

[0074] Figure 1 A map 10 abstracted based on a node graph interconnected by edges according to an example is schematically illustrated. The edges of the graph may correspond to streets of the map 10, and the nodes may correspond to intersections of the street system. In the map 10, a starting position 12 is indicated by a hollow circle, wherein the starting position 12 may correspond to, for example, a starting state associated with an edge or a node. It should be noted that an edge may be decomposed into a node and two edges, so that the starting position 12 on an edge may be converted to a starting node, and vice versa. The task of the navigation system may be to find a path through the graph of nodes and edges toward an exit 14 (e.g., selected from a plurality of potential exits 14 indicated in the example map 10). For the corresponding navigation problem, a plurality of 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 for traversing from the starting position 12 to a target destination (e.g., one of the exits 14). The edge may be associated with an edge weight, which may be related to a travel distance and / or travel time for traversing the edge toward the next node.

[0075] However, in the illustrated example, the navigation problem is perturbed by a traffic disturbance in the form of an earthquake 16, which may directly affect a given area of ​​the map 10, as indicated by the associated solid hollow circle. The earthquake 16 may be associated with an epicenter 18, which may indicate the (estimated) spatial origin of the disturbance.

[0076] In this case, traffic in the area surrounding the epicenter 18 may be directly affected by the earthquake 16, for example based on blocked roads and localized traffic jams. In addition, ongoing evacuations may make traffic along common evacuation routes, particularly near exits 14, heavier, which may develop dynamically after the earthquake 16 occurs and may negatively impact the navigation system's ability to find an optimal evacuation path. Specifically, in such a dynamically changing environment, the determination of the optimal next edge based on the current position may have to be periodically re-evaluated as part of a multi-step decision problem for optimal navigation on a graph of nodes and edges.

[0077] Figure 2An example of a quantum computing system 20 for determining an optimal action based on a current state of a multi-step decision problem is illustrated. The system includes a first qubit register 22 for a first computational qubit and a second qubit register 24 for a second computational qubit, the first computational qubit and the second computational qubit being processed by a first variational quantum circuit 26 and a second variational quantum circuit 28, respectively. The first variational quantum circuit 26 and the second variational quantum circuit 28 each include an encoding gate for modifying the state of the first computational qubit and the second computational qubit, respectively, and each further includes a variational quantum gate whose action on the qubit is parameterized by a variational parameter.

[0078] First variational quantum circuit 26 and second variational quantum circuit 28 may each include multiple layers of variational quantum gates, wherein each layer of variational quantum gates may act on each of the corresponding qubits and may include a multi-qubit gate for entangling the states of the corresponding qubits.

[0079] 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 at the states of the first computational qubit and the second computational qubit, respectively.

[0080] The first input feature vector 30 may be encoded with current state information based on the corresponding multi-step decision problem, such as information related to the current node, adjacent nodes, and location information on a map, such as 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 be encoded with disturbance information, such as disturbance information related to the earthquake 16, such as the location of the epicenter 18 and / or the severity of the earthquake 16.

[0081] After the first variational quantum circuit 26 and the second variational quantum circuit 28 have acted on the first computational qubit and the second computational qubit, the coherent interaction circuit 34 may entangle the resulting quantum states of the first computational qubit and the second computational qubit. The coherent interaction circuit 34 may, for example, include a multi-qubit gate that may prepare a coherent superposition state of the first computational qubit and the second computational qubit, and the multi-qubit gate may, for example, process the superposition state according to a further variational parameter.

[0082] The resulting quantum state of the first computation qubit and / or the second computation qubit may be measured in measurement section 36, for example based on projection measurements of the qubits by a suitable qubit state detector.

[0083] The resulting output feature vector 38 , which may be determined based on the measurement status of the measurement portion 36 , may indicate an optimal action, such as indicating a next node selected from a plurality of neighboring nodes of the map 10 .

[0084] Figure 3 Another example of a quantum computing system 20 is schematically illustrated. The quantum computing system 20 includes a first qubit register 22 for a first computing qubit and a second qubit register 24 for a second computing qubit, the first computing qubit and the second computing qubit being 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 have acted on the first computing qubit and the second computing qubit, the coherent interaction circuit 34 may be, for example, based on Figure 3 The first computational qubit and the second computational qubit are entangled by a paired CNOT operation of the illustrated first computational qubit and the second computational qubit to obtain a quantum state. After the coherent interaction circuit 34 has entangled the state of the first computational qubit with the state of the second computational qubit, the third variational quantum circuit 40 processes the first computational qubit and the obtained quantum state can be measured by the measurement portion 36.

