Method and system for training mixed quantum-classical machine learning model

Abstract

The invention relates to a method and system for training a hybrid quantum-classical machine learning model. A computer-implemented method for training a hybrid quantum-classical machine learning model comprising a variable component sub-circuit to approximate a given marker function, the method comprising: providing a variable quantum noise source in the variable component sub-circuit; training a mixed quantum-classical machine learning model based on variation of variation parameters of the variable component sub-circuit to approach a given marking function, wherein a variable quantum noise source introduces a non-zero training noise level in the variable component sub-circuit; and providing a mixed quantum-classical machine learning model trained with the training noise level as a final trained mixed quantum-classical machine learning model, wherein the variable quantum noise source is configured to introduce a noise level different from the training noise level.

Description

Technical Field

[0001] The present invention belongs to the field of quantum machine learning. More specifically, the present invention relates to training methods for hybrid quantum-classical machine learning models and associated systems. Background Art

[0002] Quantum computers provide a platform for controllable quantum mechanical systems whose states and interactions can be manipulated to perform computations. Computations are performed by deterministically evolving these controllable quantum mechanical systems, and the states of these systems can be measured to determine the results of the computations.

[0003] Quantum computers typically encode information in so-called qubits, which serve as the quantum mechanical equivalent of classical bits. A qubit is a physical system whose quantum mechanical state can be (coherently) controlled during computation time and (substantially) maintained between two basis states, hereinafter referred to as |0> and |1>. For example, qubits can be implemented by encoding information in the spin state of an electron, for example, in the "up" or "down" state of an electron, but can also be encoded in the polarization state of a photon, the state of a (superconducting) oscillator, the energy level of an atom, and so on.

[0004] The control operations on these qubits are called quantum gates. Quantum gates can act coherently on qubits to induce changes in the state of a single qubit (so-called single-qubit gates) as well as on multiple qubits (so-called multi-qubit gates) (for example, in order to entangle the states of multiple qubits) and any combination thereof. For example, a single-qubit gate can induce the spin state of an electron to rotate to a selectable value (for example, π / 2). Multi-qubit gates can act coherently on two or more qubits, such as performing a coherent CNOT operation on the states of two qubits. Multiple quantum gates can be applied to the qubits of a quantum computer in parallel or sequentially to perform calculations. Ultimately, the state of the qubit can be repeatedly measured after applying a series of quantum gates to determine the probability of each possible outcome of the calculation.

[0005] To compute solutions to problems that are considered intractable on 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 or access a large internal state space in a relatively small number of computational steps.

[0006] However, superposition / entangled 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, so that state-of-the-art quantum computers are currently limited both in the number of controllable quantum mechanical systems (qubits) and the number of control actions (quantum gates) that can be performed consecutively.

[0007] Despite these shortcomings, recently available quantum processors (i.e., noisy intermediate-scale quantum (NISQ) devices) hold great promise for applications such as variational quantum algorithms. In variational quantum algorithms, the actions of quantum gates are parameterized by variational parameters, and these can be systematically varied with the help of classical computing resources in a manner similar to machine learning. For example, kernel methods for classifying inputs can be implemented using variational quantum circuits. By varying the variational parameters to maximize a cost / loss function (which gives the cost of the variational quantum circuit's output with respect to the optimal solution), the output of the variational quantum circuit can be "trained" to provide optimal solutions for unknown input sets. In these applications, entanglement between different qubits may provide a large internal state space, providing a "quantum advantage." Summary of the Invention

[0008] However, known methods and systems for implementing machine learning-type models using variational quantum circuits often suffer from overfitting, which can reduce the predictive accuracy of the objective function and fail to generalize to the provided training data, and can suffer from the problem of barren plateaus, where hybrid quantum-classical machine learning models can get stuck in local minima and fail to provide optimal performance.

[0009] In view of this prior art, the object of the present invention is to provide a method for training a hybrid quantum-classical machine learning model and a corresponding system, which can overcome problems related to overfitting or unintentional convergence to 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 for training a hybrid quantum-classical machine learning model comprising a variational quantum circuit to approximate a given labeling function is provided. The variational quantum circuit comprises: a plurality of variational quantum gates, the effects of which on quantum bits are parameterized by associated variational parameters; and a plurality of encoding gates for encoding input features for the labeling function in the quantum state of the quantum bits. The method comprises: providing a variable quantum noise source in the variational quantum circuit; and training the hybrid quantum-classical machine learning model to approximate the given labeling function based on variations in the variational parameters of the variational quantum circuit, wherein the variable quantum noise source introduces a non-zero training noise level in the variational quantum circuit. The method further comprises: providing the hybrid quantum-classical machine learning model trained using the training noise level as a final trained hybrid quantum-classical machine learning model, wherein the variable quantum noise source is configured to introduce a noise level different from the training noise level.

[0012] Noise in quantum mechanical systems typically leads to decoherence of quantum states and is therefore often associated with a reduction in the reliability of quantum computing systems, which is typically addressed by applying error correction strategies. However, the inventors have discovered that by controlling the amount of noise used to train a hybrid quantum-classical machine learning model, the accuracy of the predicted labeling function can be improved for certain non-zero noise added to the system when the hybrid quantum-classical machine learning model is applied to validation data that is different from the training data (i.e., data that was unknown to the hybrid quantum-classical machine learning model during training).

[0013] Specifically, the inventors discovered that introducing noise during the training phase of a hybrid quantum-classical machine learning model based on training data can improve the prediction of a labeling function for validation data, whereas the hybrid quantum-classical machine learning model did not encounter this situation during training. Therefore, the introduction of noise can reduce the amount of overfitting of the training data, or can improve the generalization ability of a hybrid quantum-classical machine learning model trained using a variable quantum noise source that introduces a non-zero training noise level. The final trained hybrid quantum-classical machine learning model can be provided with a noise level that is less than the training noise level, for example, where the variable quantum noise source is removed, or has a lower noise level introduced by the variable quantum noise source.

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

[0015] Quantum decoherence channels are believed to act on the quantum state of a qubit acted upon by a variational quantum circuit, for example through random actions on the quantum state of the qubit, and / or through quantum decoherence channels inherent to the hardware implementation of the variational quantum circuit.

