Method and system for training a hybrid quantum-classical machine learning model

Abstract

A computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function.SOLUTION: The method includes providing a variable quantum noise source 30 in the variational quantum circuit, training a hybrid quantum-classical machine learning model based on variations of variational parameters of the variational quantum circuit to approximate a given labeling function with the variable quantum noise source introducing a non-zero training noise level into the variational quantum circuit, and providing the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model with the variable quantum noise source introducing a noise level different from the training noise level.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention is in the field of quantum machine learning. More precisely, the present invention relates to training methods for hybrid quantum-classical machine learning models and related systems. [Background technology]

[0002] Quantum computers provide a platform for controllable quantum mechanical systems whose states and interactions can be controlled to perform computations. Computation is realized through the deterministic evolution of the controllable quantum mechanical systems, and the state of the quantum mechanical systems can be measured to determine the outcome of the computation.

[0003] Quantum computers typically encode information in so-called qubits, which act as the quantum mechanical equivalent of classical bits. A qubit is a physical system whose quantum mechanical state can be (coherently) controlled and (effectively) preserved during a computation between two basis states, denoted in the following as |0> and |1>. As an example, qubits can be implemented by encoding information in the spin state of an electron, e.g., whether the electron is in an "up" or "down" state, but can also be encoded in the polarization state of a photon, the state of a (superconducting) oscillator, the energy levels of an atom, etc.

[0004] Control operations on these qubits are called quantum gates. Quantum gates can act coherently on qubits, e.g., to cause a change in the state of a single qubit (so-called single-qubit gates) and to act on multiple qubits (so-called multi-qubit gates), e.g., to entangle the states of multiple qubits and any combination thereof. For example, a single-qubit gate may cause a rotation of the electron's spin state by a selectable value, e.g., π / 2. A multi-qubit gate may act coherently on two or more qubits, such as a coherent CNOT operation on the states of two qubits. Multiple quantum gates can be applied to qubits in a quantum computer in parallel or in sequence to perform a computation. Finally, the states of the qubits may be repeatedly measured after applying a sequence of quantum gates to determine the probability for each possible outcome of the computation.

[0005] To compute solutions to problems that are considered intractable for classical computers, quantum computers can exploit the special properties of quantum mechanical states, in particular the superposition and entanglement of different quantum states, to find solutions in a relatively small number of computational steps or to access a large internal state space.

[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 that currently limit state-of-the-art quantum computers in both the number of controllable quantum mechanical systems (qubits) and the number of control operations (quantum gates) that can be successively performed.

[0007] Despite these drawbacks, there are promising applications for quantum processors available in the near future, namely, noisy intermediate-scale quantum (NISQ) devices, such as variational quantum algorithms. In variational quantum algorithms, the action of quantum gates is parameterized in terms of variational parameters, which can be systematically varied using classical computing resources in a manner similar to machine learning, for example, by implementing kernel methods to classify inputs using variational quantum circuits. The output of a variational quantum circuit can be "trained" to provide optimal solutions to a set of unknown inputs by varying the variational parameters to extremize a cost / loss function that attributes a cost to the output of the variational quantum circuit relative to the optimal solution. In these applications, entanglement between different qubits can provide access to a large internal state space to provide "quantum advantage." Summary of the Invention [Problem to be solved by the invention]

[0008] However, known methods and systems that implement machine learning type models using variational quantum circuits often suffer from overfitting, which reduces the accuracy of predictions of the objective function and fails to generalize to the training data provided, and the Ballen-Plateau problem, where a hybrid quantum-classical machine learning model may remain stuck in a local minimum without providing optimal performance. [Means for solving the problem]

[0009] In view of this state of the art, it is an object of the present invention to provide a method for training a hybrid quantum-classical machine learning model and corresponding system that can overcome problems associated with overfitting or unexpected convergence in local minima.

[0010] This object is solved by a method and a system according to the independent claims. The dependent claims relate to preferred embodiments.

[0011] According to a first aspect, a computer-implemented method is provided for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function. The variational quantum circuit comprises a plurality of variational quantum gates, where the actions of the plurality of variational quantum gates on qubits are parameterized by associated variational parameters, and a plurality of encoding gates for encoding input features of the labeling function in the quantum states of the qubits. The method includes providing a variable quantum noise source within the variational quantum circuit and training the hybrid quantum-classical machine learning model based on variation of the variational parameters of the variational quantum circuit to approximate the given labeling function with the variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit. The method further includes providing the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model having a variable quantum noise source configured to introduce a noise level different from the training noise level.

[0012] Noise in quantum mechanical systems typically causes decoherence of quantum states and is therefore typically associated with reduced reliability in quantum computing systems, which is often counteracted by the application of error correction strategies. However, the inventors have found that by controlling the amount of noise used to train a hybrid quantum-classical machine learning model, when the hybrid quantum-classical machine learning model is applied to validation data that differs from the training data, i.e., data not seen by the hybrid quantum-classical machine learning model during training, improvements in the accuracy of predicting the labeling function can be achieved for some non-zero addition of noise in the system.

[0013] Specifically, the inventors have found that introducing noise during the training phase, in which a hybrid quantum-classical machine learning model is trained based on training data, can improve predictions of labeling functions for validation data not encountered by the hybrid quantum-classical machine learning model during training. Thus, introducing noise can reduce the amount of overfitting on the training data or improve the generalization ability of a hybrid quantum-classical machine learning model trained with a variable quantum noise source that introduces a non-zero training noise level. The final trained hybrid quantum-classical machine learning model may be provided with a noise level that is less than the training noise level, for example, with the variable quantum noise source removed or with a lower noise level introduced by the variable quantum noise source.

[0014] In some examples, the variable quantum noise source introduces a quantum decoherence channel into the variational quantum circuit.

[0015] The quantum decoherence channel is thought to act on the quantum states of the qubits acted upon by the variational quantum circuit, for example, through a probabilistic action on the quantum states of the qubits and / or through a quantum decoherence channel that is inherent to the hardware implementation of the variational quantum circuit.

[0016] Decoherence generally arises as a result of the interaction between a quantum system and its environment. In the case of quantum processing units, the quantum state of the environment is generally not well known, and to account for imperfect knowledge, the state of the system qubits may be described in terms of a density matrix formalism. In general, the state of an N-qubit system interacting with its environment is described by a density matrix ρ as follows:

[0017]

number

[0018] This is the stochastic ensemble of pure states |ψ j >, where p j is the state of the system, |ψj >. The operation on this system is then performed using a set of Kraus operators E acting on the density matrix as follows: k can be explained in terms of:

[0019]

number

[0020] where the set of operators {E k} describes the quantum operation ε, often called the “quantum channel”, and obeys the completeness relation.

[0021]

number

[0022] In this context, the effect of noise can be understood as the effect of a particular quantum operation on the quantum states of the qubits used in a variational quantum circuit.

[0023] In some examples, the variable noise level parameterizes an additional amplitude damping channel, and / or an additional phase damping channel, and / or an additional depolarization channel.

