Abrégé

Disclosed is an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. A method includes training of a differentiable quantum circuits (DCQ) based model, where data is encoded in a latent space with a phase feature map, followed by a variational quantum circuit. The trained model is then mapped to the bit basis using a fixed unitary transformation, coinciding with a quantum Fourier transform circuit in the simplest case. This allows fast sampling from parametrized distributions using a single-shot readout. Simplified latent space training provides models that are automatically differentiable. Samples from propagated stochastic differential equations (SDEs) can be accessed by solving a stationary Fokker-Planck equation and time-dependent Kolmogorov backward equation on a quantum computer. A route to multidimensional generative modelling is opened with qubit registers explicitly correlated via a (fixed) entangling layer.

Classes IPC  ?

• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard
• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels

Abrégé

Systems and methods are disclosed for solving a differential problem using a hybrid computer system comprising a classical computer system and a quantum processor. The method comprises receiving or determining one or more variational quantum circuits defining a parameterized quantum model of a trial function, and an integral formulation of the differential equation. The integral formulation defines an equation with a differential order that is smaller than the differential order of the differential equation, and incorporates at least part of the boundary condition. The integral formulation comprises a path integral with a first integration limit corresponding to a point on the boundary. The method further comprises determining a solution to the differential problem based on the parameterized quantum model and a loss function associated with the integral formulation of the differential problem. Evaluation of the loss function for a point under consideration comprises computation of the integral based on one or more collocation points between the point on the boundary and the point under consideration. The determination of the solution includes varying the variational parameters to determine a set of optimal parameters defining a solution of the differential equation.

Classes IPC  ?

• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard
• G06N 3/084 - Rétropropagation, p. ex. suivant l’algorithme du gradient
• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels
• G06N 10/40 - Réalisations ou architectures physiques de processeurs ou de composants quantiques pour la manipulation de qubits, p. ex. couplage ou commande de qubit

Abrégé

A method and system for solving a computational problem using a hybrid data processor comprising a classical computer and quantum computer the method comprising receiving or determining information on one or more quantum circuits defining operations of a parameterized quantum model of a target function, the target function representing an approximate solution to the computational problem, preferably one or more differential equations and one or more associated boundary conditions, the one or more quantum circuits comprising one or more quantum feature maps for encoding one or more classical input features associated with the target function into the Hilbert space of the quantum register, wherein the one or more feature maps include one or more unitary operators defining a time evolution over a Hamiltonian, preferably a generator Hamiltonian, applied to quantum elements of the quantum register, the Hamiltonian evolution being parameterized by a first set of variational parameters and the one or more classical input features; and, determining the target function based on the parameterized quantum model and a loss function associated with the computational problem, the determining including varying the first set of variational parameters to determine a set of eigenfrequencies of the Hamiltonian which is optimized for the computational problem, the set of eigenfrequencies defining quantum modes, which the parameterized quantum.

Classes IPC  ?

• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard

Abrégé

Methods and systems are disclosed for solving a differential problem using a hybrid computer system. The differential problem defines a differential equation, and a target function defines an approximate solution to the differential equation. The target function is defined as a sum of basis functions with parameterized coefficients. The method comprises receiving or determining a quantum circuit defining operations of a parameterized quantum model of the differential equation, and determining the solution to the differential problem based on the parameterized quantum model and, optionally, a loss function associated with the differential problem. The quantum circuit defines operations for encoding primitive elements (e.g., terms such as f(x), f(x)/dx, g(x), etc.) of the differential equation in a plurality of quantum states of quantum elements of the quantum processor. Each quantum state of the plurality of quantum states corresponds to a set of (parametrized or unparametrized) coefficients associated with the basis functions, of which at least one quantum state of the plurality of quantum states corresponds to a set of parametrized coefficients associated with the basis functions. The determination of the solution includes varying the variational parameters to determine a set of optimal parameters. The varying of the variational parameters includes: translating the operations of the quantum circuit into control signals for control and readout of the quantum elements of the quantum register; applying the operations of the quantum circuit to the quantum elements based on the control signals; determining classical measurement data by measuring one or more comparisons, e.g. overlaps, between pairs of quantum states from the plurality of quantum states; computing a loss value based on the loss function and the classical measurement data; and adjusting the variational parameters based on the loss value.

Classes IPC  ?

• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard
• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels

Abrégé

Methods and systems are disclosed for manipulating quantum data in a real quantum basis. The method comprises formulating one or more quantum circuits including an amplitude-based feature map comprising gate operations for encoding one or more input features in a Hilbert space of quantum elements of a quantum register. The gate operations are configured to encode the one or more classical input features in amplitudes of a set of orthogonal basis states of the quantum register, wherein the amplitudes are based on one or more basis functions. This also includes a method for executing a transform associated with the feature map on a quantum processor comprising a quantum register. The method comprises preparing the quantum register in a first state representing a computational basis state; formulating a transform circuit configured to map a computational basis state to a feature- map-associated basis state; and applying the transform circuit to the quantum register.

