Quantum computing system model training

Abstract

To provide a method and system for training a quantum computing system model.SOLUTION: A method may include: selecting multiple data subsets from a data set; training multiple parameters of a quantum computing system model using the multiple data subsets and a quantum circuit depth using a quantum computer over multiple iterations; generating a solution for the plurality of data subsets using the quantum computing system model and the quantum computer; comparing the solution to a threshold solution; adjusting the quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution; and retraining, using the quantum computer, the multiple parameters of the quantum computing system model using the multiple data subsets and adjusted quantum circuit depth.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] This disclosure generally relates to training quantum computing system models. [Background technology]

[0002] Quantum computers can use quantum bits ("qubits") that can represent information as 1, 0, or 1 and 0 simultaneously. Quantum computers can train the parameters of quantum computing system models for some types of computations, such as optimization problems, integer factorization, simulation modeling, and / or data analysis, more efficiently and / or more accurately than classical computers. However, existing quantum computers contain only a limited number of qubits that are subject to errors in calculations due to noise, and are typically unable or unsuitable for training the parameters of computationally demanding models, and are therefore generally classified as noisy intermediate-scale quantum (NISQ) devices.

[0003] The subject matter claimed in this disclosure is not limited to embodiments that solve any shortcomings or that operate only in environments such as those described above. Rather, this background is provided only to illustrate one example technology area where some embodiments described herein may be practiced. Summary of the Invention [Means for solving the problem]

[0004] According to an aspect of an embodiment, a method may include selecting a plurality of data subsets from a collection of data sets, and training a plurality of parameters of a quantum computing system model using the plurality of data subsets and a quantum circuit depth using a quantum computer over a plurality of iterations. The method may include generating a solution for the data subset using the quantum computing system model and the quantum computer. The method may also include comparing the solution to a threshold solution. The method may include adjusting a quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution. The method may further include retraining a plurality of parameters of the quantum computing system model using the plurality of data subsets and the adjusted quantum circuit depth using a quantum computer.

[0005] The object and advantages of the embodiments will be realized and attained at least by the elements, features, and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are illustrative only and are not restrictive of the invention as claimed. [Brief description of the drawings]

[0006] Example embodiments will be described and explained with additional specificity and detail through the accompanying drawings.

[0007] [Figure 1] FIG. 1 illustrates an exemplary operating environment for training parameters of a quantum computing system model in accordance with one or more embodiments of the present disclosure.

[0008] [Diagram 2] 1 illustrates an example quantum circuit of a quantum computer in accordance with one or more embodiments of the present disclosure.

[0009] [Diagram 3] 1 illustrates a flowchart of an exemplary method for training parameters of a quantum computing system model in accordance with one or more embodiments of the present disclosure.

[0010] [Figure 4] 1 shows a flowchart of another exemplary method for training parameters of a quantum computing system model in accordance with one or more embodiments of the present disclosure.

[0011] [Diagram 5] 1 illustrates an exemplary computing system in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Quantum computers use quantum bits, or "qubits," configured to store values ​​of 0, 1, or a superposition of both 0 and 1. Because quantum bits can store multiple values ​​simultaneously, quantum computers can perform calculations more quickly than classical computers that use classical bits that store values ​​of either 0 or 1. As a result, quantum computers can more efficiently train models related to advanced calculations such as for optimization problems, improving computations in a variety of technological fields such as physics, chemistry, materials design, drug discovery, and machine learning.

[0013] Quantum computing system models may be used to analyze very complex data sets with a large number of parameters. For example, training a model to solve an optimization task for a large data set is generally classified as an NP-hard problem, i.e., a problem that cannot be solved in polynomial time by a non-deterministic Turing machine. Therefore, such problems may be solved using quantum computing system models on a quantum computer. However, quantum computing system models for such problems may suffer from the problem of exponentially vanishing gradients, i.e., the size of the gradients used during training becomes smaller and smaller, thereby inhibiting formative learning and increasing the time for training. In addition, quantum computing system models may also suffer from the problem of local minima / maxima being misclassified as global minima / maxima during training.

[0014] The present disclosure may relate, inter alia, to a scalable training method that utilizes data subsets of increasing size to improve the training of parameters of a quantum computing system model by scaling the quantum circuit depth and retraining on a quantum computer. Thus, by creating a method and system for more efficiently training a quantum computing system model according to the present disclosure, the computing process and performance of the quantum computer may be improved.

[0015] Additionally or alternatively, the present disclosure relates to, among other things, scaling the quantum circuit depth on a quantum computing device during training of a quantum computing system model. A quantum computing device may include a quantum circuit including one or more quantum logic gates that constitute a quantum circuit depth. Including more quantum logic gates (i.e., increasing the quantum circuit depth) may improve the computing power of a given quantum computing device by allowing more intricate superposition and entanglement patterns as well as increased quantum parallelism. For example, increasing the quantum circuit depth may allow the implementation of more complex quantum algorithms on a quantum computing device, such as Shor's algorithm, Grover's algorithm, variational quantum algorithms, etc. Increasing the quantum circuit depth may allow a quantum computing device to simultaneously explore a larger portion of the solution space (quantum parallelism), which may increase quantum computing speed, especially for calculations involving quantum algorithms that work by iteratively adjusting parameters to approximate a solution.

[0016] Increasing the number of quantum gates may also increase the noise level of the results output by a given quantum computing device due to the finite coherence time of the qubits. Because a quantum computing device may contain only a limited number of qubits on which quantum logic gates may perform operations, there may be few or no qubits available for performing quantum logic gate error correction and / or fault tolerance operations. Thus, in some embodiments of the present disclosure, the quantum circuit depth in the quantum circuit may be scaled during training of the quantum computing system model based on the results of the training. Scaling the quantum circuit depth may help reduce the noise level and / or reduce the number of qubits that may be used during training, since deeper quantum circuits have more layers of quantum logic gates to effectively detect and correct errors. In these and other embodiments, scaling the quantum circuit depth may include adjusting the number of quantum logic gates used by the quantum computer. These and other embodiments of the present disclosure may provide improvements over previous iterations of methods for training parameters of quantum computing system models by reducing the computational time for solving problems using a quantum computing device and / or reducing the effects of vanishing gradients on the computations, thereby providing more efficient and / or accurate computing results.

[0017] Embodiments of the present disclosure will now be described with reference to the accompanying drawings.

[0018] FIG. 1 illustrates an exemplary operating environment 100 for training parameters 112 of a quantum computing system model, according to one or more embodiments of the present disclosure. The environment 100 may include a classical computing device 102 and a quantum computing device 110. The classical computing device 102 may include any of a variety of devices in which computing operations may be performed, such as a computer system or components thereof. For example, the classical computing device 102 may be any computer and / or computing device that uses classical binary bits for operation, a classical binary bit being a bit that includes only two states, 1 or 0. Thus, the classical computing device 102 may be any electronic or digital device that includes hardware and programming to utilize at least one classical binary bit for processing, and does not use quantum bits or qubits for processing. As used herein, the term classical computing device 102 is not limited to integrated circuits, but refers broadly to processors, servers, microcontrollers, microcomputers, programmable logic controllers (PLCs), application specific integrated circuits, and other programmable circuits. In some embodiments, classical computing device 102 may include a processor, memory, data storage, communication units, and / or any other computing module. For example, classical computing device 102 may include one or more computers, servers, or other known computing devices as described.Some examples of classical computing devices 102 include desktop computers, laptop computers, tablet computers, server computers such as rack-mounted servers, mobile phones, smartphones, network devices, communication equipment, single board computers (SBCs), systems on chips (SOCs), microcontroller units (MCUs), and any other electronic or digital device having a processor. In some embodiments, classical computing devices 102 may include computer peripherals associated with a user interface, such as a computer mouse, keyboard, and / or scanner. Additionally, in some embodiments, classical computing devices 102 may include output channels, such as a user interface monitor and / or printer.