[0024] Amplitude damping generally corresponds to the energy loss to the environment and can be described as the probability that a quantum system (qubit) in an excited state |1> decays to the "ground" state |0>, e.g., the relaxation process of electron spin states or between atomic / molecular energy levels. This amplitude damping channel is governed by a specific amplitude damping decay parameter γ AD can be described by the following set of Kraus operators:

[0025]

number

[0026] Phase damping represents a type of noise that destroys quantum coherence and generally corresponds to a contraction of the Bloch sphere in the xy plane. This is due to the specific phase damping channel attenuation parameter γ PD , and the density matrix that describes the completely classical probability distribution of the quantum states |0> and |1>, the limit γ PD → 1, resulting in the destruction of quantum superposition. The phase-damping channel can be described by the following set of Kraus operators:

[0027]

number

[0028] Depolarization noise corresponds to a qubit experiencing an "error" with probability p. Possible error types are phase flip (E1), bit flip (E2), or simultaneous phase bit flip (E3). In this case, the specific depolarization channel attenuation parameter γ DP The Kraus operator to describe the corresponding depolarization channel with ∇ ...

[0029]

number

[0030] In some examples, the variable quantum noise source includes additional idle time for the variational quantum circuit.

[0031] Introducing additional idle time as part of applying a variational quantum circuit to multiple qubits can introduce a controlled decoherence channel, which may introduce amplitude and phase damping depending on the underlying hardware architecture. The idle time may be distributed throughout the variational quantum circuit, for example, after application of each layer of quantum gates in the variational quantum circuit, or may be introduced at the end of the variational quantum circuit before measuring the qubit states. The probability of qubit energy and / or phase relaxation may be a function of idle time, such that by varying the idle time, the amount of amplitude and / or phase damping can be variably introduced into the variational quantum circuit.

[0032] In some examples, the variable quantum noise source comprises a randomly applied quantum gate, where the action of the randomly applied quantum gate is applied to a qubit of the variational quantum circuit with a parameterized probability.

[0033] Randomly applied quantum gates can introduce a controllable depolarization channel into a variational quantum circuit. For example, a random number generator may select the identity operator or one of the three Pauli operators to be applied to the state of one of the qubits, thereby stimulating the experience of a bit flip, a phase flip, or a simultaneous phase-bit flip, e.g., as given in equation (6).

[0034] In some examples, the randomly applied quantum gate implements the action of one of three Pauli operators, specifically based on a probabilistic selection that selects one of the three Pauli operators, each with a parameterized probability of one-third.

[0035] However, arbitrary rotations of qubit states, e.g., X, Y, or Z rotations on the Bloch sphere, or probabilistic applications of other quantum gates, such as stochastically applied multi-qubit gates, may also be used to implement depolarization channels, in examples, where the magnitude of the action and / or the type of action, such as the axis of rotation, may be determined randomly for each execution of the variational quantum circuit.

[0036] After the hybrid quantum-classical machine learning model is trained, the noise level may be reduced by reducing the amount of variable noise introduced by the variable quantum noise source, by removing the variable quantum noise source, etc. In some examples, the variable quantum noise source is implemented by controlling quantum error correction operation, e.g., by reducing quantum error correction to controllably increase quantum noise in a variational quantum circuit.

[0037] In some examples, the final trained hybrid quantum-classical machine learning model does not feature a variable quantum noise source.

[0038] For example, a final trained hybrid quantum-classical machine learning model may be provided without idle time introduced as a variable quantum noise source, and / or with randomly applied quantum gates removed or replaced with the action of the identity operator, and / or with increased or maximum error correction.

[0039] In some examples, the hybrid quantum-classical machine learning model features multiple variable quantum noise sources, e.g., to introduce a particular combination of amplitude / phase damping and depolarization noise. The noise levels may be controlled to optimize generalization of the training data by the hybrid quantum-classical machine learning model answer or to minimize overfitting of the training data.

[0040] In some examples, the noise level is a training hyperparameter that is systematically varied to minimize validation loss.

[0041] The hybrid quantum-classical machine learning model may be trained based on training data to predict the labeling function, and may be tested on validation data without a variable quantum noise source, where the noise level may be systematically varied such that the test accuracy in predicting the labeling function for the validation data is maximized.

[0042] The method may include, for example, obtaining a set of training data as discretized points representing a labeling function for supervised learning, and may further include obtaining a set of validation data as further discretized points representing the labeling function. The discretized points of the training / validation data may be considered to include a set of input data values, such as a vector of input features, and may further include corresponding labels recorded for the input data in the training / validation data of the set of input data values.

[0043] As a result, a hybrid quantum-classical machine learning model trained with the method according to the first aspect may feature improved accuracy when compared to a model trained without adding noise, and may therefore result in improved accuracy for classification and / or regression problems that inform the labeling function.

[0044] In some examples, the method further includes training the hybrid quantum-classical machine learning model for two different noise levels of the variable quantum noise source; determining a validation loss for the hybrid quantum-classical machine learning model trained at the two different noise levels based on a set of validation data that differs from the set of training data used to train the hybrid quantum-classical machine learning model; and determining an optimal training noise level for training the hybrid quantum-classical machine learning model based on the value of the validation loss, wherein the final trained hybrid quantum-classical machine learning model is trained at the optimal training noise level.

[0045] In other words, the method may include training a hybrid quantum-classical machine learning model at a first noise level and determining a validation loss associated with the first noise level; training the hybrid quantum-classical machine learning model at a second noise level and determining a validation loss associated with the second noise level, where the first noise level and the second noise level are different; and determining an optimal training noise level based on the first noise level and the second noise level. The first noise level and the second noise level may be based on different configurations of variable noise sources, such as different delay times during execution of a variational quantum circuit or different probabilities of randomly introducing additional quantum operations to include random manipulation of the quantum states of qubits. Training the hybrid quantum-classical machine learning model at two different noise levels may be part of systematically varying the training noise level as a hyperparameter of the training process.

[0046] Depending on the hardware architecture for implementing the variational quantum circuit, the method may also benefit from increasing both the training noise level and the noise of the trained hybrid quantum-classical machine learning model, i.e., having a variable noise source that introduces additional noise after training is complete.

[0047] According to a second aspect, a computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit for approximating a given labeling function is provided. The method includes obtaining a set of training data and a set of validation data, and providing a variational quantum circuit having a variable quantum noise source within the variational quantum circuit. The method further includes training the hybrid quantum-classical machine learning model based on variational parameters of the variational quantum circuit to approximate the given labeling function for the training data, where the hybrid quantum-classical machine learning model is trained for two different training noise levels of the variable quantum noise source, and determining a validation loss for each of the hybrid quantum-classical machine learning models trained at the two different training noise levels based on a set of validation data that is different from the set of training data used to train the hybrid quantum-classical machine learning model. The method further includes determining an optimal training noise level for training the hybrid quantum-classical machine learning model based on the value of the validation loss.