Classes IPC  ?

• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard
• G06N 3/0475 - Réseaux génératifs
• G06N 3/065 - Moyens analogiques
• G06N 3/08 - Méthodes d'apprentissage

Abrégé

A method for solving a stochastic differential equation includes receiving by a classical computer a partial differential equation describing dynamics of a quantile function QF associated a stochastic differential equation defining a stochastic process as a function of time and variable(s) and the QF defining a modelled distribution of the stochastic process; executing by the classical computer a first training process for training neural network(s) to model an initial quantile function, the neural network(s) being trained by a special purpose processor based on measurements of the stochastic process; executing by the classical computer a second training process wherein the neural network(s) are further trained based on the QFP equation for time interval(s) to model the time evolution of the initial quantile function; and, executing by the classical computer a sampling process including generating samples of the stochastic process using the quantile function, the generated samples representing solutions of the SDE.

Classes IPC  ?

• G06N 3/08 - Méthodes d'apprentissage

Abrégé

Methods for training and sampling a quantum model are described wherein the method comprises: training a quantum model, preferably a generative quantum model, as a quantum sampler configured to produce samples which are associated with a predetermined target probability distribution and which are exponentially hard to compute classically, the training including classically computing probability amplitudes associated with an execution of a first parameterized quantum circuit that defines a sequence of gate operations for a quantum register and optimizing one or more parameters of the first parameterized quantum circuit based on the classically computed probability amplitudes; and, executing a sampling process using the hardware quantum register, the sampling process including determining an optimized quantum circuit based on the one or more optimized parameters and the first parameterized quantum circuit or a second parameterized quantum circuit, which is related to the first parameterized quantum circuit, and executing the optimized quantum circuit on the hardware quantum register and generating a sample by measuring the output of the hardware quantum register.

Classes IPC  ?

• G06N 10/20 - Modèles d’informatique quantique, p. ex. circuits quantiques ou ordinateurs quantiques universels
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard

Classes IPC  ?

• G06N 3/04 - Architecture, p. ex. topologie d'interconnexion
• G06N 3/084 - Rétropropagation, p. ex. suivant l’algorithme du gradient
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard

Classes IPC  ?

• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard

Classes IPC  ?

• G06N 10/40 - Réalisations ou architectures physiques de processeurs ou de composants quantiques pour la manipulation de qubits, p. ex. couplage ou commande de qubit
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard
• G06N 20/10 - Apprentissage automatique utilisant des méthodes à noyaux, p. ex. séparateurs à vaste marge [SVM]

Abrégé

Disclosed is an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. The method includes training of a DQC-based model, where data is encoded in a latent space with a phase feature map, followed by a variational quantum circuit. The trained model is then mapped to the bit basis using a fixed unitary transformation, coinciding with a quantum Fourier transform circuit in the simplest case. This allows fast sampling from parametrized distributions using a single-shot readout. Importantly, simplified latent space training provides models that are automatically differentiable. Samples from propagated stochastic differential equations (SDEs) can be accessed by solving a stationary Fokker-Planck equation and time-dependent Kolmogorov backward equation on a quantum computer. Finally, the approach opens a route to multidimensional generative modelling with qubit registers explicitly correlated via a (fixed) entangling layer. In this case, quantum computers can offer advantage as efficient samplers, which perform complex inverse transform sampling enabled by fundamental laws of quantum mechanics. A specific hardware withfast (optical) readoutfor sampling will provide an edge over existing quantum solutions. On a technical side, the advances are multiple, including introduction of the phase feature map and analysis of its properties, and development of frequency-taming techniques that include qubit-wise training and feature map sparsification.

Classes IPC  ?

• G06N 3/04 - Architecture, p. ex. topologie d'interconnexion
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard

Abrégé

A method for solving a stochastic differential equation, SDE, comprises receiving a partial differential equation, PDE, describing dynamics of a quantile function QF associated with the SDE, preferably the PDE defining a quantilized Fokker-Planck QFP equation, the SDE defining a stochastic process as a function of time and further variable(s) and the QF defining a modelled distribution of the stochastic process; executing a first training process for training, based on training data including measurements of the stochastic process, neural network(s) to model an initial QF; executing a second training process wherein the neural network(s) are further trained based on the QFP equation for time interval(s) to model the time evolution of the initial QF; and executing, based on the QFs for the time interval(s), a sampling process including generating, using the QF, samples of the stochastic process representing solutions of the SDE.

Classes IPC  ?

• G06F 17/13 - Opérations mathématiques complexes pour la résolution d'équations d'équations différentielles
• G06N 3/04 - Architecture, p. ex. topologie d'interconnexion
• G06N 3/08 - Méthodes d'apprentissage
• G06N 10/60 - Algorithmes quantiques, p. ex. fondés sur l'optimisation quantique ou les transformées quantiques de Fourier ou de Hadamard