[0019] In some embodiments, the quantum computing device 110 includes a quantum processor, which may comprise at least one qubit and a means for storing the at least one qubit. The at least one qubit may be physically implemented using, for example, a photon, a trapped ion, an electron, one or more nuclei, a superconductor circuit, and / or a quantum dot. A qubit may be physically implemented in a variety of ways, including the polarization state of a single photon, the spatial path of a single photon, two different energy states of an atom or ion, and / or the spin orientation of a particle or particles, such as an atomic nucleus. In some embodiments, the quantum processor may comprise at least two qubits and at least one coupler capable of coupling the qubits. Storing the at least one qubit may include maintaining the at least one qubit in a suitable environment to permit quantum computation, for example by supercooling the at least one qubit. The at least one qubit may be manipulated by one or more quantum circuits formed by an appropriate arrangement of quantum logic gates.

[0020] For example, quantum computing device 110 may be a noisy intermediate-scale quantum (NISQ) device, a quantum annealer, an analog quantum computer, a universal quantum computer, and / or any combination of computing devices having at least one qubit.

[0021] In some embodiments, quantum computing device 110 may be communicatively coupled to classical computing device 102. Classical computing device 102 may provide instructions to quantum computing device 110, pre-process data for quantum computing device 110, and interpret results from quantum computing device 110. For example, classical computing device 102 may be configured to instruct quantum computing device 110 to prepare quantum states and / or perform measurements on those quantum states according to instructions stored in memory on classical computing device 102. In some embodiments, classical computing device 102 and quantum computing device 110 may be communicatively coupled through a cloud service, such as when classical computing device 102 sends computational tasks to remote quantum computing device 110 over a network.

[0022] The environment 100 may be used to implement a process for generating a quantum computing system model using a classical computing device 102 and a quantum computing device 110. The quantum computing device 110 may generate the quantum computing system model using data subsets 108 selected using the classical computing device 102 from a set of data sets 104. The quantum computing system model may be used by the quantum computing device 110 to discern patterns or make decisions based on previously unseen data sets. For example, the model may be configured to provide a solution to a combinatorial optimization problem. The quantum computing system model may be generated using one or more quantum algorithms, such as variational quantum algorithm(s) used in quantum machine learning techniques. For example, the quantum computing system model may be generated using a quantum approximation optimization algorithm.

[0023] In some embodiments, the process of generating the quantum computing system model may include multiple operations including subset selection 106, parameter training 114, solution comparison 120, and quantum circuit depth adjustment 122. In some embodiments, the process may be an iterative process. As a result, subset selection 106, parameter training 114, solution comparison 120, and quantum circuit depth adjustment 122 may be performed multiple times to generate the quantum computing system model.

[0024] In some embodiments, the classical computing device 102 may obtain a dataset 104 to begin the process. The dataset 104 may include one or more sets of data that may be used in training the parameters 114 of the quantum computing system model. For example, the dataset 104 may be a single set of data or multiple sets of data. As an example, the dataset 104 may include a collection of data that may include multiple different data entries and may be arranged in multiple different configurations. In some embodiments, the dataset 104 may include information about an undirected graph that includes nodes and edges connecting the nodes. The nodes may represent different data in the dataset 104, and the edges may represent commonalities or connections between the nodes. Alternatively or additionally, the dataset 104 may be arranged in other configurations. In these and other embodiments, the classical computing device 102 may be configured to generate the undirected graph using the dataset. For example, the dataset 104 may initially include prices of assets, such as stocks, over a period of time. Correlations between the assets based on the prices may be determined, thus constituting a dataset for a particular time window. Dataset 104 may be a sequence of such datasets. In these and other embodiments, assets may be nodes and edges may represent correlations between pairs of assets and / or correlations between pairs of assets above or below a threshold.

[0025] In some embodiments, the dataset 104 may include data from or representing statistical metrics, lists of members of a social network, genes from a genome sequence, images, atoms in a molecule, Internet of Things (IoT) devices, business and / or financial data, and / or any other type of data. For example, the dataset 104 may include data regarding financial investments, such as data on a particular stock, multiple different stocks in an index fund, and / or products or services over a period of time. Alternatively or additionally, the dataset 104 may include data regarding quantum computing devices, such as simulated quantum circuits; quantum hardware characteristics including qubit connectivity, quantum logic gate fidelity, error rates; quantum cryptography protocols; and / or any other aspect of a quantum computer. The dataset 104 may be generated by the classical computing device 102, entered by a user, downloaded from a network, and / or created by devices such as sensors, cameras, satellites, bioinformatics devices, healthcare devices, audio devices, video devices, and / or any combination thereof. In some embodiments, it may be desired that an optimization problem or combinatorial optimization problem be solved for the dataset 104. The quantum computing system model may be configured to provide a solution to the optimization problem or combinatorial optimization problem for the dataset 104 in the environment 100. For example, the optimization problem may be a maximum independent set problem.

[0026] In some embodiments, after obtaining the dataset 104, the process may include selecting 106 a subset. The operation of selecting 106 a subset may be performed by the classical computing device 102 and may include generating one or more data subsets 108 of the dataset 104. In some embodiments, generating one or more data subsets 108 of the dataset 104 may include selecting one or more portions of the dataset 104 and generating one or more data subsets 108 using the one or more portions of the dataset 104. For example, the dataset 104 may include multiple sets of data. In these and other embodiments, one of the multiple sets of data may be selected as part of the dataset 104, and one or more data subsets 108 may be generated using that one of the sets of data.

[0027] In these and other embodiments, each of the data subsets 108 may include one or more nodes of the data set 104. For example, each of the data subsets 108 may include one node. Alternatively or additionally, each of the data subsets 108 may include multiple nodes and edges connecting the nodes. Thus, each of the data subsets 108 may include information about a node graph that includes the nodes selected for the respective data subset.

[0028] In some embodiments, the quantum computing system model may be generated using the data subset 108 as training data instead of the entire dataset 104. In these and other embodiments, the data subset 108 may be used instead of the entire dataset 104 because the dataset 104 may be too large to be used for training by the quantum computing device 110. For example, the quantum computing device 110 may not have enough qubits to make training on the entire dataset 104 acceptable. In these and other embodiments, the data subset 108 may be sized based on the qubits available for training at the quantum computing device 110.

[0029] Alternatively or additionally, training the quantum computing system model using one or more data subsets 108 that are smaller than the entire dataset 104 may make the training more efficient. For example, training in multiple iterations on a set of smaller data subsets 108 may take less time and / or produce better results than training using the entire dataset 104.

[0030] Alternatively or additionally, training the quantum computing system model using one or more data subsets 108 that are smaller than the entire set of datasets 104 can help overcome issues associated with certain quantum algorithms used to develop the quantum computing system model that is generated based on the set of datasets 104. For example, some quantum algorithms may be affected by local min / max traps. In some embodiments, training using one or more data subsets 108 that are smaller datasets than the set of datasets 104 can help avoid local min / max traps for some quantum algorithms.