[0048] Depending on the noise level inherent in the hardware for implementing the hybrid quantum-classical machine learning model, it may be sufficient or even optimal to increase both the training noise level and the noise level of the trained hybrid quantum-classical machine learning model.

[0049] In some cases, both the training noise level and the validation loss noise level are iteratively optimized to obtain an optimal set of noise levels for training the final trained hybrid quantum-classical machine learning model and / or for providing a final trained hybrid quantum-classical machine learning model with or without a variable quantum noise source at the optimal training noise level.

[0050] According to a third aspect, there is provided a trained hybrid quantum-classical machine learning model including a variational quantum circuit and trained to approximate a given labeling function, wherein the trained hybrid quantum-classical machine learning model is trained with a variational quantum circuit comprising a variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit during training such that validation loss of the hybrid quantum-classical machine learning model is minimized, and the trained hybrid quantum-classical machine learning model includes a variable quantum noise source having a noise level different from the training noise level.

[0051] The hybrid quantum-classical machine learning model may be trained by the method according to the first or second aspect and may feature any of the features imposed by the method of the first or second aspect, or any combination thereof, such as an optimal training noise level determined as part of the method according to the second aspect.

[0052] A hybrid quantum-classical machine learning model may be defined, for example, in terms of a quantum circuit architecture including several qubits and an arrangement of encoding gates, variational quantum gates, and multi-quantum gates to form a variational quantum circuit, optionally in terms of a specific hardware implementation, and to include a variable noise source. The hybrid quantum-classical machine learning model may further include variational parameters and noise levels, or any parameterization or implementation parameters thereof. The hybrid quantum-classical machine learning model may further define how inputs for a labeling function, e.g., feature vectors, are encoded in the quantum states of the qubits through the action of encoding gates, e.g., based on a selected encoding strategy and / or scaling function, and how the (measured) outputs of the variational quantum circuit are transformed toward labels of the labeling function, such as function values ​​or output classes.

[0053] The hybrid quantum-classical machine learning model may be implemented as part of a hybrid quantum-classical quantum computing system that may include quantum hardware and classical processing resources, which may include qubits and hardware for manipulating and measuring the states of the qubits according to a variational quantum circuit. The quantum hardware may be controlled to configure the classical processing resources to implement the hybrid quantum-classical machine learning model according to the first aspect and / or the second aspect and / or to implement training of the hybrid quantum-classical machine learning model.

[0054] According to a fourth aspect, there is provided a system for training a hybrid quantum-classical machine learning model including a variational quantum circuit for approximating a given labeling function. The system comprises a classical hardware-based processing system configured to establish a variational quantum circuit having a variable quantum noise source within the variational quantum circuit. The system is further configured to: train the hybrid quantum-classical machine learning model based on variational parameters of the variational quantum circuit to approximate the given labeling function with a variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit; and provide the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model with a variable quantum noise source configured to introduce a training noise level different from the training noise level.

[0055] In some examples, the variational quantum circuit is implemented in quantum hardware, and the processing system is configured to specify the quantum circuit architecture and / or variational parameters for implementing the hybrid quantum-classical machine learning model.

[0056] For example, the processing system may specify the number of qubits and the sequence of quantum gates in the variational quantum circuit as part of implementing the variational quantum circuit. The processing system may further specify operations for implementing variational noise sources, such as by specifying the location of randomly applied quantum gates within the variational quantum circuit and / or introducing idle time as part of the execution of the variational quantum circuit. In some examples, the processing system is configured to obtain a set of training data as discretized points representing a given labeling function.

[0057] In some examples, training the hybrid quantum-classical machine learning model includes iteratively optimizing variational parameters of the hybrid quantum-classical machine learning model to minimize a loss of the hybrid quantum-classical machine learning model when performing a task of providing a labeling result given an input feature vector of the set of training data.

[0058] The initial variational parameters of the variational quantum gate can encode an initial (random) guess for predicting the labeling function, and the results of evaluating the variational quantum circuit with the variational parameters can be (iteratively) measured to determine the corresponding label. Based on the label, the loss function can be classically evaluated to attribute a loss to the label, in other words, a measure of how good the label is is calculated.

[0059] Typically, the variable parameters are subsequently updated (iteratively) using a feedback loop implemented in a classical processing system so that the output approaches the optimal solution, i.e., the optimal label given the labeling function, making the entire method, including the operation of the variational quantum circuit and its control / optimization, a hybrid quantum-classical algorithm.

[0060] By training the system, one may iteratively and systematically vary the variational parameters so that the variational quantum circuit approximates the output label.

[0061] In some examples, training the hybrid quantum-classical machine learning model includes determining a loss associated with a labeling result of the hybrid quantum-classical machine learning model for a given input feature vector of the set of training data, and determining updates to variational parameters of the hybrid quantum-classical machine learning model based on the loss.

[0062] The trainable parameters may be updated with known techniques employed in classical machine learning, such as gradient-based optimization algorithms such as stochastic gradient descent or adaptive moment estimation, or gradient-free optimization such as simulated annealing. Preferably, the optimization algorithm is gradient-based, and the method may include determining the gradient of the trainable parameters with respect to a loss attributed to the output label by the loss function.

[0063] In some examples, the processing system is configured to specify the behavior of the quantum gate based on a random selection during different runs of the variational quantum circuit during training to implement a variable quantum noise source.

[0064] For example, the processing system may specify whether the quantum state of one of the qubits is modified based on the nature of the random selection and / or modification, e.g., a rotation axis and / or a rotation angle for rotating the state of one of the qubits on the Bloch sphere.

[0065] During training, a variational quantum circuit may feature a randomly applied quantum gate applied to one of the qubits, a subset of the qubits, or all of the qubits, and / or may feature multiple randomly applied quantum gates applied to one of the qubits. Corresponding randomly applied quantum gates may be distributed throughout the variational quantum circuit or may be applied at the end of the variational quantum circuit. However, because variational quantum circuits generally feature entanglement between all of the qubits, it may be sufficient to introduce quantum noise to one of the qubits, a subset of the qubits, or to all of the qubits at a particular point within the variational quantum circuit.

[0066] In some examples, the system is configured to train a hybrid quantum-classical machine learning model for two different noise levels of a variable quantum noise source and determine a validation loss for the hybrid quantum-classical machine learning model trained at the two different noise levels for a set of validation data, the system is further configured to determine an optimal training noise level for training the hybrid quantum-classical machine learning model based on the value of the validation loss, and the trained hybrid quantum-classical machine learning model is trained at the optimal training noise level.

[0067] Training the hybrid quantum-classical machine learning model for two different noise levels may be part of iteratively optimizing the training noise level to minimize the validation loss of the hybrid quantum-classical machine learning model. Those skilled in the art will understand that the optimal training noise level may be approximated or estimated based on the validation losses obtained at two different noise levels or based on previous training processes of similar quantum circuit architectures and / or labeling functions, and may not be strictly optimal when compared to an infinite number of iterative optimization steps. Rather, the optimal training noise may be an optimal noise estimate that takes into account information about the validation losses at the two different noise levels to minimize the validation loss.