[0016] Decoherence often arises as a result of the interaction between a quantum system and its environment. In the case of a quantum processing unit, the quantum state of the environment is often not well known, and the state of the system's qubits can be described in terms of a density matrix formalism to account for incomplete knowledge. Typically, the state of an N-qubit system interacting with the quantum system's environment can be described by the density matrix ρ

[0017]

[0018] It represents the pure state |ψ j > the probability ensemble, where p j The state of the system is |ψ j The operations on this system can then be expressed in terms of a set of Kraus operators E k To describe, these operators act on the density matrix as follows

[0019]

[0020] Among them, a set of operators {E k} describes a quantum operation ε, often called a 'quantum channel', and obeys the completeness relation

[0021]

[0022] In this context, the impact of noise can be understood as the effect of a particular quantum operation on the quantum state of the qubits used in the 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 energy loss to the environment and can be described as the probability that a quantum system (qubit) in an excited state "|1>" decays to a "ground" state "|0>" (e.g., relaxation between electron spin states or atomic / molecule energy levels). Amplitude damping with a specific decay parameter γ can be described by the following set of Kraus operators: A D The amplitude-damping channel:

[0025]

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

[0027]

[0028] Depolarization noise corresponds to a qubit experiencing an 'error' with probability p. Possible error types are phase flips (E1), bit flips (E2), or simultaneous phase-bit flips (E3). In this case, it can be described by the identity matrix and the three Pauli matrices describing the decay parameter γ for a specific depolarization channel. DP The Kraus operator for the corresponding depolarization channel, where the corresponding errors are applied with equal probability:

[0029]

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

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

[0032] In some examples, the variable quantum noise source includes a randomly applied quantum gate whose effects are applied with parameterized probabilities to qubits of the variational quantum circuit.

[0033] Randomly applied quantum gates can introduce controllable depolarization channels into variational quantum circuits. For example, a random number generator can select the unit 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, such as provided in Equation (6).

[0034] In some examples, the randomly applied quantum gate implements the effect of one of three Pauli operators, particularly selecting one of the three Pauli operators with a parameterized probability of one third based on random selection.

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

[0036] After a hybrid quantum-classical machine learning model has been trained, the noise level can be reduced, for example, by reducing the amount of variable noise introduced by a variable quantum noise source or by removing the variable quantum noise source. In some examples, the variable quantum noise source is implemented by controlling quantum error correction operations, for example, 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 variable quantum noise sources.

[0038] For example, a final trained hybrid quantum-classical machine learning model can be provided without introducing idle time as a source of variable quantum noise, and / or removing randomly applied quantum gates or replacing them with the actions of unit operators, and / or increasing or maximizing error correction.

[0039] In some examples, hybrid quantum-classical machine learning models have multiple variable quantum noise sources, for example to introduce a specific combination of amplitude-damping / phase-damping and depolarization noise. The noise level can be controlled to optimize the generalization of the hybrid quantum-classical machine learning model's answers to the training data 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 the validation loss.

[0041] The hybrid quantum-classical machine learning model can be trained on training data to predict a labeling function and can be tested on validation data in the absence of variable quantum noise sources, and the noise level can be systematically varied to maximize the test accuracy of predicting the labeling function for the validation data.

[0042] The method may include obtaining a training data set as discrete points representing a labeling function (e.g., for supervised learning), and may further include obtaining a validation data set as additional discrete points representing the labeling function. The discrete points of the training / validation data are considered to include a set of input data values, such as a vector of input features, and may further include corresponding labels for input data records in the training / validation data for the set of input data values.

[0043] Thus, a hybrid quantum-classical machine learning model trained using the method according to the first aspect can have higher accuracy when compared to a model trained without added noise, thereby providing higher accuracy for labeling functions in classification and / or regression problems.

[0044] In some examples, the method further includes: training the hybrid quantum-classical machine learning model for two different noise levels of a variable quantum noise source; determining a validation loss of the hybrid quantum-classical machine learning model trained using the two different noise levels based on a validation dataset different from the training dataset 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 hybrid quantum-classical machine learning model finally trained is trained using the optimal training noise level.

[0045] In other words, the method may include: training a hybrid quantum-classical machine learning model using a first noise level; determining a verification loss associated with the first noise level; training the hybrid quantum-classical machine learning model using a second noise level; and determining a verification loss associated with the second noise level, wherein 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 manipulations of the quantum state of a qubit. Training the hybrid quantum-classical machine learning model using 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 used to implement the variational quantum circuits, this approach may also benefit from increases in both the training noise level and the noise of the trained hybrid quantum-classical machine learning model, i.e., where variable noise sources introduce additional noise after training has been completed.

[0047] According to a second aspect, a computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function is provided. The method includes: obtaining a training dataset and a validation dataset; and providing a variable quantum noise source in the variational quantum circuit for the variational quantum circuit. The method further includes: training the hybrid quantum-classical machine learning model to approximate the given labeling function for the training data based on variations in a variational parameter of the variational quantum circuit, wherein the hybrid quantum-classical machine learning model is trained for two different training noise levels of the variable quantum noise source, and a validation loss corresponding to the hybrid quantum-classical machine learning model trained with the two different training noise levels is determined based on a validation dataset different from the training dataset 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 used to implement the hybrid quantum-classical machine learning model, increasing both the training noise level and the noise level of the trained hybrid quantum-classical machine learning model may be sufficient or even optimal.

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

[0050] According to a third aspect, a trained hybrid quantum-classical machine learning model is provided, which includes a variational quantum circuit and is trained to approximate a given labeling function, wherein the trained hybrid quantum-classical machine learning model has been trained using a variational quantum circuit including a variable quantum noise source so that a verification loss of the hybrid quantum-classical machine learning model is minimized, the variable quantum noise source introducing a non-zero training noise level in the variational quantum circuit during training, wherein 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 can be trained using the method according to the first aspect or the second aspect, and can have any features imposed by the method of the first aspect or the 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] The hybrid quantum-classical machine learning model can be defined according to a quantum circuit architecture, for example, including a plurality of qubits and an arrangement of encoding gates, variational quantum gates, and multi-quantum gates, optionally according to a specific hardware implementation, to form a variational quantum circuit, and including a variable noise source. The hybrid quantum-classical machine learning model can further include variational parameters and noise levels or any parameterized parameters or implementation parameters thereof. The hybrid quantum-classical machine learning model can further define how the input (e.g., feature vector) of the labeling function is encoded in the quantum state of the qubit through the action of the encoding gate (e.g., based on a selected encoding strategy and / or scaling function), and can further define how the (measured) output of the variational quantum circuit is transformed toward the label (e.g., function value or output class) of the labeling function.