[0031] In some embodiments, the size of the data subsets 108, e.g., the number of data entries or nodes in each of the data subsets, may be one. Alternatively or additionally, the size of the data subsets 108 may be greater than one. For example, the size of the data subsets 108 may be 2, 3, 4, 5, 6, 7, 8, 12, 15, 20, 25, 30, 50, 75, 100, 150, 200, 250, 500, 750, 1000, 2000, 4000, 7500, or more. The size of the data subsets 108 may be based on the complexity of the edges between the nodes in the data subsets 108. For example, the size of the data subsets 108 may be selected such that variations in the structure of the subgraphs formed by the nodes in the data subsets 108 begin to occur. In these and other embodiments, the size of the data subsets 108 may be increased during successive iterations of the process performed to generate the quantum computing system model.

[0032] In some embodiments, the number N of data subsets 108 selected may be determined by a user and / or by the classical computing device 102. In some embodiments, the number of data subsets 108 selected may be based on available computational resources, such as available memory, and / or a statistical model that indicates the number of data subsets 108 to approximate the behavior of the dataset 104 to a specified confidence level.

[0033] In some embodiments, the classical computing device 102 may select the data subsets 108 by selecting a node (i.e., an initial node) in the dataset 104 for each of the data subsets 108. After selecting an initial node for a particular data subset 108, the classical computing device 102 may select one or more other nodes based on the number of nodes in each of the data subsets 108. In some embodiments, the initial node may be selected randomly or based on one or more factors. For example, a user wishing to train a quantum computing system model may select an initial model that is central to that particular data subset 108 based on some measure of centrality or local node-based centrality.

[0034] In some embodiments, the classical computing device 102 may randomly select the other nodes of the dataset 104, or the other nodes may be selected based on being in a neighborhood of the initial node in the dataset 104. In some embodiments, selecting the data subsets 108 may include continuing to select one or more neighboring nodes of the initial node until the data subsets 108 reach the number of nodes to be included in each data subset 108. In these and other embodiments, a search algorithm may be used to select the neighboring nodes of the initial node.

[0035] In these and other embodiments, the search algorithm may be a linear search algorithm, a sentinel linear search algorithm, a binary search algorithm, a meta-binary search algorithm, a ternary search algorithm, a jump search algorithm, an interpolation search algorithm, an exponential search algorithm, a Fibonacci search algorithm, a breadth-first search algorithm, a depth-first search algorithm, Dijkstra's algorithm, Floyd-Warshall's algorithm, Prim's algorithm, Kruskal's algorithm, and / or any other algorithm used to determine neighboring nodes.

[0036] In some embodiments, data subset 108 may be provided to quantum computing device 110 for use in training a quantum computing system model. Data subset 108 may be provided to quantum computing device 110 via one or more physical networks, cloud networks, random access memory (RAM) drives, flash memory devices (e.g., solid-state memory devices), and / or any other manner in which data may be transferred between devices.

[0037] In some embodiments, the process of generating the quantum computing system model may include a parameter training operation 114. The parameter training operation 114 may be performed by the quantum computing device 110 and may include training and / or tuning one or more parameters 112 of the quantum computing system model. The quantum computing system model parameters 112 may determine how the quantum computing device may function to find a solution to a quantum system algorithm and / or optimization given a dataset 104, such as an unseen dataset. The functioning of the quantum computing device 110 may include how the quantum computing device 110 uses one or more qubits, measures properties of the one or more qubits in response to performing a quantum operation, and / or outputs and / or stores such measured properties. In some embodiments, the parameters 112 may include a quantum circuit depth. In these and other embodiments, the quantum circuit depth may refer to the number of layers of quantum logic gates used to complete a computation on the quantum computing device 110.

[0038] In some embodiments, the parameters 112 may be initialized with particular values ​​before training begins. In these and other embodiments, the initialized values ​​may be zero or some other value based on the dataset 104. In some embodiments, the quantum circuit depth may be initialized with a value of one or more. For example, the quantum circuit depth may be initialized with a value of two, indicating that two layers of quantum circuits may be used during training.

[0039] In some embodiments, the quantum computing device 110 may train one or more parameters 112 by adjusting the one or more parameters 112 to achieve a particular result, such as minimizing or maximizing an objective function to solve an optimization problem given the data set 104. To train the parameters 112, for example, multiple training iterations may occur. During each training iteration, one of the data subsets 108 may be selected and a particular quantum circuit layer of the quantum circuit may be selected based on the selected quantum circuit depth. For example, if the selected quantum circuit depth is 2, one of two layers may be selected. If the selected quantum circuit depth is 4, one of four layers may be selected. In these and other embodiments, the same one of four layers may be selected until the quantum circuit depth is adjusted. After the quantum circuit depth is adjusted, previous layers and additional layers may be selected. In some embodiments, the one of the data subsets 108 and the particular quantum circuit layer may be selected randomly.

[0040] In some embodiments, training the parameters 112 may include adjusting one or more of the parameters 112 based on a selected one of the data subsets 108 and an algorithm for solving an optimization problem with respect to the particular quantum circuit layer, but not the quantum circuit depth. In these and other embodiments, the parameters 112 to be adjusted may be parameters for a selected layer of the quantum circuit layers. For example, training the training parameters 112 may include applying a stochastic gradient descent algorithm from which it is determined how to adjust the parameters 112 given the selected one of the data subsets 108 and the particular quantum circuit layer. In these and other embodiments, the parameters 112 may be adjusted during each training iteration associated with a selected layer of the quantum circuit layers. Thus, for a first iteration, the parameters 112 may have an initial value and may be adjusted to a first value. For a second training iteration, the parameters 112 may have a first value and may be adjusted to a second value.

[0041] After training the parameters 112, a quantum computing system model may be generated using the parameters 112 and the quantum circuit depth. In these and other embodiments, an optimization problem for one or more of the data subsets 108 may be solved by the quantum computing device 110, which is configured according to the quantum computing system model. In this manner, the quantum computing device 110 may generate a solution for each of the subsets 108 provided to the quantum computing device 110. For example, in some embodiments, all of the data subsets 108 may be provided to the quantum computing device 110 for solution generation.

[0042] The quantum computing device 110 may provide the solutions to the classical computing device 102 via one or more physical networks, cloud networks, random access memory (RAM) drives, flash memory devices (e.g., solid-state memory devices), and / or any other means by which data may be transferred between devices. In some embodiments, the classical computing device 102 may generate a solution that may be a mathematical combination of the solutions 116 for each of the data subsets 108 provided by the quantum computing device 110. The mathematical combination may be an average, median, weighted average, or some other mathematical combination of the solutions 116 for each subset 108.

[0043] In some embodiments, the classical computing device 102 may be configured to obtain a threshold solution 118 for the data subsets 108. The threshold solution 118 may be based on a calculated solution and a threshold quality. For example, the calculated solution may be a mathematical combination of actual solutions to the optimization problem being solved by the quantum computing device 110 using the data subsets 108. The calculated solution may be based on the same mathematical combination of solutions from the same data subsets 108. In early iterations, the calculated solution may be based on actual solutions for each data subset 108 that may have been brute-force solved by the classical computing device 102 or provided to the classical computing device 102. The actual solutions may be mathematically combined in a manner similar to how the solutions 116 may be combined to obtain a calculated solution. In subsequent iterations, the calculated solution may be approximated by the quantum computing device 102 using the parameters 112 trained in the previous round of training the parameters 114. For example, during a current round of training, the quantum computing device 102 may use parameters 112 from the previous round of training to generate a solution 116 using the data subset 108 for the current round of training, and may use the solution 116 to generate a calculated solution that is used to generate a threshold solution 118 for the current round of training.