[0085] Both the first variational quantum circuit 26 and the second variational quantum circuit 28 include a layer of variational quantum gates 26a, 28a and a layer of encoding gates 26b, 28b, denoted as unitary U(θ) and V(x), respectively. The unitary U(θ) may include a plurality of quantum gates that may rotate the state of a qubit around a given axis by an angle θ based on a corresponding variational parameter. For example, each unitary U(θ) may include a single-qubit rotation gate for each computational qubit that may rotate the quantum state of the corresponding qubit by an associated angle, e.g., angles θ1, θ2, ..., θ for n computational qubits. n Each angle may be based on a corresponding variational parameter, wherein the variational parameter for each layer 26a, 28a may be different for different layers of variational quantum gates 26a, 28a.

[0086] Similarly, the layers of encoding gates 26b, 28b may each include a plurality of quantum gates for encoding the values ​​of the first and second input feature vectors 30, 32. The action of the encoding gate 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, which may be encoded over six layers of encoding gates 26b, 28b, i.e., wherein each layer of encoding gates 26b, 28b encodes five values ​​of the input feature vector by rotating the quantum states of five qubits of the first qubit register based on the corresponding values.

[0087] The application of certain layers of encoding gates 26 b, 28 b may be repeated as part of the first variational quantum circuit 26 and / or the second variational quantum circuit 28, for example, re-uploading the second eigenvector 32 multiple times using multiple layers of encoding gates 28 b that modify the quantum state of the second computational qubit according to the same rotation between the applications of the layers of variational quantum gates 28 a.

[0088] Layers of variational quantum gates 26a, 28a and layers of encoding gates 26b, 28b may act on the state of the computation qubit in an alternating manner to improve the encoding of features of the input feature vector 30, 32 in the quantum state of the computation qubit.

[0089] As an example, the second input feature vector 32 may include the coordinates of the epicenter 18 and the first input feature vector 30 may include information about the current state of the navigation problem, such that the quantum state of the second computational qubit may be affected based on the location of the earthquake 16 and the state of the first computational qubit may be affected based on locally available navigation information.

[0090] The entangled state produced by the coherent interaction circuit 34 can be processed according to the third variational quantum circuit 40, which can affect the quantum state based on the corresponding variational parameter, which can again be implemented as a plurality of single-qubit rotations based on the corresponding angle θ and a multi-qubit gate for entangled qubits. It should be noted that the third variational quantum circuit 40 can also include multiple layers of variational quantum gates, wherein each layer of variational quantum gates can include variational quantum gates that act on qubits based on associated variational parameters and multi-qubit gates that induce entanglement between some or all of the computational qubits processed by the third variational quantum circuit 40 (wherein the multi-qubit gates can also be generally associated with variable actions).

[0091] A quantum computing circuit may be trained based on a training data set, wherein the training data set may include multiple optimal routes for associated evacuation scenarios, wherein each optimal route may include multiple decision steps, such as multiple decision steps based on selection of an optimal next node.

[0092] The variational parameters can be optimized based on multiple decision steps so that the quantum computing system 20 can predict the optimal action predicted by the supervisor algorithm that created the optimal route of the training data set. For example, the gradient of a cost function that gives the cost of a node predicted by the system 20 relative to the optimal node can be determined, for example, based on a measurement of a partial derivative of the quantum computing system 20, and the variational parameters can be updated to minimize the cost. The variational parameters of the first variational quantum circuit 26, the second variational quantum circuit 28, and the third variational quantum circuit 40 should be jointly updated to obtain a quantum computing system 20 that efficiently determines the next optimal action.

[0093] It has been found that the separation of input features into a first input feature vector 30 and a second input feature vector 32 and independent processing by the first variational quantum circuit 26 and the second variational quantum circuit 28, respectively, can improve the processing of disturbance information by the quantum computing system 20 and can improve the convergence to the optimal extreme value of the variational parameter, so that the quality of the optimal action can be improved for corresponding multi-step decision problems with dynamically developing conditions and disturbances (for example, in the case of a navigation problem on a map considering an earthquake 16 as a disturbance affecting multiple different possible states).