[0053] The hybrid quantum-classical machine learning model can be implemented as part of a hybrid quantum-classical quantum computing system, which can include classical processing resources and quantum hardware. The quantum hardware can include qubits and hardware for manipulating and measuring the states of the qubits according to variational quantum circuits. The classical processing resources can be configured to control the quantum hardware to implement the hybrid quantum-classical machine learning model and / or perform training of the hybrid quantum-classical machine learning model according to the first and / or second aspects.

[0054] According to a fourth aspect, a system for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function is provided. The system includes a processing system based on classical hardware, the processing system being configured to establish a variational quantum circuit with a variable quantum noise source in the variational quantum circuit. The system is further configured to train the hybrid quantum-classical machine learning model to approximate the given labeling function based on variations in a variational parameter of the variational quantum circuit, wherein the variable quantum noise source introduces a non-zero training noise level in the variational quantum circuit, and provide the hybrid quantum-classical machine learning model trained using the training noise level as a final trained hybrid quantum-classical machine learning model, wherein the variable quantum noise source is 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, as part of implementing the variational quantum circuit, the processing system can specify the number of qubits and the sequence of quantum gates for the variational quantum circuit. The processing system can further specify operations for implementing a variational noise source, such as by specifying the locations of randomly applied quantum gates in the variational quantum circuit and / or by introducing idle time as part of executing the variational quantum circuit. In some examples, the processing system is configured to obtain a training dataset as discrete 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 the loss of the hybrid quantum-classical machine learning model when given an input feature vector of the training dataset to provide labeled results.

[0058] The initial variational parameters of the variational quantum gate can encode an initial (random) guess for predicting the label function, and the evaluation results of the variational quantum circuit with the variational parameters can be (repeatedly) measured to determine the corresponding label. Based on the label, the loss function can be classically evaluated to give the loss for the label, or in other words, to calculate a metric about how good the label is.

[0059] Typically, a feedback loop implemented in a classical processing system is then used to update (iterate) the variable parameters so that the output approaches the optimal solution (i.e., the optimal label given the labeling function), making the overall approach including the operation of the variational quantum circuit and its control / optimization a hybrid quantum-classical algorithm.

[0060] By training the system, the variational parameters can be systematically varied in an iterative manner so that the variational quantum circuit approximates the output label.

[0061] In some examples, training a hybrid quantum-classical machine learning model includes: determining a loss associated with a labeled result of the hybrid quantum-classical machine learning model for a given input feature vector of a training dataset; and determining an update to a variational parameter of the hybrid quantum-classical machine learning model based on the loss.

[0062] The trainable parameters can be updated using known techniques employed in classical machine learning, such as gradient-based optimization algorithms (e.g., stochastic gradient descent or adaptive moment estimation), or gradient-free optimization (e.g., 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 given by a loss function for the output label.

[0063] In some examples, the processing system is configured to specify roles of quantum gates during training based on random selections during different executions of the variational quantum circuit 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 a randomly selected and / or modified property, such as a rotation axis and / or rotation angle used to rotate the state of one of the qubits on the Bloch sphere.

[0065] During training, a variational quantum circuit can have randomly applied quantum gates applied to a single qubit, a subset of qubits, or all qubits in the qubits, and / or can have multiple randomly applied quantum gates applied to one qubit in the qubits. The corresponding randomly applied quantum gates can be distributed throughout the variational quantum circuit or applied at the end of the variational quantum circuit. However, since variational quantum circuits typically have entanglement between all qubits, it may be sufficient to introduce quantum noise to one qubit or a subset of qubits in the qubits, or to all qubits at a specific point in the variational quantum circuit.

[0066] In some examples, a 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 using the two different noise levels on a validation dataset. 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, wherein the trained hybrid quantum-classical machine learning model is trained using the optimal training noise level.

[0067] Training the hybrid quantum-classical machine learning model for two different noise levels can be part of iteratively optimizing the training noise level to minimize the verification loss of the hybrid quantum-classical machine learning model. A skilled person will understand that the optimal training noise level can be approximated or estimated based on the verification losses obtained for the two different noise levels or based on a previous training process for a similar quantum circuit architecture and / or labeling function, and that the optimal training noise level may not be strictly optimal when compared to an infinite number of iterative optimization steps. Instead, the optimal training noise can be an optimal noise estimate that takes into account information about the verification losses for the two different noise levels in order to minimize the verification loss.

[0068] The system may implement the method according to the first aspect or any combination of its embodiments. In particular, the system according to the fourth aspect may also benefit from any features 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, the system may be configured to implement the method of the second aspect based on corresponding processing steps of the processing system.

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

[0070] The system may include multiple servers for performing the corresponding steps, but the processing steps may also be performed by a single server or server system, which may distribute internal computations across multiple processing devices.

[0071] A hybrid quantum-classical computing system can be implemented using a classical processing system that can include classical processing resources that process binary features based on deterministic algorithms and a quantum processing system that is implemented using a plurality of computational qubits that can be coherently manipulated through control operations.

[0072] A quantum processing system may include hardware for implementing quantum gates, such as by controlling the evolution of qubit states (e.g., by controlling the action of a function generator or laser on a computational qubit).

[0073] The classical processing system can determine the quantum circuit, variational parameters, encoding gate actions based on input characteristics, or a combination thereof, and can initiate or control the actions of the hardware used to manipulate the quantum state of the computational qubit. The classical processing system can receive and process the measured output of the variational quantum circuit and can determine updated variational parameters or output labels based on the measured output. In addition, the classical processing system can specify the noise level of the variable quantum noise source and / or can specify the action of the variational quantum circuit that implements the variable quantum noise source, for example, based on random selections from a random number generator. For example, the classical processing system can instruct the quantum hardware to implement the state manipulation of the qubit based on the random selections. Alternatively, the random selections can be generated by the quantum hardware, and the classical processing system can be unaware of the selection of the gate action that implements the variable quantum noise source.