[0044] In some embodiments, the threshold quality may be a value based on how closely the quantum computing system model solution 116 approximates the computed solution. For example, the threshold quality may be a percentage between 1 and 100, where 100 percent may indicate that the solution 116 is an exact solution and lower percentages may indicate how close the solution 116 is to the exact solution. For example, a value of 10 percent may indicate that the solution 116 is only marginally related to the exact solution. In these and other embodiments, the threshold quality may be selected by a user and may be based on time constraints, resource constraints, and / or user preferences.

[0045] In some embodiments, the threshold solution 118 may be calculated through a mathematical combination of a calculated solution and a threshold quality. For example, the calculated solution may be an actual solution obtained for an optimization problem solved in a brute force manner by the classical computing system 102 on the small data subset 108, the threshold quality may be a percentage selected by a user (e.g., 85%), and the threshold solution 118 may be obtained by multiplying the calculated solution by the threshold quality.

[0046] In some embodiments, after obtaining the threshold solution 118 and the solution, the process may include an operation of comparing the solutions 120. The operation of comparing the solutions 120 may be performed by the classical computing device 102. In these and other embodiments, the solution may be compared to the threshold solution 118, and it may be determined whether the solution satisfies the threshold solution 118. The solution satisfying the threshold solution 118 may indicate that the quantum computing system model has determined a solution for the data subset 108 with an accuracy acceptable to the user who selected the threshold solution 118. In these and other embodiments, as a result of the solution satisfying the threshold solution 118, the process may expand the size of the data subset 108 and continue iteratively. This may reduce the possibility of vanishing gradients due to selecting initial parameters in subsequent iteration steps as parameters 112 found for a set of smaller sized data subsets 108. For example, the operation of selecting a subset 106 may be performed again. In the next iteration, each of the data subsets 108 may include more nodes than the previous data subset for each data subset 108. For example, the number of nodes in each data subset 108 may be increased by 1, 2, 3, 4, 5, or some other value. After determining the data subsets 108 with the increased number of nodes, the process may include an operation 114 of training parameters. In some embodiments, the values ​​of the parameters 112 may be maintained from the previous operation 114 of training parameters. Using the parameters 112 from the previous operation to generate the calculated solution may help recognize high quality minima and help reduce effects associated with misidentifying low quality minima as high quality minima. Alternatively or additionally, the values ​​of the parameters 112 may be set to other values. The other values ​​may be, for example, zero or some derivative of the values ​​of the parameters 112 from the previous iterations. In these and other embodiments, the process may continue as described above.

[0047] In some embodiments, the solution may not meet the threshold solution 118. Failure of the solution to meet the threshold solution 118 may indicate that the quantum computing system model has not determined a solution for the data subset 108 with acceptable accuracy. In these and other embodiments, the parameters 112 may be further adjusted. First, the quantum circuit depth may be adjusted.

[0048] In some embodiments, adjusting the quantum circuit depth may include adding to the quantum circuit depth. Adding to the quantum circuit depth may include adding one or more layers to the quantum circuit depth. In these and other embodiments, the added layer may be added to the beginning of an existing layer, between existing layers, or at the end of an existing layer. In some embodiments, the added layer may be added in the middle of an existing layer.

[0049] In some embodiments, the parameters 112 of the recently added layer may be initialized with values ​​based on the values ​​of the parameters 112 in other layers. This may help overcome vanishing gradients in training, since initial values ​​are selected from previous training, and those parameters were successful in finding a solution for a set of small data subsets 108 previously considered. Alternatively or additionally, the values ​​of the parameters 112 of the recently added layer may be initialized to 0. In these and other embodiments, the parameters 112 of the recently added layer may be trained. For example, the data subset 108 may be randomly selected, one of the recently added layers may be randomly selected, and the parameters 112 of the selected layer may be trained in a manner similar to that described above. The parameters 112 of the recently added layer may be trained over multiple iterations. After training the parameters 112 of the recently added layer, the operation 114 of training parameters may be performed again as previously described. In these and other embodiments, the previous and recently added layers of the quantum circuit layer may be randomly selected for a single training iteration.

[0050] In some embodiments, the selection of the data subsets 108 during the operation 114 of training the parameters may be completely random, as described above. Alternatively or additionally, in some embodiments, some of the data subsets 108 may be weighted. As a result, data subsets 108 that are weighted more heavily than other data subsets 108 may be selected more frequently for training the parameters 112. In these and other embodiments, the selection may be pseudo-random. For example, the selection may be made randomly based on weights applied to the data subsets 108. For example, there may be 500 data subsets 108. A random selection selects one of the 500. In a weighted random selection, 100 of the data subsets 108 may be weighted and have two entries, resulting in 600 data subsets 108. In a random selection among the 600 data subsets 108, the weighted data subsets may be selected more frequently.

[0051] In some embodiments, the weighting of the data subsets 108 may be based on how well a parameter-based quantum computing system model can solve the problem for the data subsets 108. For example, after multiple iterations, a quantum computing system model may be generated using the parameters 112 and the quantum circuit depth. In these and other embodiments, an optimization problem for each of the data subsets 108 may be solved by a quantum computing device 110 configured according to the quantum computing system model. Thus, the quantum computing device 110 may generate a solution for each of the data subsets 108. The solution may be compared to a known solution or any previous solution, as in a solution comparison operation 120. In these and other embodiments, a data subset 108 that produces a solution that is less similar to a known or previous solution compared to other data subsets 108 may be weighted more heavily than the other data subsets 108. As a result, the parameter training operation 114 may be trained more frequently with the poorly performing data subsets 108. Training the parameters 112 more frequently on poorly performing data subsets may increase the likelihood that the parameters 112 will be trained to perform better on those poorly performing data subsets in subsequent iterations.

[0052] In some embodiments, weighting of data subsets 108 may occur randomly, at specified intervals, or based on other factors during parameter training operation 114. For example, if 10,000 parameter training iterations occur, weighting of data subsets 108 may occur every 1,000 iterations or randomly during the 10,000 parameter training iterations.

[0053] In some embodiments, after the classical computing device 102 performs the solution comparison operation 120, in response to the size of the data subset 108 being smaller than the size of the data set 104 and / or the quantum computing device 110 having available qubits, e.g., unused qubits, the classical computing device 102 may perform the subset selection process 106 described above.

[0054] In some embodiments, after the classical computing device 102 performs the solution comparison operation 120, in response to the size of the data subset 108 being equal to the size of the dataset 104 or the quantum computing device 110 having qubits utilized, the training of the parameters 112 may be terminated and the parameters may be used to generate a quantum computing system model that may be used for unseen datasets.

[0055] An example of the operation of the environment 100 is now provided. In this example, the environment 100 may be used to identify low-risk financial investment strategies. The dataset 104 may include stock market index tracking data, such as data for companies listed on a national stock exchange. Within the dataset 104, each node may represent a financial asset, and an edge may exist between two nodes if the correlation between the assets is above a specified threshold. The parameters 112 may be trained to solve a minimal optimization problem to identify financial assets with low correlation. As a result, a quantum computing system model may be generated using the parameters 112 to identify financial assets with low correlation based on the current trading trends of the financial assets.