[0068] The system may implement the method according to the first embodiment, or any combination of the embodiments. In particular, the system according to the fourth aspect may also benefit from any feature of the preferred embodiments of the first or second aspects. In addition, the system according to the fourth aspect may be configured to provide the model of the third aspect. As a further alternative aspect, the system may be configured to implement the method of the second aspect based on corresponding processing steps of a processing system.

[0069] The system may be controlled using a processing system, which may include a single processing unit or multiple processing units that may be operatively connected. The processing unit may include a microcontroller, an ASIC, a PLA (CPLA), an FPGA, or other processing device, including processing devices that operate based on software, hardware, firmware, or a combination thereof. The processing device may include integrated memory or communicate with external memory, or both, and may further include interfaces for connecting to sensors, devices, instruments, integrated logic circuits, other controllers, etc., which may be configured to receive or transmit signals, such as electrical, optical, radio, acoustic, etc.

[0070] The system may comprise multiple servers for performing each step, although the processing steps may equally be performed by a single server or server system that may distribute internal computations across multiple processing devices.

[0071] A hybrid quantum-classical computing system may be implemented with a classical processing system that may have classical processing resources that process binary features based on a deterministic algorithm, and a quantum processing system implemented with multiple computational qubits that can be coherently manipulated with control operations.

[0072] A quantum processing system may comprise hardware for implementing quantum gates, such as by controlling the evolution of the state of a qubit through, for example, controlling the action of a function generator or laser on the computational qubit.

[0073] The classical processing system may determine the quantum circuit, variational parameters, coded gate actions based on input features, or a combination thereof, and may initiate or control the actions of hardware to manipulate the quantum state of the computational qubit. The classical processing system may receive and process the measurement output of the variational quantum circuit and may determine updated variational parameters or output labels based on the measurement output. Furthermore, the classical processing system may specify the noise level of the variable quantum noise source and / or specify the action of the variational quantum circuit implementing the variable quantum noise source based on, for example, a random selection of a random number generator. For example, the classical processing system may instruct the quantum hardware to implement the qubit state manipulation based on the random selection. Alternatively, the random selection may be generated by the quantum hardware, and the classical processing system may not be involved in selecting the gate action implementing the variable quantum noise source.

[0074] In some examples, the control system comprises a classical processing system implemented in classical hardware.

[0075] According to a fifth aspect, there is provided a computer program comprising machine-readable instructions which, when executed by a processing unit, causes the processing unit to implement a method according to the first aspect and / or the second aspect, a trained hybrid quantum-classical machine learning model according to the third aspect, and / or a system according to the fourth aspect.

[0076] The computer program may be provided on a non-transitory machine-readable medium. Thus, the non-transitory medium may be provided comprising machine-readable instructions which, when executed by a processing system, implement a method according to the first aspect or the second aspect, a trained hybrid quantum-classical machine learning model according to the third aspect, and / or a system according to the fourth aspect.

[0077] The machine-readable instructions may coordinate the training of a hybrid quantum-classical computing model or may implement a hybrid quantum-classical computing system to approximate a given labeling function based on previously obtained trainable parameters.

[0078] The machine-readable instructions may configure a plurality of variational quantum circuits, for example, by determining architecture or variational parameters of the variational quantum circuits and by instructing quantum manipulation hardware, such as a function generator for controllably manipulating the states of qubits in the quantum hardware, laser control hardware, etc., to implement the variational quantum circuits, including a variable quantum noise source. During implementation of the system or method, the computer program may provide an input vector of features to the variational quantum circuits and may receive measurement outputs of the variational quantum circuits.

[0079] In some examples, the machine-readable instructions determine parameter updates for the variational parameters. [Brief explanation of the drawings]

[0080] The features and many advantages of the methods, hybrid quantum-classical machine learning models and systems according to the present invention will be best understood from the detailed description of the preferred embodiments, when read in conjunction with the accompanying drawings. [Figure 1] FIG. 1 shows a schematic diagram of an example of a hybrid quantum-classical computing system for implementing and driving a variational quantum circuit. [Figure 2] FIG. 10 shows a schematic diagram of another example of a hybrid quantum-classical computing system for implementing and driving a variational quantum circuit. [Figure 3]1 is a flow diagram of a training method for determining optimal training noise according to an example. [Figure 4A] FIG. 1 illustrates an example of a variational quantum circuit including a variable quantum noise source. [Figure 4B] FIG. 1 illustrates an example of a variational quantum circuit including a variable quantum noise source. [Figure 5] FIG. 4C shows the results of simulating the training process of a variational quantum circuit similar to the circuit shown in FIGS. 4A and 4B. [Figure 6] FIG. 4C shows further results from simulating the training process of a variational quantum circuit similar to the circuit shown in FIGS. 4A and 4B. [Figure 7] FIG. 7 shows additional results of simulating the training process of a variational quantum circuit based on the example described in connection with FIGS. 5 and 6. [Figure 8] 1 is a flowchart of a training method for obtaining a trained hybrid quantum-classical machine learning model according to an example. [Figure 9] FIG. 1 illustrates an exemplary flowchart of a method for determining an optimized variational quantum circuit architecture for approximating a given labeling function. DETAILED DESCRIPTION OF THE INVENTION

[0081] FIG. 1 schematically illustrates an example of a hybrid quantum-classical computing system 10 for implementing and driving a variational quantum circuit, according to a schematic quantum circuit diagram. The schematic quantum circuit diagram illustrates the left-to-right evolution of quantum states for an exemplary number of computational qubits, and control operations for the qubits can be arranged along the lines of the qubit state evolution to illustrate the architecture or time sequence associated with the quantum circuit. Those skilled in the art will understand that additional coherent operations may be included as part of the quantum circuit, and that quantum circuits may be extended to any number of qubits. Furthermore, while the following description may refer to specific control operations, those skilled in the art will understand that different control operations may be used to implement the systems and methods of the present disclosure, depending, for example, on the physical representation of the qubits.

[0082] 1 includes a qubit register 12 that includes a plurality of computational qubits. A plurality of quantum gates 14 may act on the computational qubits of qubit register 12 to perform a computation / controlled evolution, and the variable actions of the plurality of quantum gates 14 may be parameterized by variational parameters. The results of the computation may be measured by measurement sensors 16 that project the states of the computational qubits onto the computational basis states of hybrid quantum-classical computation system 10. The results may be received by control system 18.

[0083] Control system 18 may be configured to repeatedly perform a computation sequence. The computation sequence may include initializing the computation qubits in qubit register 12 before each computation, such as to a basis state of each computation qubit to form an initial computation qubit state of |00...0>. Initialization of the computation qubits to their respective basis states may, in some examples, include a relaxation process, and initialization of the computation qubits may not require active control of the computation qubits.