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

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

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

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

[0079] In some examples, the machine-readable instructions determine a parameter update for a variational parameter. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The features and numerous 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 with reference to the accompanying drawings, in which:

[0081] Figure 1 schematically illustrates an example of a hybrid quantum-classical computing system for implementing and driving a variational quantum circuit;

[0082] Figure 2 Another example of a hybrid quantum-classical computing system for implementing and driving a variational quantum circuit is schematically illustrated;

[0083] Figure 3 illustrates a flow chart of a training method for determining optimal training noise according to an example;

[0084] Figure 4A 、 Figure 4B An example of a variational quantum circuit including a variable quantum noise source is illustrated;

[0085] Figure 5 The diagram shows a simulation similar to Figure 4A 、 Figure 4B Results of the variational quantum circuit training process for the circuit shown in ;

[0086] Figure 6 The diagram shows a simulation similar to Figure 4A 、 Figure 4B Further results of the training process of the variational quantum circuit for the circuit shown in ;

[0087] Figure 7 The diagram shows the Figure 5 、 Figure 6 Additional results from the training process of the discussed example simulated variational quantum circuits;

[0088] Figure 8 illustrates a flow chart of a training method for obtaining a trained hybrid quantum-classical machine learning model according to an example; and

[0089] Figure 9 An example flow chart of a method for determining an optimized variational quantum circuit architecture for approximating a given labeling function is illustrated. DETAILED DESCRIPTION

[0090] Figure 1An example of a hybrid quantum-classical computing system 10 for implementing and driving a variational quantum circuit according to a schematic quantum circuit diagram is schematically illustrated. The schematic quantum circuit diagram depicts the evolution of the quantum state of an exemplary number of computational qubits from left to right, wherein control operations on the qubits can be arranged along the lines of the qubit state evolution to indicate the architecture or time sequence associated with the quantum circuit. A skilled person will appreciate that additional coherent operations can be included as part of the quantum circuit, and that the quantum circuit can be extended to any number of qubits. Furthermore, while reference may be made to specific control operations in the following description, a skilled person will appreciate that different control operations can be used to implement the systems and methods of the present disclosure, for example, depending on the physical representation of the qubits.

[0091] Figure 1 The illustrated system 10 includes a qubit register 12 containing a plurality of computational qubits. A plurality of quantum gates 14 can act on the computational qubits of the qubit register 12 to perform computations / controlled evolutions, wherein the variable actions of the plurality of quantum gates 14 can be parameterized by variational parameters. The results of the computations can be measured by a measurement sensor 16, which projects the states of the computational qubits onto a computational basis state of the hybrid quantum-classical computing system 10. The results can be received by a control system 18.

[0092] Control system 18 can be configured to repeatedly perform a computation sequence. The computation sequence can include initializing computation qubits in qubit register 12 prior to each computation, such as initializing each computation qubit to a ground state, for example, to form an initial state of the computation qubits |00…0>. In some examples, initializing the computation qubits to their respective ground states can include a relaxation process, and initialization of the computation qubits may not require active control of the computation qubits.

[0093] The control system 18 may then apply multiple quantum gates 14 to the computational qubits in the qubit register 12 to drive the coherent evolution of the computational qubits. The control system 18 may optionally generate a superposition state of all computational qubits, such as by applying a Hadamard gate to each computational qubit, and may then apply multiple quantum gates 14 including variational quantum gates with variable actions.

[0094] In a variational quantum circuit, the actions of at least some of the quantum gates in the variational quantum circuit are parameterized so that the measured output of a computational qubit is a function of a variational parameter (e.g., a rotation angle) that parameterizes the variable actions of the variational quantum gates. The combined action of at least partially parameterized quantum gates can be referred to as a variational quantum circuit.

[0095] After the coherent evolution, the state of the computational qubits in the qubit register 12 may be measured with a sensor 16. The measurement sensor 16 may be a plurality of single qubit state detectors for measuring the state of each computational qubit after evolution according to the plurality of quantum gates 14. Repeated measurements may allow the probability of each measurement outcome to be determined, and the results may be used to assign labels to the input vectors of the feature. Based on the measurement outputs, the control system 18 may classically calculate the "energy" / "cost" / "loss" of the label using a cost / loss function based on a labeling task. The labeling task may be specified in terms of a function that assigns a loss to the measurement output or a label derived from the measurement output, or the labeling task may be specified in terms of a sample input vector of the feature and a sample label pair, for example as a point in the training data representing the labeling function, where the loss may be based on the difference between the output label and the sample label.

[0096] Conventionally, the control system 18 can repeat the computation sequence with an adjusted variable action based on the result to gradually improve the quality of the output label associated with the measurement result. For example, the control system 18 can repeat the computation sequence with adjusted operating parameters for the variational quantum gates to determine the gradients or energy landscapes associated with the plurality of quantum gates 14 based on the measurement results, and can update the variational parameters based on the estimated gradients to gradually adjust the variational quantum circuit toward an improved solution.

[0097] Figure 2 Another example of a hybrid quantum-classical computing system 10 for implementing and driving a variational quantum circuit is illustrated. System 10 includes a qubit register 12 containing multiple computational qubits. Multiple quantum gates 14 are arranged in layers of quantum gates 20. These quantum gates can sequentially act on the computational qubits in qubit register 12 to perform computations. Each layer of quantum gates 20 can include an encoding layer 22 and a variational layer 24. Variational layer 24 includes multiple variational quantum gates, and the actions of these variational quantum gates can be parameterized by different variational parameters in each layer of quantum gates 20. Encoding layer 22 includes multiple encoding gates, whose actions are parameterized based on the values ​​of an input vector of features to be labeled, according to a given labeling task. Encoding layers 22 in different layers of quantum gates 20 can be based on different subvectors 26 of the input vector of features, allowing different layers of quantum gates 20 to encode different values ​​of the input vector of features into the states of computational qubits. Each layer of quantum gates 20 (e.g., as part of each variational layer 24) may include a multi-qubit gate (e.g., a plurality of CNOT gates) for entangling the states of different computational qubits of the qubit register 12, as an entanglement gate for entangling the quantum states of at least two qubits in the computational qubits.