[0056] Modifications, additions, or omissions may be made to environment 100 without departing from the scope of the present disclosure. For example, the designation of different elements in the manner described is intended to aid in illustrating the concepts described herein and is not intended to be limiting. For example, classical computing device 102 and quantum computing device 110 are depicted in the particular manner described to aid in illustrating the concepts described herein, but such depictions are not intended to be limiting. Additionally, environment 100 may include any number of other elements or may be implemented in other systems or contexts other than those described.

[0057] 2 illustrates an exemplary quantum circuit of a quantum computer according to one or more embodiments of the present disclosure. Quantum circuit 200 may include multiple quantum logic gates 202. For example, quantum circuit 200 may include one or more CNOT gates, Hadamard gates, Toffoli gates, phase gates, T gates, one or more other quantum logic gates, and / or any combination of quantum logic gates. Quantum circuit 200 may be implemented in a quantum computing device, such as quantum computing device 110 of FIG. 1.

[0058] In some embodiments, the quantum circuit 200 may include multiple quantum logic gates 202, where each of the quantum logic gates may be configured to perform one or more operations on one or more qubits associated with the quantum circuit 200 to generate a particular output corresponding to a particular input. Similar to classical computing bits, a qubit may have a value "1" or a value "0". Additionally, a qubit may include superposition states in which a qubit simultaneously represents values ​​of 1 and 0, rather than only values ​​of 1 or 0 as with classical bits. In some embodiments, when the quantum circuit 200 has multiple quantum logic gates 202, a particular quantum logic gate may be designated as a first quantum logic gate 204, a second quantum logic gate 206, etc. In some embodiments, the quantum circuit depth 210 may be adjusted by adding one or more additional quantum logic gates 208 to the quantum circuit 200. For example, the one or more additional quantum logic gates 208 may be disposed between the first quantum logic gate 204 and the second quantum logic gate 206. In some embodiments, quantum circuit depth 210 may refer to the number of time steps or layers of quantum logic gates 202 to complete a calculation on a quantum computer.

[0059] A quantum computing device, such as quantum computing device 110 of FIG. 1, may include at least one quantum circuit 200 corresponding to quantum circuit 200 of FIG. 2. In some embodiments, a quantum circuit depth of quantum circuit 200 may be adjusted. Adjusting the quantum circuit depth may include disposing one or more quantum logic gates 208 in quantum circuit 200. In some embodiments, disposing the one or more additional quantum logic gates 208 between first quantum logic gate 204 and second quantum logic gate 206 may improve quantum entanglement, quantum parallelism, error correction, and / or other properties of quantum circuit 200. In some embodiments, the type of one or more additional quantum logic gates 208 that may be disposed may be selected based on the parameters being trained.

[0060] Modifications, additions, or omissions may be made to quantum circuit 200 without departing from the scope of the present disclosure. For example, the designation of different elements in the manner described is intended to aid in explaining the concepts described herein and is not intended to be limiting. For example, the plurality of quantum logic gates 202, the first quantum logic gate 204, the second quantum logic gate 206, and the one or more additional quantum logic gates 208 are depicted in the particular manner described to aid in explaining the concepts described herein, but such depictions are not intended to be limiting. Additionally, quantum circuit 200 may include any number of other elements or be implemented in other systems or contexts other than those described.

[0061] 3 is a flowchart of an example method 300 of training parameters of a quantum computing system model using a quantum computer, according to one or more embodiments of the present disclosure. Method 300 may be performed by any suitable system, apparatus, or device. For example, classical computing device 102 and / or quantum computing device 110 may perform one or more of the operations associated with method 300. Although shown in discrete blocks, one or more associated steps and operations of the blocks of method 300 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the particular implementation.

[0062] The method 300 may begin at block 302, where data subsets may be selected from a dataset. In some embodiments, the dataset may include interconnected nodes, and selecting the data subsets from the dataset may include, for each data subset, selecting a node and applying a search algorithm to select one or more neighboring nodes of the node. In some embodiments, the data subsets may be weighted. In these and other embodiments, training the parameters may include selecting one of the data subsets based on the respective weights of the data subsets and training the parameters using the one of the multiple data subsets and the quantum circuit depth. In these and other embodiments, training may also include adjusting a weight applied to the one of the data subsets based on training performed using the one of the data subsets.

[0063] At block 304, a plurality of parameters of the quantum computing system model may be trained using the data subsets and the quantum circuit depth. The parameters may be trained using the quantum computer over a plurality of iterative steps. In some embodiments, training the parameters may include selecting one of the data subsets based on a respective weight of the data subset, training the parameters using the one of the data subsets and the quantum circuit depth, and adjusting the weight applied to the one of the data subsets based on the training performed using the one of the data subsets.

[0064] Solutions for the data subsets may be generated using the quantum computing system model and the quantum computer in block 306. In some embodiments, the solutions for each of the data subsets may be mathematically combined by a classical computing device to generate a solution.

[0065] At block 308, the solution may be compared to a threshold solution. In some embodiments, comparing the solutions may be performed by a classical computing device. In some embodiments, comparing the solutions may include determining the accuracy of the solution for the quantum computing system model and the data subset generated by the quantum computer.

[0066] At block 310, in response to the solution of the quantum computing system model not satisfying the threshold solution, the quantum circuit depth may be adjusted. In some embodiments, adjusting the quantum circuit depth may include disposing one or more additional quantum logic gates in a quantum circuit of the quantum computer. In these and other embodiments, the quantum circuit may include a plurality of quantum logic gates. The one or more additional quantum logic gates may be disposed between a first quantum logic gate and a second quantum logic gate of the plurality of quantum logic gates.

[0067] In block 312, parameters of the quantum computing system model may be retrained on the quantum computer using the data subset and the adjusted quantum circuit depth.

[0068] Modifications, additions, or omissions may be made to method 300 without departing from the scope of the present disclosure. For example, the designation of different elements in the described manner is meant to help explain the concepts described herein, and is not intended to be limiting. Additionally, method 300 may include any number of other elements or may be implemented in other systems or contexts other than those described.

[0069] For example, method 300 may further include selecting a plurality of second data subsets. In these and other embodiments, each of the plurality of second data subsets may be of a size greater than the plurality of data subsets. Method 300 may further include training the plurality of parameters of the quantum computing system model using the plurality of second data subsets and the quantum circuit depth using the quantum computer over the plurality of iterations.

[0070] As another example, method 300 may further include generating a solution to a second data set using the trained quantum computing system model. In some embodiments, generating a solution to the second data set may be in response to at least one of the data subsets having a size equal to the size of the data set and all available quantum computing qubits having been utilized to train the parameters of the quantum computing system model.

[0071] Further, method 300 may include adjusting the threshold solution based on the solution of the quantum computing system model. For example, the threshold solution may be adjusted to be the average of the smallest value that a solution of the quantum computing system model provides to the minimization optimization problem after a specified number of iterations of training parameters of the quantum computing system model for each data subset.

[0072] FIG. 4 illustrates a flowchart of an example method 400 for selecting a data subset and training parameters of a quantum computing system model using a quantum computer, according to one or more embodiments of the present disclosure.

[0073] Method 400 may be performed by any suitable system, apparatus, or device. For example, classical computing device 102 and / or quantum computing device 110 may perform one or more of the operations associated with method 400. Although shown in discrete blocks, one or more associated steps and operations of the blocks of method 400 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the particular implementation.