[0094] Therefore, the quantum computing system 20 can be used for multi-step decision problems to predict the next optimal state based essentially on local information about the current state and scene information about the traffic disturbance, the local information can be encoded in the first input feature vector 30, and the scene information can be encoded in the second input feature vector 32.

[0095] Figure 4 An example of a hybrid quantum-classical computing system 42 is shown. Figure 3 The quantum computing system 20 illustrated in FIG. 4 is combined with a machine learning model 44 to improve predictions of optimal actions.

[0096] The machine learning model 44 is implemented as a neural network of artificial neurons, which includes 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 intermediate layers of the artificial neurons 50 of the first sub-model 46 so as to introduce an interaction between the perturbation-based features (encoded as the second input feature vector 32) and the features based on the locally available current state information processed by the first sub-model 46. The resulting features are processed by the third sub-model 52 for determining the output feature vector of the machine learning model 44.

[0097] The resulting output feature vector of the machine learning model 44 can be cascaded with the output feature vector based on the measured output of the quantum computing system 20 to obtain a cascaded output feature vector. Subsequently, the cascaded output feature vector can be processed for combining the output features of the machine learning model 44 and the quantum computing system 20 through a combination module 54, which can be implemented as a second machine learning model based on another neural network of artificial neurons.

[0098] The output 56 of the hybrid quantum-classical computing system 42 can indicate the optimal action for a multi-step decision problem based on the corresponding training of the system 42, such as indicating the next optimal node for solving a navigation problem, where, for example, an agent instructing the actions of a car can select the next node / edge at each intermediate step in traversing a graph of nodes interconnected by edges.

[0099] The inventors have discovered that the hybrid quantum-classical computing system 42 can generate an output 56 that is improved relative to the individual components of the hybrid quantum-classical computing system 42 (i.e., the machine learning model 44 or the quantum computing system 20) themselves.

[0100] Parameters (e.g., weights and / or biases) of the machine learning model 44 and the second machine learning model 54 and the variational parameters of the quantum computing system 20 can be trained as a joint set of trainable parameters in a joint training algorithm, where the algorithm iteratively updates the trainable parameters to optimize the prediction of the optimal action given the current state and perturbation of the scene information that serves as a multi-step decision problem to be solved.

[0101] The algorithm may iteratively provide the first input feature vector 30 and the second input feature vector 32 to the quantum computing system 20 and the machine learning model 44, and may provide the corresponding output feature vector to the second machine learning model 54. Subsequently, the algorithm may 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 of the optimal action for the input feature vectors 30, 32. The trainable parameters are typically jointly updated in an iterative manner to maximize the cost function associated with the output 56 of the hybrid quantum-classical computing system 42.

[0102] Typically, gradients for multiple predicted optimal actions can be determined, and trainable parameters can be updated based on multiple optimal sequences of optimal actions (e.g., based on multiple routes). The cost attributed to each optimal action can be based on an optimal solution determined by a supervisor algorithm in a supervised learning approach or can be based on reinforcement learning, for example, based on a cost attributed to a solution to a navigation problem, e.g., the time required to navigate a map 10 from a starting location 12 to an exit 14, where the time can be calculated based on the time required to traverse each edge in the graph when following the predicted sequence.

[0103] In the training algorithm, the learning rates used to update the variational parameters and the parameters of the machine learning model 44 can be different so as to adjust the convergence time of the respective models during training to obtain a balanced contribution of the quantum computing system 20 and the machine learning model 44 to the solution.

[0104] In the following, a specific application of the hybrid quantum-classical computing system 42 and the corresponding training process will be described, although those skilled in the art will understand that various aspects of the examples may be applied to other problems and scenarios.

[0105] Figure 5 An example of a flow chart of a method for generating a training data set is illustrated. The method can begin by initializing (S10) a map 10 (e.g., a city) as a weighted computational graph, wherein edges interconnecting nodes can be associated with weights indicating travel times across the edges. The method can be performed for a data set of a predetermined size, which can be determined based on the m epicenter 18 locations on the map 10 and the n paths to be generated for each earthquake scenario (S12). Subsequently, the algorithm can randomly generate the coordinates of each earthquake 16, and the coordinates of the epicenter 18 can be stored as part of the data set generation (S16). For each earthquake 16, the algorithm can randomly select n starting nodes and corresponding exit nodes, which can be selected from a list of specified exits 14 (S16, S18), and the starting node and exit node can be stored in the data set.