[0098] Applying variational layer 24 to the state of computational qubit 24 following the action of encoding layer 22 may prepare the quantum state of the computational qubit for use in 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 feature values.

[0099] To encode the value of an input vector of features into the quantum Hilbert space, an “angle embedding” method can be utilized, which involves rotating the corresponding qubit around an axis (such as the Z axis on the Bloch sphere (it could also be the X axis or the Y axis)) by an angle proportional to the value corresponding to the corresponding feature.

[0100] Subsequent application of multiple layers of quantum gates to qubits can form a variational quantum circuit, where the variational quantum circuit is parameterized by the variational parameters of each layer. Each layer of quantum gates can include an entanglement gate for each computational qubit to create a superposition state of the computational qubits. In some examples, each layer of quantum gates is configured to entangle the state of each computational qubit with the state of at least one other qubit in the computational qubits. In some examples, each layer includes multiple entanglement gates to create a superposition state of all computational qubits.

[0101] The result of the computation can be measured by measurement sensor 16 after all layers of quantum gates 20 have acted on the computation qubit, wherein the measurement sensor 16 can project the state of the computation qubit onto the computation basis state of the hybrid quantum-classical computing system 10. Based on the measurement output (which can be based on a measurement result obtained using measurement sensor 16 or based on a measurement result obtained using measurement sensor 16 during multiple repetitions of applying the variational quantum circuit to the computation qubit), control system 18 can determine the output label for the input vector used to label the feature according to a given labeling task. Measuring the computation qubit multiple times can allow the probability of each computation basis state of the measurement qubit to be determined for the quantum state generated by applying multiple quantum gates.

[0102] The variational parameters should be optimized to predict the optimal output label for the input vector of features, given the labeling task according to a training algorithm, which can be an iterative process of updating the variational parameters based on estimated gradients associated with a plurality of quantum gates 14. However, the inventors have discovered that varying the noise level in the variational quantum circuit can improve the accuracy of the predicted output label if the noise level is appropriately selected.

[0103] Figure 3A computer-implemented method for training a hybrid quantum-classical machine learning model including a variational quantum circuit to approximate a given labeling function is illustrated. The method includes obtaining a training dataset and a validation dataset (S10), for example, as corresponding discrete points representing the given labeling function, and providing a variable quantum noise source in the variational quantum circuit (S12). The method further includes training the hybrid quantum-classical machine learning model to approximate the given labeling function based on changes in a variational parameter of the variational quantum circuit for two different training noise levels of the variable quantum noise source (S14), and determining corresponding validation losses for the hybrid quantum-classical machine learning model trained with the two different training noise levels based on a validation dataset different from the training dataset 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 value of the validation loss (S18).

[0104] Thus, the method provides a variable quantum noise source whose noise level can be varied during the training of a hybrid quantum-classical machine learning model and can exceed the baseline noise level of the hardware used to implement the variational quantum circuit. In principle, adding noise to a quantum circuit increases the randomness of the measured output, thereby reducing the accuracy of the quantum computation performed by the variational quantum circuit. However, the inventors discovered that when the noise level is optimized (e.g., as a hyperparameter of training), regularization can be achieved in the quantum circuit, thereby improving the prediction accuracy of quantum machine learning with increased noise, which significantly contradicts the findings and implications of previous research.

[0105] A training algorithm for training a hybrid quantum-classical machine learning model may include: applying a variational quantum circuit to a sample input vector representing a feature of a point in the training data; determining a loss associated with an output label of the sample input vector of the feature and an optimal label of the sample input vector of the feature recorded in the training data, wherein the output label is based on a measured output state of the variational quantum circuit for the input vector of the feature; and determining an update to the variational parameters based on the loss. The update can be determined based on the loss for all points in the training data, and applying the cumulative update to all points in the training data can complete one training cycle of the iterative training algorithm. As an example of determining the update, the variational quantum circuit can be executed using shifted variational parameters to determine partial derivatives of the loss function, and the variational parameters of the variational quantum circuit can be updated based on the partial derivatives, for example, in a manner similar to stochastic gradient descent. The noise level can be iteratively improved based on training the variational quantum circuit with different noise levels to minimize the model verification loss for approximating the labeling function by controlling the variable quantum noise source.

[0106] Figure 4AAn example of a variational quantum circuit 28 including a variable quantum noise source 30 is illustrated. The variational quantum circuit 28 shown includes a plurality of single-qubit gates 32 (illustrated as blocks) (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). After the variational quantum circuit 28 has been executed, the measurement sensor 16 can measure the states of the qubits in order to infer the characteristics of the eigenvectors of the input data encoded in the states of the qubits by the encoding gates.

[0107] Additionally, the variational quantum circuit 28 includes a variable quantum noise source 30 that is applied to the state of each qubit after application of one of the quantum gates 32, 34. In the example shown, the variable quantum noise source 30 consists of a gate delay that introduces a variable time period after application of each quantum gate 32, 34 so that energy or phase relaxation processes inherent to the hardware can introduce quantum noise in the qubit state.

[0108] The gate delay for introducing a specific noise level can be determined by the processing system based on a specified attenuation parameter γ and can be calculated according to Equation (2) by applying a set of Kraus operators E k The operation described is represented by the Krauss operator in equation (4) and equation (5) for amplitude damping and phase damping, respectively.

[0109] Figure 4B Another example of a variational quantum circuit 28 including a variable quantum noise source 30 is shown. Figure 4B In the example shown, instead of introducing gate delays, single-qubit operations are introduced as variable quantum noise sources 30, which introduce depolarization noise based on the random application of additional quantum gates. In the example shown, a random number generator 36 can determine whether the state of the qubit is manipulated at a specific point in the variational quantum circuit 28 based on a random selection for each execution of the variational quantum circuit 28, and how the state of the qubit is affected. In the example shown, the random number generator 36 determines whether the qubit is subjected to the action of a unit operator (no change in the qubit state) or whether the state of the qubit is subjected to the action of one of the Pauli operators (corresponding to a phase flip (E1), a bit flip (E2), or a simultaneous phase-bit flip (E3)) based on a given decay parameter γ, where the corresponding Krauss operators are given in equation (6).

[0110] Random manipulation of the qubit state can simulate additive depolarization noise in quantum systems, where the decay parameter γ can determine the size of the depolarization noise in a variable manner.