[0074] Method 400 may begin at block 402, where a selection of a data subset from a dataset, a quantum circuit depth, and a threshold quality may occur. Selecting the data subset may be random, performed by a user, based on preliminary calculations, and / or performed in any convenient manner. In some embodiments, selecting the data subset may include randomly selecting a node in the dataset and applying a search algorithm to locate / discover one or more neighboring nodes until a data subset of a specified size is found. The operations of block 402 may be performed by one or more classical computing devices or by a quantum computing device.

[0075] At block 404, the method 400 may include an act of training parameters of the quantum computing system model using the data subset and the quantum circuit depth using a quantum computer over iterations. In some embodiments, the quantum computer may be the quantum computing device 110 described in FIG. 1. Each iteration may be performed within an epoch of a specified number of iterations. For example, an epoch may include training over 1000, 2000, 4000, or any number of iterations before the method 400 proceeds from block 404 to 406. The training may include adjusting parameters of the quantum computing system model such that a goal is achieved. For example, if the quantum computing system model is an optimization problem, the parameters may be adjusted based on the data subset and the quantum circuit depth until a solution is generated.

[0076] At block 406, method 400 may include an act of generating a solution for the data subsets using the quantum computing system model and the quantum computer. In some embodiments, the solution may be a mathematical combination of the solutions for each data subset generated using the quantum computing system model and the quantum computer. For example, the solution may be generated by a classical computing device.

[0077] At block 408, for example, it may be determined whether the solution of the quantum computing system model satisfies a threshold solution. In some embodiments, the threshold solution may be based on a threshold quality. For example, the threshold quality may be a percentage (e.g., 50%, 65%, 75%, 85%, or any other percentage that may indicate how well the solution of the quantum computing system model approximates the calculated solution) that may be mathematically combined (e.g., through multiplication) with the calculated solution to obtain a threshold solution. The solution satisfying the threshold solution may indicate that the quantum computing system model has determined a solution for the data subsets with acceptable accuracy. In response to the solution satisfying the threshold solution, method 400 may proceed to block 412.

[0078] At block 410, in response to the solution not satisfying the threshold solution, the method 400 may include adjusting the quantum circuit depth. The solution not satisfying the threshold solution may indicate that the quantum computing system model has not determined a solution for the data subsets with acceptable accuracy. In these and other embodiments, the parameters may be further adjusted. First, the quantum circuit depth may be adjusted. In some embodiments, adjusting the quantum circuit depth may include adding to the quantum circuit depth. Adding to the quantum circuit depth may include adding one or more layers to the quantum circuit depth. In these and other embodiments, the added layer may be added to the beginning of an existing layer, between existing layers, or at the end of an existing layer. In some embodiments, the added layer may be added in the middle of an existing layer.

[0079] At block 412, it may be determined whether the size of the data subset is less than the size of the data set and / or all available qubits have been utilized. An available qubit may be any qubit that is not encoded to perform a specific task, such as performing a computation or error mitigation at a given time. If it is determined at block 412 that the size of the data subset is the size of the data set or that all available qubits have been utilized, the method may proceed to block 414. If it is determined at block 412 that the size of the data subset is the size of the data set or that all available qubits have been utilized, the method may proceed to block 416.

[0080] At block 414, method 400 may include an act of adjusting the sizes of the data subsets. Adjusting the sizes of the data subsets may include increasing the number of nodes in each data subset. For example, the data subsets may have a number of nodes n, and each of the data subsets may be increased to have a number of nodes n+1. In some embodiments, when act 414 of adjusting the sizes of the data subsets is performed, utilization of available qubits may be changed such that one or more available qubits that were not utilized are utilized based on the additional nodes in each of the data subsets.

[0081] At block 416, the method 400 may include generating a quantum computing system model using the trained parameters. In some embodiments, the method 400 may further include generating a solution to a second data set using the quantum computing system model.

[0082] Modifications, additions, or omissions may be made to method 400 without departing from the scope of the present disclosure. For example, the designation of different elements in the manner described is intended to help explain the concepts described herein and is not intended to be limiting. Additionally, method 400 may include any number of other elements or may be implemented in other systems or contexts other than those described.

[0083] 5 illustrates an exemplary computing system 500 in accordance with one or more embodiments of the present disclosure. The computing system 500 may include a processor 502, a memory 504, a data storage 506, and / or a communication unit 508, all of which may be communicatively coupled. For example, the classical computing device 102 in the environment 100 of FIG. 1 may be implemented as a computing system consistent with the computing system 500.

[0084] In general, the processor 502 may include any suitable special purpose or general purpose computer, computing entity, or processing device, including various computer hardware or software modules, and may be configured to execute instructions stored on any applicable computer-readable storage medium. For example, the processor 502 may include a microprocessor, a microcontroller, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or any other digital or analog circuitry configured to interpret and / or execute program instructions and / or process data.

[0085] 5 as a single processor, it is understood that processor 502 may include any number of processors distributed across any number of networks or physical locations configured to individually or collectively perform any number of operations described in this disclosure. In some embodiments, processor 502 may interpret and / or execute program instructions and / or process data stored in memory 504, data storage 506, or memory 504 and data storage 506. In some embodiments, processor 502 may fetch program instructions from data storage 506 and load the program instructions into memory 504.

[0086] After the program instructions are loaded into memory 520, the processor 502 may execute the program instructions, such as instructions to cause the computing system 500 to perform method 300 of Figure 3 and method 400 of Figure 4. For example, the computing system 500 may execute program instructions to select 302 a data subset from a dataset, compare 306 a solution of the quantum computing system model to a threshold solution, and / or adjust 308 the quantum circuit depth.

[0087] Memory 504 and data storage 506 may include a computer-readable storage medium or one or more computer-readable storage media for storing computer-executable instructions or data structures. Such computer-readable storage media may be any available media that can be accessed by a general-purpose or special-purpose computer, such as processor 502. In some embodiments, computing system 500 may or may not include either memory 504 or data storage 506.

[0088] By way of example, and not limitation, such computer-readable storage media may include non-transitory computer-readable storage media including random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), compact disk read-only memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid-state memory devices), or any other storage medium that can be used to store desired program code in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computer. Combinations of the above may also be included within the scope of computer-readable storage media. Computer-executable instructions may include, for example, instructions and data configured to cause processor 502 to perform a certain operation or group of operations.

[0089] The communication unit 508 may include any component, device, system, or combination thereof configured to transmit or receive information over a network. In some embodiments, the communication unit 540 may communicate with other devices at other locations, at the same location, or even other components in the same system. For example, the communication unit 508 may include a modem, a network card (wireless or wired), an optical communication device, an infrared communication device, a wireless communication device (such as an antenna), and / or a chipset (such as a Bluetooth device, an 802.6 device (e.g., a metropolitan area network (MAN)), a WiFi device, a WiMax device, a cellular communication facility, etc.). The communication unit 508 may enable data to be exchanged with a network and / or any other device or system described in this disclosure. For example, the communication unit 508 may allow the computing system 500 to communicate with other systems, such as computing devices and / or other networks.

[0090] Those skilled in the art, after reviewing this disclosure, may recognize that modifications, additions, or omissions may be made to computing system 500 without departing from the scope of the disclosure. For example, computing system 500 may include more or fewer components than explicitly illustrated and described.

[0091] The foregoing disclosure is not intended to limit the disclosure to the precise form or specific field of use disclosed. Thus, various alternative embodiments and / or modifications to the disclosure are contemplated in light of the disclosure, whether expressly described or implied herein. Although embodiments of the disclosure have been thus described, it will be recognized that changes can be made in form and details without departing from the scope of the disclosure. Thus, the disclosure is limited only by the scope of the claims.