[0084] Control system 18 may then apply multiple quantum gates 14 to the computation qubits in qubit register 12 to drive the coherent evolution of the computation qubits. Control system 18 may optionally generate a superposition state of all of the computation qubits, for example, by applying a Hadamard gate to each of the computation qubits, and subsequently apply multiple quantum gates 14, including variational quantum gates with variable action.

[0085] In a variational quantum circuit, the actions of at least some of the quantum gates in the variational quantum circuit are parameterized such that the measurement output of a computational qubit is a function of variational parameters, such as rotation angles, that parameterize the variable actions of the variational quantum gates. The combinatorial actions of at least partially parameterized quantum gates are sometimes referred to as variational quantum circuits.

[0086] Following coherent evolution, the state of the computational qubit in qubit register 12 may be measured by sensor 16. Measurement sensors 16 may be multiple single qubit state detectors for measuring the state of each computational qubit following evolution by multiple quantum gates 14. By repeating the measurements, the probability of each measurement outcome may be determined, and the results may be used to assign a label to an input vector of features. Based on the measurement outputs, control system 18 may classically calculate the "energy" / "cost" / "loss" of the label with a cost / loss function based on the labeling task. The labeling task may be specified according to a function that assigns a loss to the measurement output or the label derived therefrom, or may be specified according to pairs of sample input vectors of features and sample labels, e.g., as training data points representing the labeling function, and the loss may be based on the difference between the output label and the sample label.

[0087] Conventionally, control system 18 may repeat a computation sequence with adjusted variable actions based on the measurement results, such as to incrementally improve the quality of an output label associated with the measurement results. For example, control system 18 may repeat a computation sequence with adjusted operating parameters of the variational quantum gates to determine a gradient or energy landscape associated with multiple quantum gates 14 from the measurement results, and may update the variational parameters based on the estimated gradient to incrementally tune the variational quantum circuit toward an improved solution.

[0088] FIG. 2 illustrates another example of a hybrid quantum-classical computing system 10 for implementing and operating a variational quantum circuit. The system 10 includes a qubit register 12 including a plurality of computation qubits. A plurality of quantum gates 14 are arranged in layers of quantum gates 20 that can operate sequentially on the computation qubits of the qubit register 12 to perform a computation. Each layer of quantum gates 20 can include an encoding layer 22 and a variational layer 24, where the variational layer 24 includes a plurality of variational quantum gates, whose operations can be parameterized by different variational parameters in each layer of quantum gates 20. The encoding layer 22 includes a plurality of encoding gates, whose operations are parameterized based on values ​​of an input vector of features that are labeled according to a given labeling task. The encoding layers 22 in different layers of quantum gates 20 may be based on different subvectors 26 of an input vector of features, such that different layers of quantum gates 20 can encode different values ​​of the input vector of features into the states of the computation qubits. Each layer of quantum gates 20 may comprise, for example, as part of each variational layer 24, a multi-qubit gate for entangling the states of different computation qubits of qubit register 12, such as a plurality of CNOT gates as an entanglement gate for entangling the quantum states of at least two qubits of the computation qubits.

[0089] Application of variational layer 24 to the state of computation qubit 24 after the action of encoding layer 22 may prepare the quantum state of the computation qubit for encoding different features of the input vector of features in the next layer of quantum gate 20, or for encoding the same feature multiple times, optionally with scaling factors applied to the value of the feature.

[0090] To encode the values ​​of an input vector of features into quantum Hilbert space, one can use an "angle embedding" method, which involves rotating each qubit around an axis on the Bloch sphere, such as the Z axis (which could also be the X or Y axis), by an angle proportional to the value corresponding to each feature.

[0091] Subsequent application of multiple layers of quantum gates to the qubits may form a variational quantum circuit, where the variational quantum circuit is parameterized by the variational parameters of each layer. Each layer of quantum gates may comprise an entanglement gate for each computation qubit, such as to create a superposition state of the computation qubit. In some examples, each layer of quantum gates is configured to entangle the state of each computation qubit with at least one other qubit of the computation qubit. In some examples, each layer comprises multiple entanglement gates to create a superposition state of all of the computation qubits.

[0092] After all layers of quantum gates 20 act on the computation qubit, the result of the computation may be measured by measurement sensor 16, which may project the state of the computation qubit into a computational basis state of hybrid quantum-classical computation system 10. Based on the measurement output, which may be determined based on the measurement results obtained by measurement sensor 16 or based on measurement results obtained by measurement sensor 16 in multiple iterations of applying the variational quantum circuit to the computation qubit, control system 18 may determine an output label for labeling an input vector of features according to a given labeling task. Measuring the computation qubit multiple times allows the probability of measuring each of the computational basis states of the qubit to be determined for quantum states generated by the application of multiple quantum gates.

[0093] The variational parameters should be optimized to predict the best output label for an input vector of features given the labeling task according to a training algorithm, which may be an iterative process of updating the variational parameters according to estimated gradients associated with multiple quantum gates 14. However, the inventors have found that varying the level of noise in a variational quantum circuit can improve the accuracy of predicting the output label, if the noise level is chosen appropriately.

[0094] 3 illustrates a computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function. The method includes, for example, obtaining a set of training data and a set of validation data as discretized points representing the given labeling function (S10) and providing a variable quantum noise source within the variational quantum circuit (S12). The method further includes training the hybrid quantum-classical machine learning model based on variational parameters of the variational quantum circuit to approximate the given labeling function for two different training noise levels of the variable quantum noise source (S14). The method further includes determining a validation loss for each of the hybrid quantum-classical machine learning models trained at the two different training noise levels based on a validation data set different from the training data set used to train the model (S16). The method further includes determining an optimal training noise level for training the hybrid quantum-classical machine learning model based on the validation loss value (S18).

[0095] Thus, the present method provides a variable quantum noise source that can vary the noise level during training of a hybrid quantum-classical machine learning model and increase it above the baseline noise level of the implementation hardware for implementing a variational quantum circuit. In principle, adding noise to a quantum circuit increases the randomness of the measurement output and therefore reduces the accuracy of the quantum computation performed by the variational quantum circuit. However, the inventors have found that, for example, when optimizing the level of noise as a training hyperparameter, regularization can be achieved in the quantum circuit, thereby improving the quantum machine learning prediction accuracy with added noise, achieving a notable departure from the findings and associations of previous research.

[0096] A training algorithm for training a hybrid quantum-classical machine learning model may include applying a variational quantum circuit to a sample input vector of features representing a point in training data; determining a loss associated with an output label for the sample input vector of features and an optimal label recorded in the training data for the sample input vector of features, where the output label is based on the measured output state of the variational quantum circuit for the input vector of features; and determining an update to variational parameters based on the loss. The update may be determined based on the loss for all points in the training data, and applying the cumulative update for all points in the training data may complete a training epoch of the iterative training algorithm. As an example of determining the update, the variational quantum circuit may be run with shifted variational parameters to determine a partial derivative of the loss function, and the variational parameters of the variational quantum circuit may be updated based on the partial derivative, for example, in a manner similar to stochastic gradient descent. The noise level may be iteratively improved by training the variational quantum circuit at different noise levels to minimize the validation loss of a model for approximating a labeling function by controlling a variable quantum noise source.