[0111] Figure 5 The diagram shows that Figure 4A and Figure 4B During the simulation of the training process of the variational quantum circuit 28 of the circuit shown, the training loss and validation loss for three different types of noise (amplitude damping AD; phase damping PD; and depolarization noise DP) and three different noise levels are shown in the legend. The variational quantum circuit 28 is trained to approximate the "diabetes dataset" commonly used in machine learning as a benchmark, from which two baseline measurements (BMI and the logarithm of serum triglyceride level (ltg)) are selected as input features, and the model is trained based on the input features to predict quantitative measurements of disease progression one year after the baseline measurement. The dataset is divided into 40 training samples (each sample consisting of an input feature and a corresponding predicted value) and 400 validation samples. The hybrid quantum-classical machine learning model is trained only based on the training samples, and the curve graph on the left illustrates the mean squared error (MSE) of the prediction results of the training samples ("training loss"). The curve graph on the right illustrates the mean squared error (MSE) of the prediction results of the validation samples that were not encountered during model training ("validation loss").

[0112] The simulation used to construct the variational quantum circuit 28 consists of four qubits initially prepared in the |0> state. Two data features are then encoded on the first and third qubits, respectively, via two RX gates (x-axis rotations proportional to the eigenvalues), referred to as the feature encoding layer 22. This feature encoding layer 22 is followed by a layer of single-qubit RY gates (y-axis rotations) and a symmetric ring of RXX Ising gates, referred to as the variational layer 24.

[0113] The alternating feature encoding layer 22 and variation layer 24 can be repeated L times, for a total depth of 4L quantum gates per qubit.Finally, a simultaneous Pauli-Z measurement is performed on all four qubits, and the expected value is interpreted as the normalized predicted value.

[0114] In the simulations, a variable quantum noise source 30 is introduced via application of the decoherence channel operation as discussed in conjunction with equations (2) to (6) for a particular type of noise, with the noise level parameterized by the corresponding attenuation parameter γ and using a variational quantum circuit 28 with a coding layer 22 and a variational layer 24 having L=5.

[0115] In the figure, the mean squared error (MSE) of the predicted values ​​compared to the correct labels of the training dataset is plotted against the number of cycles (i.e., the number of times the hybrid quantum-classical machine learning model is trained and the variational parameters are updated) over which the variational parameters of the variational quantum circuit 28 are optimized. As can be seen from the 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 with increasing attenuation parameter γ, is minimized when the error rate is lowest, and is maximized when the error rate is highest.

[0116] In contrast, for the validation loss indicated 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. Instead, the intermediate "optimal" noise level results in a lower mean squared error in validation loss for the trained model, indicating that the presence of noise during training may favorably affect the generalization and / or predictive capabilities of the hybrid quantum-classical machine learning model.

[0117] Figure 6 The diagram shows that by simulating Figure 4A and Figure 4B The training loss and validation loss as a function of the noise rate of three types of noise (amplitude damping AD; phase damping PD; and depolarization noise DP) generated by the training process of the variational quantum circuit 28 shown. Figure 5 Example discussed, where the number of epochs is fixed at 20 and a variational quantum circuit 28 with an encoding layer 22 and a variational layer 24 of L = 5 is used again. The solid line indicates the validation loss based on the MSE for predicting disease progression for the validation samples, and the dashed line indicates the test loss based on the MSE for predicting disease progression for the training samples. The horizontal dashed line indicates the MSE of a naive model that always predicts y = o / 1 for quantitative measurement of disease progression. The vertical error bars show the standard error on 16 models trained with randomly initialized variational parameters for each value of the decay parameter γ.

[0118] As expected, for all types of noise sources, the test loss (dashed line) increases monotonically with increasing decay parameter γ, i.e., the additional quantum noise in the variational quantum circuit 28 reduces the accuracy of predicting disease progression for training samples using the hybrid quantum-classical machine learning model. However, when the validation loss is considered, i.e., the accuracy of predicting disease progression as a function of the labeling of unknown validation samples, the mean squared error appears to reach a minimum at a specific decay parameter γ. In other words, in the example of validation samples, the presence of noise appears to improve the accuracy of predicting disease progression. In the example, for a specific range of decay parameters, the validation loss with added noise is less than the validation loss without noise. In the example problem shown, it is observed that the noisy model's ability to represent the validation dataset is improved by up to 8% relative to the noiseless model.

[0119] It should be noted that based on the inventors' analysis, the noise level currently achieved with contemporary quantum computing systems may already be lower than the noise level introduced by the variable quantum noise source 30 in the example. Specifically, based on T1, T2, and T G Time, the estimated attenuation parameters of amplitude damping and phase damping are less than 10 -3 , where for Google Sycamore quantum processor, γ AD ≈8*10 -4 And γ PD ≈6.3*10 -4 (Based on values ​​reported in Arute et al., “Quantum supremacy using a programmable superconducting processor,” Nature 574, 505 (2019).) Thus, the beneficial effects of increasing noise during training may have been achieved using currently available quantum processing resources.

[0120] Figure 7 The diagram shows the Figure 5 and Figure 6 Additional results of the training process for the simulated variational quantum circuit 28 of the discussed example. The graph illustrates: for depolarization noise (DP), relative to the training noise γ T and feedforward noise γ F The optimal MSE values ​​obtained for different values ​​of σ (i.e., the noise used to determine the predicted value using the validation samples). The MSE values ​​are provided according to a color scale, where solid squares indicate that the validation loss is below a first threshold, empty squares indicate that the validation loss is above a second threshold, and dashed squares indicate a validation loss between the first and second thresholds.

[0121] The distribution of validation loss is found to be asymmetric with respect to the diagonal line 38, which indicates that the noise levels during training and validation are equal. T Relative to the feedforward noise level γ F The enlarged region has islands 40 of reduced MSE.

[0122] Thus, an optimal model can be provided based on an optimal choice of training noise that is different from the noise level introduced by the variable quantum noise source 30 in the final trained quantum-classical machine learning model. For example, the noise level of the training phase and the final model can be iteratively optimized.

[0123] In some examples, the amount of noise during training can be increased based on the effect of the variable quantum noise source 30, while the final trained quantum-classical machine learning model does not have the variable quantum noise source 30, or has a different (particularly lower) noise level than the training noise level.