[0106] Subsequently, for each pair of start and exit nodes, the edge weights of the map 10 may be initialized based on the coordinates of the epicenter 18 (S20). The Dijkstra algorithm is then run from the current node to the specified exit node for determining the optimal next node, and the next node is saved in the data set as part of the currently generated path between the selected pair of start and exit nodes (S22). The current node is then updated according to the optimal next node predicted in the previous step (S24), and the conditions of the map 10 are updated according to the dynamic development of the evacuation / earthquake scenario, and steps S22 and S24 are repeated until the current node is equal to the exit node, thereby generating one of the n paths for the earthquake scenario.

[0107] 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 exits 14 .

[0108] The static effect of an earthquake can be modeled by increasing edge weights at the beginning of the simulation. Later, the earthquake may have a persistent dynamic effect, increasing nearby edge weights, with the impact area also increasing over time. The flow of travel near an exit node can dynamically increase edge weights as cars move from one node to another.

[0109] To simulate these three mechanisms, three active independent models are used simultaneously. The first two models simulate the effect of the earthquake on the travel time between nodes. The epicenter is considered to have a circular area of ​​influence that grows over time. Its radius is represented as r epi =0.5+√(0.0002t) of damage radius, where t is the number of nodes traveled to reach the current node. The first model simulates the initial impact and increases the edge weight once, i.e. at time t = 0. The second model covers the ongoing impact of the earthquake and increases the edge weight in the impact area over time.

[0110] For both models, the edge weight can be increased depending on the corresponding Euclidean distance between a given edge and the epicenter coordinates, which is denoted as d epi The smaller the distance, the greater the increase.

[0111] In the inventors' experiments, the update function of each edge weight w of the first model is defined as:

[0112]

[0113] And the second model updates the edge weights as:

[0114]

[0115] To simulate traffic flow, a third model is selected to dynamically increase the edge weights near the exit node when traveling from the start node to the exit node. For earthquake simulation, the exit point has a radius of r. exit The radius of influence increases over time. Within the influence region, all edge weights increase. Each edge increases depending on its distance to the exit node coordinates, denoted as d exit The smaller the distance, the greater the increase. The corresponding update function for each edge weight w is defined as:

[0116]

[0117] in, And t is the number of nodes traveled to reach the current node.

[0118] Thus, after each data point of the data set is generated, the weight of the node can be updated, and the supervisor algorithm can determine a new optimal path from the next node using the updated weight based on the map 10. Multiple earthquake scenarios can be processed in this manner to generate a data set for training the quantum computing system 20 and / or the hybrid quantum-classical computing system 42. Each earthquake scenario can be associated with a fixed epicenter 18 location, wherein multiple navigation paths can be generated for the same epicenter 18 location, for example, based on different pairs of starting locations 12 and exits 14.

[0119] Figure 6 An example of a method for training a hybrid quantum-classical computing system 42 is illustrated. In the training algorithm, the coordinates of the epicenter 18 are encoded in 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 sub-model 48 of the machine learning model 44). Further, current state information is encoded in a first input feature vector 30 processed by a first portion of the hybrid quantum-classical computing system 42 (i.e., the first variational quantum circuit 26 and the first sub-model 46 of the machine learning model 44).

[0120] Subsequently, the algorithm can establish quantum circuits 26, 28, 34, 40 to process the first input feature vector 30 and the second input feature vector 32 and obtain the corresponding output feature vector 38 from the measurement portion 36. In addition, the algorithm can forward propagate the classical machine learning model 44 to obtain the corresponding output feature vector, and the output feature vectors of the quantum computing system 20 and the machine learning model 44 can be combined using a combination layer. The combination layer can be a linear combination of the corresponding output feature vectors based on a combination parameter (the combination parameter assigns weights to the corresponding outputs of the quantum computing system 20 and the machine learning model 44), or it can be a machine learning model that can generate the output of the hybrid quantum-classical computing system 42 based on trainable parameters (e.g., weights and biases of the underlying artificial neural network). Based on the output 56 of the hybrid quantum-classical computing system 42, a prediction of a label can be obtained, which can indicate a prediction for the next node among a plurality of adjacent nodes.