[0097] 4A shows an example of a variational quantum circuit 28 that includes a variable quantum noise source 30. The illustrated variational quantum circuit 28 comprises a plurality of single-qubit gates 32 (shown as square boxes), such as encoding gates or variational gates, and a plurality of multi-qubit gates 34 that affect the states of the plurality of qubits, e.g., to induce entanglement between the respective qubits. Measurement sensor 16 may measure the states of the qubits after variational quantum circuit 28 has been executed, such as to infer a characteristic outcome for a feature vector of input data encoded in the qubit states through the encoding gates.

[0098] Additionally, variational quantum circuit 28 comprises a variable quantum noise source 30 that is applied to the state of each qubit after the application of one of quantum gates 32, 34. In the illustrated example, variable quantum noise source 30 consists of a gate delay that introduces a variable period of time after the application of each quantum gate 32, 34 so that energy relaxation or dephasing processes inherent in the hardware can introduce quantum noise in the qubit state.

[0099] The gate delay for introducing a particular noise level may be determined by the processing system based on a specified damping parameter γ, using the Krauss operators of Equations (4) and (5) for amplitude damping and phase damping, respectively, and the set of Kraus operators E according to Equation (2): k can be expressed by application of the operators described in section .

[0100] 4B shows another example of a variational quantum circuit 28 that includes a variable quantum noise source 30. In FIG. 4B, instead of introducing a gate delay, a single qubit operation is introduced as the variable quantum noise source 30, which introduces depolarization noise based on the probabilistic application of an additional quantum gate. In the illustrated example, a random number generator 36 may determine, based on a random selection for each run of the variational quantum circuit 28, whether the state of the qubit is manipulated at a particular point within the variational quantum circuit 28 and how the state of the qubit is affected. In the illustrated example, the random number generator 36 determines, based on a given damping parameter γ, whether the qubit is affected by an identity operator (no change in the qubit state) or whether the state of the qubit is affected by one of the Pauli operators, which correspond to the occurrence of a phase flip (E1), a bit flip (E2), or a simultaneous phase bit flip (E3), using the corresponding Krauss operator given in Equation (6).

[0101] Random manipulation of qubit states can simulate additional depolarization noise in the quantum system, and the damping parameter γ can variably determine the magnitude of the depolarization noise.

[0102] Figure 5 shows the training and validation losses for three different types of noise (amplitude damping AD, phase damping PD, and depolarization noise DP) and three different noise levels, as indicated in the legend, during a simulation of the training process of a variational quantum circuit 28, similar to the circuit shown in Figures 4A and 4B. The variational quantum circuit 28 is trained to approximate the "Diabetes Dataset," a commonly employed benchmark in machine learning, from which two baseline measurements (BMI and the logarithm (ltg) of serum triglyceride levels) are selected as input features, and the model is trained to predict a quantitative measure of disease progression one year after the baseline measurements. The dataset is separated into 40 training samples (each consisting of an input feature and a corresponding predicted value) and 400 validation samples. A hybrid quantum-classical machine learning model is trained based only on the training samples, and the graph on the left shows the mean squared error (MSE) of the prediction results for the training samples ("training loss"). The graph on the right shows the mean squared error (MSE) of prediction results for validation samples that were not encountered during training of the model ("validation loss").

[0103] The assumption for constructing the variational quantum circuit 28 initially consists of four qubits prepared in the |0> state. Two data features are then encoded onto the first and third qubits via two RX gates (x-axis rotations proportional to the feature value), respectively, referred to as the feature encoding layer 22. The feature encoding layer 22 is followed by a layer of single qubit RY gates (y-axis rotations) and a ring of symmetric RXX Ising gates, referred to as the variational layer 24.

[0104] The alternating feature encoding 22 and variational layers 24 can be repeated L times for a total depth of 4L quantum gates per qubit. Finally, simultaneous Pauli-Z measurements are performed on all four qubits and the expectation values ​​are interpreted as normalized predictions.

[0105] In the simulations, a variable quantum noise source 30 is introduced via application of a decoherence channel operation as described in relation to equations (2)-(6) for a particular type of noise, with the noise level parameterized by a respective decay parameter γ, using a variational quantum circuit 28 with L=5 coding layers 22 and variational layers 24.

[0106] In the figure, the resulting mean squared error (MSE) of the predicted values ​​compared to the correct labels of the training dataset is plotted against the number of epochs over which the variational parameters of the variational quantum circuit 28 were optimized, i.e., over which the hybrid quantum-classical machine learning model was trained and the variational parameters were updated. As can be seen from this data, for all types of noise (i.e., AD amplitude damping, PD phase damping, and DP depolarization noise), the mean squared error of the predicted values ​​of the training samples increases as the damping parameter γ increases, being lowest for the lowest error rate and highest for the highest error rate.

[0107] Conversely, for the validation loss shown on the right side of the figure, the lowest error rate / noise level is not associated with the lowest mean squared error in prediction quality, at least after about 10 training epochs. Rather, intermediate "optimal" noise levels result in low mean squared errors in validation loss in the trained models, indicating that the presence of noise during training can favorably affect the generalization and / or predictive ability of hybrid quantum-classical machine learning models.

[0108] Figure 6 shows the training loss and validation loss as a function of noise rate for three types of noise (amplitude damping AD, phase damping PD, and depolarization noise DP) resulting from simulating the training process of a variational quantum circuit 28 similar to the circuit shown in Figures 4A and 4B. The results are based on the example described in connection with Figure 5, again using a variational quantum circuit 28 with a fixed number of epochs of 20 and L = 5 coding layers 22 and variational layers 24. The solid line shows the validation loss in terms of MSE for predicting disease progression of the validation samples, and the dotted line shows the test loss in terms of MSE for predicting disease progression of the training samples. The horizontal dotted line shows the MSE of a naive model that always predicts y = 0 / 1 for the quantitative measure of disease progression. The vertical error bars show the standard error across 16 models trained with randomly initialized variational parameters for each value of the damping parameter γ.

[0109] As expected, the testing loss (dotted line) increases monotonically with increasing decay parameter γ for all types of noise sources, i.e., additional quantum noise in the variational quantum circuit 28 reduces the accuracy of predicting disease progression in training samples using a hybrid quantum-classical machine learning model. However, when considering validation loss, i.e., the accuracy of predicting disease progression as a labeling function for unseen validation samples, the mean squared error appears to feature a minimum for a particular decay parameter γ. In other words, the presence of noise appears to increase the accuracy of predicting disease progression in validation sample examples. In this example, for a particular range of decay parameters, the validation loss is smaller with additional noise than without any noise at all. In the illustrated example problem, an improvement of up to 8% is observed in the noisy model's ability to characterize the validation dataset relative to the noise-free model.