[0092] In some embodiments, the different components, modules, engines, and services described herein may be implemented as objects or processes (e.g., as separate threads) executing on a computing system. Although some of the systems and processes described herein are generally described as being implemented in software (stored and / or executed on general-purpose hardware), specific hardware implementations, or combinations of software and specific hardware implementations, are also possible and contemplated.

[0093] The terms used in this disclosure, and particularly in the appended claims (e.g., the body of the appended claims), are generally intended as "open terms" (e.g., the term "including" should be interpreted as "including, but not limited to").

[0094] Furthermore, if a specific number of claim recitations to be introduced is intended, such intent is expressly stated in the claim, and in the absence of such a statement, no such intent exists. For example, as an aid to understanding, the following appended claims may include the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation with the indefinite article "a" or "an" limits any particular claim that includes such an introduced claim recitation to an embodiment that includes only one such recitation, even if the same claim includes the introductory phrase "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should be construed to mean "at least one" or "one or more"). The same applies to the use of definite articles used to introduce claim recitations.

[0095] In addition, even when a particular number of introduced claim recitations is explicitly recited, one of ordinary skill in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the recitation "two recitations" without other modifiers means at least two recitations, or more than two recitations). Furthermore, when idiomatic expressions similar to "at least one of A, B, and C, etc." or "one or more of A, B, and C, etc." are used, such constructions are generally intended to include A only, B only, C only, both A and B, both A and C, both B and C, or all of A, B, and C, etc.

[0096] Moreover, any disjunctive phrase preceding two or more alternative terms, whether in the present text, claims, or drawings, should be understood to contemplate the possibility of including one of those terms, either of those terms, or both of those terms. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B."

[0097] Additionally, the use of terms such as "first", "second", "third", etc., is not necessarily used herein to imply a particular order or number of elements. In general, terms such as "first", "second", "third", etc., are used as general identifiers to distinguish between different elements. In the absence of any indication that terms such as "first", "second", "third", etc., imply a particular order, these terms should not be understood to imply a particular order. Additionally, in the absence of any indication that terms such as "first", "second", "third", etc., imply a particular number of elements, these terms should not be understood to imply a particular number of elements. For example, a first widget may be described as having a first side and a second widget may be described as having a second side. Use of the term "second side" with respect to a second widget may be to distinguish such side of the second widget from the "first side" of the first widget, and not to imply that the second widget has two sides.

[0098] All examples and conditional language described in this disclosure are intended for educational purposes to help the reader understand the concepts contributed by the inventor to further the art, and should be interpreted without limitation to such specifically described examples and conditions. Although the embodiments of the present disclosure have been described in detail, various changes, substitutions, and alterations can be made without departing from the spirit and scope of the present disclosure.

[0099] The following supplementary notes are further disclosed regarding the embodiments including the above examples. (Appendix 1) selecting a plurality of data subsets from the data set; training, using a quantum computer over a plurality of iterations, a plurality of parameters of a quantum computing system model using the plurality of data subsets and the quantum circuit depth; generating solutions for the plurality of data subsets using the quantum computing system model and the quantum computer; comparing the solution to a threshold solution; adjusting the quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution; and retraining, using the quantum computer, the parameters of the quantum computing system model using the plurality of data subsets and the adjusted quantum circuit depth. method. (Appendix 2) selecting a plurality of second data subsets, each of the plurality of second data subsets being a size greater than each of the plurality of data subsets; and training the parameters of the quantum computing system model using the second subsets of data and the quantum circuit depth using the quantum computer over the multiple iterations. The method described in Appendix 1. (Appendix 3) 3. The method of claim 2, wherein the second subsets of data are selected in response to a size of one of the plurality of data subsets being smaller than a size of the data set and not all available qubits of the quantum computer being utilized to train the parameters of the quantum computing system model. (Appendix 4) The method may further include generating a solution for a second data set using the trained quantum computing system model, wherein generating a solution for the second data set includes: a size of one of the plurality of data subsets is equal to the size of the data set; and all available qubits of the quantum computer are utilized to train the plurality of parameters of the quantum computing system model; 4. The method of claim 3, wherein the method is in response to at least one of the following: (Appendix 5) The dataset includes a plurality of interconnected nodes, and selecting the plurality of data subsets from the dataset includes: For each of said plurality of data subsets: Select the node; applying a search algorithm to select one or more neighbouring nodes of said node; The method described in Appendix 1. (Appendix 6) 2. The method of claim 1, wherein adjusting the quantum circuit depth includes placing one or more additional quantum logic gates in a quantum circuit of the quantum computer. (Appendix 7) 7. The method of claim 6, wherein the quantum circuit includes a plurality of quantum logic gates, the one or more additional quantum logic gates being disposed between a first quantum logic gate and a second quantum logic gate of the plurality of quantum logic gates. (Appendix 8) Each of the plurality of data subsets is weighted, and training the plurality of parameters comprises: selecting one of the plurality of data subsets based on a respective weight of the plurality of data subsets; training the plurality of parameters using the one of the plurality of data subsets and the quantum circuit depth; adjusting a weight applied to the one of the plurality of data subsets based on the training performed using the one of the plurality of data subsets. The method described in Appendix 1. (Appendix 9) adjusting the threshold solution based on the solution of the quantum computing system model. The method described in Appendix 1. (Appendix 10) generating a solution based on a second data set using the quantum computing system model trained using the plurality of parameters and the adjusted quantum circuit depth. The method described in Appendix 1. (Appendix 11) One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform the operations recited in Clause 1. (Appendix 12) a quantum computing device configured to train a plurality of parameters of a quantum computing system model over a plurality of iterations using a plurality of data subsets and a quantum circuit depth; a classical computing device communicatively coupled to the quantum computing device; 1. A system comprising: selecting said plurality of data subsets from the dataset; generating a solution for the plurality of data subsets using the quantum computing system model and the quantum computing device; comparing said solution to a threshold solution; adjusting the quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution and after adjusting the quantum circuit depth, the quantum computing device retrains the plurality of parameters of the quantum computing system model using the plurality of data subsets and the adjusted quantum circuit depth. (Appendix 13) the classical computing device is further configured to select a plurality of second data subsets, each of the plurality of second data subsets being a size greater than the plurality of data subsets; the quantum computing device is further configured to train the parameters of the quantum computing system model using the second subsets of data and the quantum circuit depth over the multiple iterations. 13. The system of claim 12. (Appendix 14) 14. The system of claim 13, wherein the second subsets of data are selected in response to a size of one of the plurality of data subsets being smaller than a size of the data set and not all available qubits of the quantum computing device being utilized to train the parameters of the quantum computing system model. (Appendix 15) The classical computing device further comprises: a size of one of the plurality of data subsets is equal to the size of the data set; and all available qubits of the quantum computing device are utilized to train the plurality of parameters of the quantum computing system model. and generating a solution to a second data set using the trained quantum computing system model in response to at least one of 15. The system of claim 14. (Appendix 16) The dataset includes a plurality of interconnected nodes, and the classical computing device extracts the plurality of data subsets from the dataset, and for each of the plurality of data subsets: Select the node; applying a search algorithm to select one or more neighboring nodes of said node; 13. The system of claim 12, configured to select by: (Appendix 17) 13. The system of claim 12, wherein adjusting the quantum circuit depth comprises placing one or more additional quantum logic gates in the quantum circuit of the quantum computing device. (Appendix 18) 18. The system of claim 17, wherein the quantum circuit includes a plurality of quantum logic gates, the one or more additional quantum logic gates being disposed between a first quantum logic gate and a second quantum logic gate of the plurality of quantum logic gates. (Appendix 19) Each of the plurality of data subsets is weighted, and training the plurality of parameters comprises: selecting one of the plurality of data subsets based on a respective weight of the plurality of data subsets; training the plurality of parameters using the one of the plurality of data subsets and the quantum circuit depth; adjusting a weight applied to the one of the plurality of data subsets based on the training performed using the one of the plurality of data subsets. 13. The system of claim 12. (Appendix 20) 13. The system of claim 12, wherein the classical computing device is further configured to generate a solution based on a second dataset using the quantum computing system model trained using the plurality of parameters and the adjusted quantum circuit depth. [Explanation of symbols]