[0124] although Figure 7 Only the case of depolarization noise is illustrated, but similar effects can be observed for other quantum noise types (e.g., amplitude damping or phase damping). The skilled person will further understand that Figure 7 The positions and shapes of the islands 40 in are based on the choice of threshold parameters for illustrating the MSE values ​​in a limited color scale and should not be considered to imply any limitation.

[0125] Figure 8 A method for training a hybrid quantum-classical machine learning model is schematically illustrated. The method includes providing a variable quantum noise source 30 in a variational quantum circuit 28 (S20). The method further includes: training the hybrid quantum-classical machine learning model to approximate a given labeling function based on changes in a variational parameter of the variational quantum circuit 28, wherein the variable quantum noise source 30 introduces a non-zero training noise level in the variational quantum circuit 28 (S22), and providing the hybrid quantum-classical machine learning model trained using the training noise level as a final trained hybrid quantum-classical machine learning model, wherein the variable quantum noise source 30 is configured to introduce a noise level different from the training noise level (S24).

[0126] The training noise level can be obtained through experience (e.g., based on Figure 3 The noise level can be determined by a method and / or iterative optimization of the training noise level and the noise level of the trained hybrid quantum-classical machine learning model), or can be selected based on an estimate of the optimal noise (for example, based on historical data of similar circuit architectures or similar labeling functions).

[0127] The noise level of the final trained hybrid quantum-classical machine learning model can be estimated based on historical data and can be reduced relative to the training noise level. The variational parameters of the final trained hybrid quantum-classical machine learning model can be unaffected / changed by changes in the noise level, or can be adjusted to compensate for mean state manipulation resulting from differences in the training noise level and the noise level of the trained model. The trained quantum-classical machine learning model can then be deployed on the hybrid quantum-classical computing system 10 to predict label functions of unknown data.

[0128] The amount of noise added by variable quantum noise source 30 to optimize the training process may depend on the hardware implementation used to implement variational quantum circuit 28 and the variational quantum circuit architecture.

[0129] Figure 9 An example flow chart of a method for determining an optimized variational quantum circuit (VQN) architecture for approximating a given labeling function, for example, based on a regression task or a classification task, is illustrated. The illustrated method begins by determining a VQN architecture (e.g., based on a "presumption"), for example, based on a selection of layers and their number, as well as the number of qubits, which, for a given labeling function, can determine the number of quantum gates of the VQN architecture and their arrangement, such as the depth of the variational quantum circuit 28.

[0130] The cumulative noise (CN) of the hardware implementation of the quantum gates for the variational quantum circuit 28 may then be determined, for example, based on the characteristic gate execution time, energy relaxation time, and phase relaxation time, and gate error probabilities measured or estimated for the hardware implementation.

[0131] Additionally, an optimal noise level can be determined for the VQN architecture, which can be based on Figure 3 The method shown in , or can be based on historical data of the same or similar VQN architecture.

[0132] The accumulated noise inherent to the hardware implementation of the variational quantum circuit 28 can then be compared to the optimal noise level. If the accumulated noise is less than the optimal noise level, it can be determined that additional noise can improve the model accuracy of unknown data (e.g., validation data), and the processing system can estimate or calculate the parameters of the variable quantum noise source 30 introduced into the VQN architecture to increase the training noise level of the variational quantum circuit 28 to the optimal noise level.

[0133] If the cumulative noise of a hardware implementation of a VQN architecture is approximately equal to the optimal noise level, then no additional variable quantum noise sources are added, and the VQN architecture is provided as the optimal VQN architecture.

[0134] If it is determined that the cumulative noise of the hardware implementation is greater than the optimal noise level, the complexity of the VQN architecture can optionally be reduced to reduce the effective cumulative noise. For example, the depth (e.g., number of layers) of the variational quantum circuit 28 can be reduced to adjust the cumulative noise to be approximately equal to or less than the optimal noise level, which can depend on the training data, the VQN architecture, and / or the labeling function.

[0135] The skilled person will appreciate that the labeling function can be based on a regression task or a classification task for a set of input data values, and can be similar to corresponding tasks encountered in classical machine learning, such as image classification, predicting the 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 salesperson problem, or drug response prediction), just to give some examples.

[0136] 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 operating parameters and known information about the satellite (e.g., position).

[0137] Thus, in general, a vector reflecting the input features of a set of data values ​​can be encoded into the quantum state of a qubit, and the measured output of the variational quantum circuit can be used to determine the output label for the input feature set, which optimally solves the labeling task based on a previous training process of the variational parameters.

[0138] The variational quantum circuits 28 can be implemented in quantum hardware. In preliminary experiments by the inventors, the variational quantum circuits 28s were typically implemented as simulations of quantum devices running on classical hardware. In some examples, even simulated variational quantum circuits 28 can be beneficial, and thus the variational quantum circuits 28 can be implemented using a quantum simulator on a classical computer. However, the system is preferably implemented using variational quantum circuits 28s implemented in quantum hardware to reduce the classical processing power and computation time required to simulate complex quantum hardware.

[0139] On the quantum hardware, the output of the variational quantum circuit 28 can be measured as a measured output, for example, a quantum bit state projection of each quantum bit between "0" and "1." Subsequently, the classical portion of the hybrid quantum-classical computing system (i.e., a processing system based on deterministic hardware) can use the measured output to determine an output label corresponding to the input vector of features, for example, by a predetermined mapping or using a classical machine learning model for interpreting the output of the variational quantum circuit 28, which can be trained jointly or independently with respect to the variational parameters of the variational quantum circuit 28.

[0140] The values ​​of the input vector provided to the features of the quantum hardware can be obtained from the set of input data values ​​by a transformation, such as a scaling function as part of a suitable normalization function to, for example, scale the input values ​​to an angular range between 0 and 2π, which normalization function can map the input data values ​​to the value range used for the angular embedding.

[0141] In some examples, variational quantum circuitry 28 can be combined with a classical machine learning classifier (e.g., a neural network based on artificial neurons) to solve the labeling task, such that the output of the classical machine learning classifier is processed by variational quantum circuitry 28, the output of the classical machine learning classifier is provided based on the measured output of variational quantum circuitry 28, or both. The classical machine learning classifier can be trained together with or separately from the optimization of the variational parameters.