[0121] The predicted labels and the best labels in the dataset can be compared, and the loss function and its gradient can be calculated based on the difference between the predictions and the stored best labels.

[0122] The previous steps may be repeated for all data points in the data set, and the average gradient may be calculated over all data points. Based on the calculated gradients, all trainable parameters (i.e., variational parameters) of the quantum computing system 20, the machine learning model 44, and all trainable parameters of the combined layers may be updated, for example, based on an optimization algorithm (e.g., gradient descent or momentum-based gradient descent, such as adaptive moment estimation).

[0123] The training algorithm may be repeated until a predetermined number of iterations have been achieved or until the quality of the predicted labels reaches or exceeds (alternatively, falls below) a predetermined quality threshold.

[0124] A hybrid quantum-classical computing system 42 is implemented based on a quantum computing system 20 implemented on a hybrid quantum cloud, wherein the system 42 is trained to navigate a graph of 357 nodes interconnected by 549 edges, and the graph represents Furubira, Japan. The minimum connectivity and maximum connectivity of the map 10 are two and five. The minimum connectivity greater than one ensures that the graph is fully connected. Each edge in the graph has a weight proportional to the travel time through the road.

[0125] The output 56 of the architecture is five numbers that act as a logit layer of node classifiers, where the number of the five output numbers is selected based on the maximum connectivity of map 10 being five in the example. The adjacent node corresponding to the highest number is selected as the next node. The coordinates of the epicenter 18 are encoded as a second input feature vector 28, where the x and y coordinates are encoded in the first and second qubits of the second qubit register 24, respectively, where the corresponding encoding gates are applied five times to each of the two "epicenter qubits", and where the encoding gates alternate with layers of variational quantum gates 28a.

[0126] In parallel, five (5) first computational qubits in first qubit register 22 are processed based on the action of first variational quantum circuit 26, wherein layers of encoding gates 26b and layers of variational quantum gates 26a are alternately applied to the first computational qubits, and wherein the layers of encoding gates 26b encode the first input feature vector based on current state information, and wherein different layers of encoding gates 26b encode different sub-vectors of first input feature vector 30.

[0127] In an implementation example, the two "epicenter qubits" are partially entangled with the current state-based portion of the quantum computing system 20 using a CNOT gate 34 controlled by the two qubits and a NOT applied to all first computational qubits. Finally, another variational basic entangler layer 40 is applied to the first computational qubit of the first qubit register 22, and the first computational qubit is measured in the Pauli-Z basis. The output of the measurement portion 36 is cascaded with the output of the classical machine learning model 44 through a fully connected layer of artificial neurons.

[0128] Additionally, a classical machine learning model 44 is trained to predict the next node based on its own same data set and used for the hybrid quantum-classical computing system 42 as a comparison.

[0129] The classical machine learning model 44 itself achieved an average accuracy of 87% in predicting the optimal next node and an exit node arrival rate of 95%, thereby demonstrating the ability to simulate the Dijkstra algorithm used to generate the training dataset. The accuracy can be, for example, calculated according to accuracy = |∑ 权重 path Dij -∑ 权重 path model | / ∑ 权重 path Dij Based on the solution obtained by node-by-node Dijkstra algorithm (path Dij ) is determined by the cumulative edge weight difference.

[0130] In addition, the classical model itself was found to be two times faster in terms of runtime compared to the node-by-node Dijkstra algorithm (which recalculates the optimal path after each step to the next node based on an update condition for the evacuation scenario). This runtime advantage refers to the time required by the model to predict the next node compared to the Dijkstra algorithm. The average runtime of Dijkstra and the corresponding variance are μ Dij =1.3×10 -3 s,σ Dij =4.2×10 -4 s, while the classical model realizes μ NN =4.9×10 -4 s and σ NN =5.7×10 -5 s.

[0131] It was found that the hybrid quantum computing system 42 significantly outperformed the classical machine learning model 44 itself, achieving an average accuracy of 94%. This means that on average, the paths predicted by the hybrid quantum computing system 42 are 7% closer than the predicted paths of the node-by-node Dijkstra. In addition, it was found that the paths predicted by the hybrid quantum computing system 42 were more successful than the classical machine learning model 44 itself, and it was further found that when the entire trajectory was considered, the hybrid quantum computing system found more paths faster or at the same speed as the Dijkstra algorithm.