[0100] 102 Classical Computing Devices 104 Datasets 106 Subset Selection 108 Data Subset 110 Quantum Computing Devices 112 Parameters 114 Training parameters 116 solution 118 Threshold Solution 120 Compare Solutions 122 Adjusting quantum circuit depth Select a data subset from a 302 dataset 304 The parameters of the quantum computing system model are trained using a quantum computer over multiple iterations using the data subset and quantum circuit depth. 306 Generate solutions for those data subsets using a quantum computing system model and a quantum computer. 308 The solution is compared with the threshold solution 310 Adjusting quantum circuit depth in response to the solution of a quantum computing system model not satisfying a threshold solution 312 Retrain the parameters of the quantum computing system model using a quantum computer with the data subset and adjusted quantum circuit depth. Selection of data subsets from the 402 dataset, quantum circuit depth, and threshold quality Using a quantum computer over 404 iterations, train the parameters of the quantum computing system model using the data subset and the quantum circuit depth. 406 Using a quantum computing system model and a quantum computer to generate solutions for said subsets of data. 408 Does the solution of the quantum computing system model satisfy the threshold solution? 410 Adjusting quantum circuit depth 412 Is the size of the data subset smaller than the size of the data set and / or are the available qubits not being utilized? 414 Adjust the size of the data subset Generate 416 quantum computing system models 500 Systems 502 processor 504 Memory 506 Data Storage 508 Communication Unit

Claims

1. selecting a plurality of data subsets from the dataset; training a plurality of parameters of a quantum computing system model using the plurality of data subsets and the quantum circuit depth using a quantum computer over a plurality of iterations; generating a solution for the plurality of data subsets using the quantum computing system model and the quantum computer; comparing the solution to a threshold solution; adjusting the quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution; and retraining the parameters of the quantum computing system model using the quantum computer using the plurality of data subsets and the adjusted quantum circuit depth. method.

2. selecting a plurality of second data subsets, each of the plurality of second data subsets being of a size greater than each of the plurality of data subsets; and training the parameters of the quantum computing system model using the second subsets of data and the quantum circuit depth using the quantum computer over the multiple iterations. The method of claim 1.

3. 3. The method of claim 2, wherein the second plurality of data subsets are selected in response to a size of one of the plurality of data subsets being smaller than a size of the data set and not all available qubits of the quantum computer being utilized to train the plurality of parameters of the quantum computing system model.

4. The method further includes generating a solution for a second data set using the trained quantum computing system model, wherein generating a solution for the second data set includes: a size of one of the plurality of data subsets equal to the size of the data set; and all available qubits of the quantum computer are utilized to train the plurality of parameters of the quantum computing system model; The method of claim 3, in response to at least one of:

5. The dataset includes a plurality of interconnected nodes, and selecting the plurality of data subsets from the dataset includes: For each of the plurality of data subsets: Select the node; applying a search algorithm to select one or more neighbouring nodes of said node; The method of claim 1.

6. 10. The method of claim 1, wherein adjusting the quantum circuit depth comprises placing one or more additional quantum logic gates in a quantum circuit of the quantum computer.

7. 7. The method of claim 6, wherein the quantum circuit comprises a plurality of quantum logic gates, and the one or more additional quantum logic gates are disposed between a first quantum logic gate and a second quantum logic gate of the plurality of quantum logic gates.

8. Each of the plurality of data subsets is weighted, and training the plurality of parameters includes: selecting one of the plurality of data subsets based on a respective weight of the plurality of data subsets; training the plurality of parameters using the one of the plurality of data subsets and the quantum circuit depth; adjusting a weight applied to the one of the plurality of data subsets based on the training performed using the one of the plurality of data subsets. The method of claim 1.

9. adjusting the threshold solution based on the solution of the quantum computing system model. The method of claim 1.

10. generating a solution based on a second data set using the quantum computing system model trained using the plurality of parameters and the adjusted quantum circuit depth. The method of claim 1.

11. One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause a system to perform the operations recited in claim 1.

12. a quantum computing device configured to train a plurality of parameters of a quantum computing system model over a plurality of iterations using a plurality of data subsets and a quantum circuit depth; a classical computing device communicatively coupled to the quantum computing device; 1. A system comprising: selecting the plurality of data subsets from a dataset; generating a solution for the plurality of data subsets using the quantum computing system model and the quantum computing device; comparing the solution to a threshold solution; adjusting the quantum circuit depth in response to the solution of the quantum computing system model not satisfying the threshold solution; and after adjusting the quantum circuit depth, the quantum computing device retrains the plurality of parameters of the quantum computing system model using the plurality of data subsets and the adjusted quantum circuit depth.

13. The classical computing device is further configured to select a plurality of second data subsets, each of the plurality of second data subsets being a size larger than the plurality of data subsets; the quantum computing device is further configured to train the parameters of the quantum computing system model using the second subsets of data and the quantum circuit depth over the multiple iterations. The system of claim 12.

14. 14. The system of claim 13, wherein the second plurality of data subsets are selected in response to a size of one of the plurality of data subsets being smaller than a size of the data set and not all available qubits of the quantum computing device being utilized to train the plurality of parameters of the quantum computing system model.

15. The classical computing device further comprises: a size of one of the plurality of data subsets equal to the size of the data set; and all available qubits of the quantum computing device are utilized to train the parameters of the quantum computing system model; and generating a solution to the second data set using the trained quantum computing system model in response to at least one of The system of claim 14.

16. The dataset includes a plurality of interconnected nodes, and the classical computing device extracts the plurality of data subsets from the dataset, and for each of the plurality of data subsets: Select the node; applying a search algorithm to select one or more neighboring nodes of said node; The system of claim 12 , configured to select by:

17. 13. The system of claim 12, wherein adjusting the quantum circuit depth comprises placing one or more additional quantum logic gates in a quantum circuit of the quantum computing device.

18. 20. The system of claim 17, wherein the quantum circuit comprises a plurality of quantum logic gates, and the one or more additional quantum logic gates are disposed between a first quantum logic gate and a second quantum logic gate of the plurality of quantum logic gates.

19. Each of the plurality of data subsets is weighted, and training the plurality of parameters includes: selecting one of the plurality of data subsets based on a respective weight of the plurality of data subsets; training the plurality of parameters using the one of the plurality of data subsets and the quantum circuit depth; adjusting a weight applied to the one of the plurality of data subsets based on the training performed using the one of the plurality of data subsets. The system of claim 12.

20. 13. The system of claim 12, wherein the classical computing device is further configured to generate a solution based on a second dataset using the quantum computing system model trained using the plurality of parameters and the adjusted quantum circuit depth.

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