[0110] It should be noted that, based on our analysis, the noise levels currently realized in modern quantum computing systems can, in our example, already be lower than the noise levels introduced by variable quantum noise source 30. In particular, the noise levels T1, T2, and T3 realized in models known from the literature G Based on time, the amplitude and phase damping decay parameters have already been measured in the Google Sycamore quantum processor (based on values ​​reported in Arute et al., "Quantum supremacy using a programmable superconducting processor," Nature 574, 505 (2019)). -3 smaller, γ AD ≒8*10 -4 , and γ PD ≒6.3*10 -4 Therefore, the beneficial effects of increasing noise during training may already be obtained using currently available quantum processing resources.

[0111] Figure 7 shows additional results from simulating the training process of a variational quantum circuit 28 based on the example described in connection with Figures 5 and 6. The graph shows the relationship between the training noise γ T and feedforward noise γ F Figure 1 shows the optimal MSE values ​​obtained for different values ​​of σ, i.e., the noise used to determine the predictions using the validation samples. The MSE values ​​are presented according to a color scale with solid squares indicating validation losses below a first threshold, empty squares indicating validation losses above a second threshold, and hatched squares indicating validation losses between the first and second thresholds.

[0112] The distribution of validation loss is found to be asymmetric about the diagonal line 38, which indicates equal noise levels during training and validation, and is characterized by subregions 40 of reduced MSE within the region, with the training noise level γ T is the feedforward noise level γ F increases relative to

[0113] Thus, an optimal model may be provided based on an optimal selection of training noise that differs from the noise level introduced by variable quantum noise source 30 in the final trained quantum-classical machine learning model. For example, the noise level of both the training phase and the final model may be iteratively optimized.

[0114] In some examples, the amount of noise during training can be increased based on the effect of the variable quantum noise source 30, and the final trained quantum-classical machine learning model does not feature the variable quantum noise source 30 or does not feature a particularly low noise level that is different from the training noise level.

[0115] Although Figure 7 only illustrates the case of depolarization noise, similar effects can be observed for other quantum noise types, such as amplitude or phase damping. Those skilled in the art will further understand that the location and shape of the subregions 40 in Figure 7 are based on the selection of threshold parameters for showing MSE values ​​on a limited color scale and should not be considered to imply any limitations.

[0116] 8 schematically illustrates a method for training a hybrid quantum-classical machine learning model. The method includes providing a variable quantum noise source 30 within a variational quantum circuit 28 (S20). The method further includes training the hybrid quantum-classical machine learning model based on variational parameters of the variational quantum circuit 28 to approximate a given labeling function with the variable quantum noise source 30 that introduces a non-zero training noise level into the variational quantum circuit 28 (S22), and providing the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model having the variable quantum noise source 30 configured to introduce a noise level different from the training noise level (S24).

[0117] The training noise level may be determined empirically, for example, based on the method of FIG. 3 and / or iterative optimization of the training noise level and noise level of the trained hybrid quantum-classical machine learning model, or may be selected based on an estimate of the optimal noise, for example, based on historical data of similar circuit architectures or similar labeling functions.

[0118] The noise level of the final trained hybrid quantum-classical machine learning model may be estimated based on historical data and may be reduced relative to the training noise level. The variational parameters of the final trained hybrid quantum-classical machine learning model may be unaffected / unchanged by fluctuations in the noise level or may be adjusted to compensate for mean state manipulations resulting from differences between the training noise level and the noise level of the trained model. The trained quantum-classical machine learning model may then be deployed in a hybrid quantum-classical computing system 10 to predict labeling functions for unseen data.

[0119] The amount of noise added by variable quantum noise source 30 to optimize the training process may depend on the hardware implementation for implementing variational quantum circuit 28 and the variational quantum circuit architecture.

[0120] 9 shows an example flowchart of a method for determining an optimized variational quantum circuit (VQN) architecture for approximating a given labeling function, e.g., based on a regression or classification task. The illustrated method begins with determining a VQN architecture (e.g., in terms of a “hypothesis”), e.g., based on a selection of layers and their number, and the number of qubits, which may determine the number of quantum gates in the VQN architecture and the arrangement of the quantum gates, such as the depth of the variational quantum circuit 28, for the given labeling function.

[0121] The cumulative noise (CN) of a hardware implementation of a quantum gate of variational quantum circuit 28 may then be determined based on, for example, characteristic gate execution times, energy relaxation times, and phase relaxation times, as well as gate error probabilities measured or estimated for the hardware implementation.

[0122] Additionally, an optimal noise level may be determined for a VQN architecture, which may be based on the method shown in FIG. 3 or may be based on historical data of the same or similar VQN architectures.

[0123] The accumulated noise inherent in the hardware implementation of variational quantum circuit 28 may then be compared to an optimal noise level. If the accumulated noise is less than the optimal noise level, it may be determined that additional noise may improve model accuracy for unseen data (e.g., validation data), and the processing system may estimate or calculate parameters of variable quantum noise source 30 introduced into the VQN architecture to increase the training noise level of variational quantum circuit 28 to the optimal noise level.

[0124] If the cumulative noise of a hardware implementation of a VQN architecture is approximately equal to the optimal noise level, no additional variable quantum noise sources are added and the VQN architecture is provided as an optimal VQN architecture.

[0125] If the cumulative noise of a hardware implementation is determined to be greater than an optimal noise level, the complexity of the VQN architecture may be optionally reduced, such as to reduce the effective cumulative noise. For example, the depth of variational quantum circuit 28, e.g., the number of layers, may be reduced to adjust the cumulative noise to approximately equal to or below an optimal noise level, which may depend on the training data, the VQN architecture, and / or the labeling function.

[0126] Those skilled in the art will appreciate that the labeling function may be based on a regression or classification task on a set of input data values ​​and may be similar to corresponding tasks encountered in classical machine learning, such as image classification, predicting an optimal action based on a given set of state information, or estimating solutions to problems that are considered computationally difficult, e.g., estimating parameters of a fluid dynamics problem, satellite mission planning, the traveling salesman problem, or drug response prediction, to name a few.

[0127] The labeling task may include determining an optimal output label, e.g., an optimal next node, during satellite mission planning based on a set of data values ​​provided to the hybrid quantum-classical computing system as an input vector of features, such as a current snapshot state of operational parameters and known information such as the satellite's position.

[0128] Thus, in general, a vector of input features reflecting a set of data values ​​may be encoded into the quantum states of qubits, and the measurement outputs of the variational quantum circuit may be used to determine output labels for the set of input features, which optimally solves the labeling task based on a prior training process of the variational parameters.

[0129] The variational quantum circuit 28 may be implemented on quantum hardware. In our preliminary experiments, the variational quantum circuits 28s were generally implemented in simulations of quantum devices running on classical hardware. Even simulated variational quantum circuits 28s are often useful in some cases, and therefore the variational quantum circuit 28 may be implemented on a classical computer using a quantum simulator. However, the system is preferably implemented with variational quantum circuits 28s implemented on quantum hardware to reduce the classical processing power and computation time required to simulate complex quantum hardware.