[0142] The description of the preferred embodiments and the accompanying drawings is only for illustrating the present invention and its associated advantageous effects, and should not be understood as implying any limitation. The scope of the present invention will be determined solely by the appended claims.

[0143] List of Reference Numerals

[0144] 10 System

[0145] 12-qubit register

[0146] 14 Multiple quantum gates

[0147] 16 measuring sensors

[0148] 18 Control System

[0149] 20 quantum gate layers

[0150] 22 Coding Layer

[0151] 24 Variation Layer

[0152] 26 subvectors of input data

[0153] 28 Variational Quantum Circuits

[0154] 30 Variable Quantum Noise Source

[0155] 32 single-qubit gates

[0156] 34 multi-qubit gates

[0157] 36 Random Number Generator

[0158] 38 diagonal

[0159] 40 islands

Claims

1. A computer-implemented method for training a hybrid quantum-classical machine learning model comprising a variational quantum circuit to approximate a given labeling function, the variational quantum circuit comprising a plurality of variational quantum gates and a plurality of encoding gates, the effects of the plurality of variational quantum gates on qubits being parameterized by associated variational parameters, the plurality of encoding gates being used to encode input features for the labeling function in the quantum states of the qubits, the method comprising: providing a variable quantum noise source in the variational quantum circuit; training the hybrid quantum-classical machine learning model to approximate the given labeling function based on changes in the variational parameter of the variational quantum circuit, wherein the variable quantum noise source introduces a non-zero training noise level in the variational quantum circuit; and The hybrid quantum-classical machine learning model trained using the training noise level is provided as a final trained hybrid quantum-classical machine learning model, wherein the variable quantum noise source is configured to introduce a noise level different from the training noise level.

2. The method according to claim 1, wherein The variable quantum noise source introduces a quantum decoherence channel into the variational quantum circuit.

3. The method according to claim 1 or 2, wherein The variable noise level parameterizes the additional amplitude damping channel and / or the additional phase damping channel and / or the additional depolarization channel.

4. A method as claimed in any one of the preceding claims, wherein The variable quantum noise source comprises additional idle time of the variational quantum circuit; and / or The variable quantum noise source comprises a randomly applied quantum gate, the action of which is applied to the quantum bits of the variational quantum circuit with parameterized probability.

5. The method according to claim 4, wherein: The randomly applied quantum gate implements the effect of one of the three Pauli operators, in particular selecting one of the three Pauli operators with one third of the parameterized probability based on a random selection.

6. A method as claimed in any one of the preceding claims, wherein The training noise level is a hyperparameter of the training that is systematically varied to minimize the validation loss.

7. A method as claimed in any one of the preceding claims, wherein The method further comprises: training the hybrid quantum-classical machine learning model for two different training noise levels of the variable quantum noise source; determining respective validation losses for the hybrid quantum-classical machine learning model trained with the two different training noise levels based on a validation dataset different from a training dataset used to train the hybrid quantum-classical machine learning model; An optimal training noise level for training the hybrid quantum-classical machine learning model is determined based on the value of the validation loss, wherein the final trained hybrid quantum-classical machine learning model is trained using the optimal training noise level.

8. A computer-implemented method for training a hybrid quantum-classical machine learning model comprising a variational quantum circuit to approximate a given labeling function, the method comprising: Obtain training and validation datasets; providing a variable quantum noise source in the variational quantum circuit for the variational quantum circuit; training the hybrid quantum-classical machine learning model to approximate the given labeling function of the training data based on changes in a variational parameter of the variational quantum circuit, wherein the hybrid quantum-classical machine learning model is trained for two different training noise levels of the variable quantum noise source; determining respective validation losses for the hybrid quantum-classical machine learning model trained with the two different training noise levels based on the validation dataset that is different from the training dataset used to train the hybrid quantum-classical machine learning model; and An optimal training noise level for training the hybrid quantum-classical machine learning model is determined based on the value of the validation loss.

9. A trained hybrid quantum-classical machine learning model comprising a variational quantum circuit and trained to approximate a given labeling function, wherein The trained hybrid quantum-classical machine learning model has been trained using the variational quantum circuit including a variable quantum noise source to minimize a validation loss of the hybrid quantum-classical machine learning model, wherein the variable quantum noise source introduces a non-zero training noise level in the variational quantum circuit during the training, wherein the trained hybrid quantum-classical machine learning model includes the variable quantum noise source having a noise level different from the training noise level.

10. A system for training a hybrid quantum-classical machine learning model comprising a variational quantum circuit to approximate a given labeling function, the system comprising a classical hardware-based processing system configured to: establishing the variational quantum circuit with a variable quantum noise source in the variational quantum circuit; training the hybrid quantum-classical machine learning model to approximate the given labeling function based on changes in a variational parameter of the variational quantum circuit, wherein the variable quantum noise source introduces a non-zero training noise level in the variational quantum circuit; The hybrid quantum-classical machine learning model trained using the training noise level is provided as a final trained hybrid quantum-classical machine learning model, wherein the variable quantum noise source is configured to introduce a noise level different from the training noise level.

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

12. The system of claim 10 or 11, wherein: Training the hybrid quantum-classical machine learning model includes iteratively optimizing the variational parameters of the hybrid quantum-classical machine learning model to minimize the loss of the hybrid quantum-classical machine learning model when tasked with providing a labeled result given an input feature vector of a training dataset.

13. The system of any one of claims 10 to 12, wherein: Training the hybrid quantum-classical machine learning model includes: determining a loss associated with a labeled result of the hybrid quantum-classical machine learning model for a given input feature vector of a training dataset; and determining an update to the variational parameters of the hybrid quantum-classical machine learning model based on the loss.

14. The system of any one of claims 10 to 13, wherein: The processing system is configured to specify roles of quantum gates to implement the variable quantum noise source during the training based on random selections during different executions of the variational quantum circuit.

15. A computer program comprising machine-readable instructions which, when executed by a processing system, cause the processing system to implement the method according to any one of claims 1 to 8 and / or to implement the trained hybrid quantum-classical machine learning model according to claim 9 and / or to implement the system according to any one of claims 10 to 14.

Images