[0132] Therefore, given the foreseeable development of quantum circuit technology, the hybrid quantum-classical computing system 42 can outperform classical methods for complex multi-step decision problems. Further, the hybrid quantum-classical computing system 42 can be trained based on a reinforcement learning algorithm, so that the hybrid quantum-classical computing system 42 can be further trained to outperform the supervisor algorithm used in the above example.

[0133] The description of the preferred embodiments and the accompanying drawings are only for illustrating the present invention and its associated advantages, and should not be understood as implying any limitations. The scope of the present invention will be determined only by the appended claims.

[0134] List of Reference Numerals

[0135] 10 Map

[0136] 12 Starting Position

[0137] 14 Exit

[0138] 16 earthquake

[0139] 18 Epicenter

[0140] 20 Quantum computing systems

[0141] 22 First qubit register

[0142] 24 Second qubit register

[0143] 26 First Variation Quantum Circuit

[0144] 28 Second Variation Quantum Circuit

[0145] 30 First input feature vector

[0146] 32 Second input feature vector

[0147] 34 Coherent Interaction Circuit

[0148] 36 Measurement section

[0149] 38 Output eigenvectors of quantum computing systems

[0150] 40 The third quantum computing circuit

[0151] 42 Hybrid quantum-classical computing systems

[0152] 44 Machine Learning Model

[0153] 46 First sub-model

[0154] 48 Second sub-model

[0155] 50 Intermediate layer of artificial neurons

[0156] 52 The third sub-model

[0157] 54 Second Machine Learning Model

[0158] 56 Output of a hybrid quantum-classical computing system

Claims

1. A quantum computing system (20) for determining an optimal action in a multi-step decision problem based on a current state, the quantum computing system (20) comprising: A first qubit register (22), the first qubit register comprising a first computational qubit; a second qubit register (24), the second qubit register comprising a second computational qubit; a first variational quantum circuit (26), the first variational quantum circuit comprising a plurality of quantum gates acting on the first computational qubit; a second variational quantum circuit (28), the second variational quantum circuit comprising a plurality of quantum gates acting on the second computational qubit; wherein the plurality of quantum gates of the first variational quantum circuit (26) and the plurality of quantum gates of the second variational quantum circuit (28) each include a variational quantum gate (26a, 28a) and an encoding gate (26b, 28b) for modifying the state of the first computational quantum bit and the state of the second computational quantum bit, respectively; wherein the parameterization effect of the variational quantum gate (26a, 28a) on the quantum bits of the quantum bit register is parameterized according to the associated variational parameters; wherein the encoding gates (26b, 28b) are configured to encode the first input feature vector (30) and the second input feature vector (32) under the quantum state of the first computing quantum bit and the quantum state of the second computing quantum bit, respectively; and wherein the quantum gate of the second variational quantum circuit (28) does not act on the first computational quantum bit; A coherently interacting quantum circuit (34), wherein the coherently interacting quantum circuit (34) comprises a plurality of multi-qubit gates for entangling the quantum states of the first computational qubit and the second computational qubit acted upon by the first variational quantum circuit (26) and the second variational quantum circuit (28), respectively; and A measuring section (36) is configured to determine an output feature vector (38) indicating the optimal action by measuring the quantum state of one or both of the first computational qubit and the second computational qubit.

2. The system (20) of claim 1, wherein: The first input vector (30) is based on the current state, and wherein the second input vector (32) is based on scenario information valid for a plurality of different states of the multi-step decision problem; The scene information is particularly a constant or smooth function in the sequence of steps of the multi-step decision problem.

3. The system (20) of claim 2, wherein: defining the multi-step decision problem on a graph of interconnected nodes, wherein the multi-step decision problem is based on selecting a next node based on a current node; wherein the current state specifically includes information about the current node, and wherein the scene information is independent of the current node; and / or Wherein 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.

4. A system (20) as claimed in any one of the preceding claims, wherein: The multi-step decision problem is a navigation problem, and the optimal action indicates an optimal direction of travel on a map featuring intersections interconnected by edges, Therein, the scene information in particular encodes information about a traffic disturbance, preferably about the spatial origin of the traffic disturbance, and wherein the multi-step decision problem relates to an evacuation route taking into account the traffic disturbance.