[0130] On quantum hardware, the output of variational quantum circuit 28 may be measured as a measurement output, e.g., a projection of the qubit state between "0" and "1" for each qubit. The measurement output may then be used by the classical part of the hybrid quantum-classical computing system, i.e., a processing system based on deterministic hardware, to determine an output label corresponding to an input vector of features, e.g., by a predetermined mapping or using a classical machine learning model to interpret the output of variational quantum circuit 28, which may be trained jointly or independently with respect to the variational parameters of variational quantum circuit 28.

[0131] The values ​​of the input vector of features provided to the quantum hardware may be obtained from the set of input data values ​​through a transformation, such as a scaling function that scales the input values ​​to a range of angles between 0 and 2π, as part of an appropriate normalization function that may map the input data values ​​to a range of values ​​for the angle embedding.

[0132] In some examples, variational quantum circuit 28 may be combined with a classical machine learning classifier, such as, for example, an artificial neuron-based neural network, to solve a labeling task, such as by processing the output of the classical machine learning classifier with variational quantum circuit 28, by providing the output of the classical machine learning classifier based on the measurement output of variational quantum circuit 28, or both. The classical machine learning classifier may be trained together with the variational parameter optimization or separately.

[0133] The description of the preferred embodiment and the drawings merely serve to illustrate the invention and its associated beneficial effects and should not be understood as implying any limitation, the scope of which should be determined solely by the appended claims. [Explanation of symbols]

[0134] 10 Systems 12 qubit register 14 Multiple quantum gates 16 Measurement Sensors 18 Control System 20 layers of quantum gates 22 Coding Layers 24 Variational Layers 26 Subvectors of input data 28 Variational Quantum Circuits 30 Variable quantum noise source 32 Single-qubit gates 34 Multi-qubit gates 36 Random Number Generator 38 diagonal 40 small areas

Claims

1. 1. A computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit for approximating a given labeling function, the variational quantum circuit comprising: a plurality of variational quantum gates, the actions of the plurality of variational quantum gates on qubits being parameterized by associated variational parameters; and a plurality of encoding gates for encoding input features of the labeling function in quantum states of the qubits, the method comprising: providing a variable quantum noise source within the variational quantum circuit; training the hybrid quantum-classical machine learning model based on variations of the variational parameters of the variational quantum circuit to approximate the given labeling function with the variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit; providing the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model, the variable quantum noise source being configured to introduce a noise level different from the training noise level. Computer-implemented methods.

2. the variable quantum noise source introduces a quantum decoherence channel into the variational quantum circuit; The method of claim 1.

3. A variable noise level parameterizes an additional amplitude damping channel, and / or an additional phase damping channel, and / or an additional depolarization channel.

3. The method according to claim 1 or 2.

4. the variable quantum noise source includes additional idle time for the variational quantum circuit; and / or the variable quantum noise source comprises a randomly applied quantum gate, the action of which is applied to a qubit of the variational quantum circuit with a parameterized probability; 3. The method according to claim 1 or 2.

5. the randomly applied quantum gate implements the action of one of the three Pauli operators based on a probabilistic selection of one of the three Pauli operators, in particular with one-third of the parameterized probability, each of the three Pauli operators. The method of claim 4.

6. The training noise level is a hyperparameter of the training that is systematically varied to minimize validation loss.

3. The method according to claim 1 or 2.

7. The method comprises: training the hybrid quantum-classical machine learning model for two different training noise levels of the variable quantum noise source; determining a validation loss for each of the hybrid quantum-classical machine learning models trained at the two different training noise levels based on a set of validation data that is different from a set of training data used to train the hybrid quantum-classical machine learning models; determining an optimal training noise level for training the hybrid quantum-classical machine learning model based on the validation loss value, wherein the final trained hybrid quantum-classical machine learning model is trained at the optimal training noise level.

3. The method according to claim 1 or 2.

8. 1. A computer-implemented method for training a hybrid quantum-classical machine learning model that includes a variational quantum circuit for approximating a given labeling function, the method comprising: obtaining a set of training data and a set of validation data; providing a variational quantum circuit having a variable quantum noise source within the variational quantum circuit; training the hybrid quantum-classical machine learning model based on variations of variational parameters of the variational quantum circuit to approximate the given labeling function for the training data, wherein the hybrid quantum-classical machine learning model is trained for two different training noise levels of the variable quantum noise source; determining a validation loss for each of the hybrid quantum-classical machine learning models trained at the two different training noise levels based on a set of validation data that is different from the set of training data used to train the hybrid quantum-classical machine learning models; determining an optimal training noise level for training the hybrid quantum-classical machine learning model based on the validation loss value. Computer-implemented methods.

9. A trained hybrid quantum-classical machine learning model including a variational quantum circuit and trained to approximate a given labeling function, wherein the trained hybrid quantum-classical machine learning model is trained with the variational quantum circuit comprising a variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit during the training such that a validation loss of the hybrid quantum-classical machine learning model is minimized, and the trained hybrid quantum-classical machine learning model includes the variable quantum noise source having a noise level different from the training noise level. A trained hybrid quantum-classical machine learning model.

10. 1. A system for training a hybrid quantum-classical machine learning model including a variational quantum circuit for approximating a given labeling function, the system comprising: establishing a variational quantum circuit having a variable quantum noise source within the variational quantum circuit; training the hybrid quantum-classical machine learning model based on variations of variational parameters of the variational quantum circuit to approximate the given labeling function with the variable quantum noise source that introduces a non-zero training noise level into the variational quantum circuit; providing the hybrid quantum-classical machine learning model trained with the training noise level as a final trained hybrid quantum-classical machine learning model, the variable quantum noise source being configured to introduce a noise level different from the training noise level. system.

11. the variational quantum circuit is implemented in quantum hardware, and the processing system is configured to specify a quantum circuit architecture and / or variational parameters for implementing the hybrid quantum-classical machine learning model. The system of claim 10.

12. training the hybrid quantum-classical machine learning model includes iteratively optimizing the variational parameters of the hybrid quantum-classical machine learning model to minimize a loss of the hybrid quantum-classical machine learning model when performing a task of providing a labeling result given an input feature vector of a set of training data.

12. A system according to claim 10 or 11.

13. training the hybrid quantum-classical machine learning model includes determining a loss associated with a labeling result of the hybrid quantum-classical machine learning model for a given input feature vector of a set of training data; and determining updates to the variational parameters of the hybrid quantum-classical machine learning model based on the loss.

12. A system according to claim 10 or 11.

14. the processing system is configured to specify quantum gate behavior based on a random selection during different runs of the variational quantum circuit during the training to implement the variable quantum noise source.

12. A system according to claim 10 or 11.

15. 12. A computer program comprising machine-readable instructions, which when executed by a processing system, causes the processing system to implement the method of claim 1 or 2, or to implement the trained hybrid quantum-classical machine learning model of claim 9, or to implement the system of claim 10 or 11. Computer program.

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