Key Concepts

Automatic Differentiation

Automatically computing derivatives of the steps of computer programs.

Barren Plateaus

Areas in the cost landscape where the gradient of a parameterized circuit disappears. The mortal enemy of many a variational algorithm, the variance of the gradient at these points is also close to zero in all directions.

Circuit Ansatz

An ansatz is a basic architecture of a circuit, i.e., a set of gates that act on specific subsystems. The architecture defines which algorithms a variational circuit can implement by fixing the trainable parameters. A circuit ansatz is analogous to the architecture of a neural network.

Hybrid Computation

A computation that includes classical and quantum subroutines, executed on different devices.

Parameter-shift Rule

The parameter-shift rule is a recipe for how to estimate gradients of quantum circuits. See also quantum gradient.

Quantum Approximate Optimization Algorithm (QAOA)

A hybrid variational algorithm that is used to find approximate solutions for combinatorial optimization problems. Characterized by a circuit ansatz featuring two alternating parameterized components.

Quantum Boltzmann Machine

Quantum analog of a classical Boltzmann machine, in which nodes are replaced by spins or qubits. An energy-based quantum machine learning model.

Quantum Convolutional Neural Network

A quantum neural network that mirrors the structure of a convolutional neural network. Characterized by alternating convolutional layers, and pooling layers which are effected by performing quantum measurements.

Quantum Differentiable Programming

The paradigm of making quantum algorithms differentiable, and thereby trainable. See also quantum gradient.

Quantum Embedding

Representation of classical data as a quantum state.

Quantum Feature Map

The mathematical map that embeds classical data into a quantum state. Usually executed by a variational quantum circuit whose parameters depend on the input data. See also Quantum Embedding.

Quantum Generative Adversarial Network

Quantum analog of Generative Adversarial Networks (GANs).

Quantum Gradient

The derivative of a quantum computation with respect to the parameters of a circuit.

Quantum Machine Learning

A research area that explores ideas at the intersection of machine learning and quantum computing.

Quantum Neural Network

A term with many different meanings, usually referring to a generalization of artificial neural networks to quantum information processing. Also increasingly used to refer to variational circuits in the context of quantum machine learning.

Quantum Node

A quantum computation executed as part of a larger hybrid computation.

Quanvolutional Neural Network

A hybrid classical-quantum model in which classical CNNs are augmented by layers of variational quantum circuits.

Variational Circuit

Variational circuits are quantum algorithms that depend on tunable parameters, and can therefore be optimized.

Variational Quantum Classifier (VQC)

A supervised learning algorithm in which variational circuits (QNNs) are trained to perform classification tasks.

Variational Quantum Eigensolver (VQE)

A variational algorithm used for finding the ground-state energy of a quantum system. The VQE is a hybrid algorithm that involves incorporating measurement results obtained from a quantum computer running a series of variational circuits into a classical optimization routine in order to find a set of optimal variational parameters.

Variational Quantum Linear Solver (VQLS)

An algorithm for solving systems of linear equations on quantum computers. Based on short variational circuits, it is amenable to running on near-term quantum hardware.

Variational Quantum Thermalizer (VQT)

A generalization of the VQE to systems with non-zero temperatures. Uses QHBMs to generate thermal states of Hamiltonians at a given temperature.

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