5. The system (20) according to any one of the preceding claims, wherein: The quantum computing system (20) includes a first number of first computing qubits and a second number of second computing qubits, wherein the first number and the second number are different.

6. The system (20) according to any one of the preceding claims, wherein: The system (20) further comprises a third variational quantum circuit (40), wherein the third variational quantum circuit (40) acts on the output quantum state of the coherent interaction quantum circuit (34).

7. The system (20) according to any one of the preceding claims, wherein: training the variational parameters based on a training algorithm to predict a selected action of a multi-step decision making algorithm based on the current state, wherein the variational parameters are specifically trained based on a navigation algorithm for navigating a node graph, wherein the optimal action is based on a predicted next node for optimally navigating the node graph; and The current state particularly includes neighbor node information of each neighbor node, wherein the neighbor node information preferably includes one or more information fields selected from the group consisting of: 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 about the Euclidean distance between the adjacent node and the current node, edge centrality information about the neighboring nodes, and Based on cosine norm information of coordinates of the current node, the adjacent nodes and the destination node.

8. A hybrid quantum computing system (42) comprising a quantum computing system (20) as claimed in any one of the preceding claims, in, The system (42) further includes a first machine learning model (44) implemented on classical hardware, wherein 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), wherein the hybrid quantum computing system (42) further comprises a combining module (54), wherein the combining module (54) is configured to combine the output feature vector (38) of the first machine learning model (44) and the output feature vector (38) of the measurement part (36) and is configured to determine an output state indicating the optimal action based on a combined parameter, Wherein, the variational parameters, the machine learning parameters and the combined parameters are obtained based on a common training algorithm, wherein the variational parameters, the machine learning parameters and the combined parameters are jointly updated in an iterative manner to improve the prediction of the optimal action.

9. The system (20, 42) of claim 8, wherein: The combining module (54) includes a second machine learning module (54) for combining the first machine learning model and the output feature vector (38) of the measurement portion (36) of the quantum computing system (20).

10. The system (20, 42) of claim 8 or 9, wherein: The first machine learning model (44) comprises a first sub-model (46) and a second sub-model (48, 50) for processing the first feature vector (30) and the second feature vector (32), respectively, and further comprises a feature-by-feature modulation layer (50), wherein the feature-by-feature modulation layer (50) acts on an output (56) of the first sub-model (46), and wherein weights and / or biases of the feature-by-feature modulation layer (50) are modulated based on the output (56) of the second sub-model (48, 50); Therein, the machine learning model (44, 54) in particular further includes a third sub-model (52) configured to process the output (56) of the feature-by-feature modulation layer (50).

11. The system (20, 42) of any one of claims 8 to 10, wherein: The system (42) is obtained based on training using training hyperparameters selected to promote balanced contributions of the first machine learning model (44) and the quantum computing system (20) to the optimal action, and in particular based on training with different learning rates for updating the parameters of the machine learning model (44, 54) and for updating the variational parameters of the quantum computing system (20).

12. A navigation system (20, 42) comprising a system (20, 42) as claimed in any one of the preceding claims.

13. A method for training a system (20, 42) as claimed in any one of the preceding claims to predict the optimal action in a multi-step decision problem based on the current state, wherein: The conditions of the multi-step decision problem evolve over time, wherein the method comprises: Determine the scenario information and current state information of the multi-step decision problem, Candidate solutions to the multi-step decision problem are iteratively determined by: Based on the supervisor algorithm to predict the optimal step, obtaining, by the system (20, 42), a prediction of the optimal step; and updating the current state and the condition of the multi-step decision problem; The variational parameters of the quantum computing system (20) are updated based on an optimization algorithm so that the prediction of the optimal step predicted by the system (20, 42) is close to the optimal step predicted by the supervisor algorithm.

14. The method of claim 13, wherein: The supervisor algorithm determines the optimal step based on a complete solution to the multi-step problem starting from the current state, In this case, the conditions are in particular fixed for determining the complete solution.

15. A computer program comprising machine-readable instructions, which, when executed by a processing unit, cause the processing unit to implement the system according to any one of claims 1 to 12 and / or implement the method according to claim 13 or 14.

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