Gate-Based Quantum Computing

Use Grover's algorithm on a quantum computer to solve graph coloring problems. Grover's algorithm, also called the quantum search algorithm, is a fast method to perform unstructured searches. This example applies the algorithm to a problem where a bit string of a given length is classified as valid or invalid, and the goal is to retrieve one of the valid bit strings. The algorithm uses a state oracle to determine whether a bit string is valid. Although this application of Grover's algorithm is not the most efficient method to solve the graph coloring problem in practice, it illustrates how a quantum algorithm can be applied to a well-known problem.

An efficient method for using qubits to encode a protein fold on a 3-D tetrahedral lattice [1], [2]. The ground-state is found through a simulated variational quantum eigensolver (VQE) routine. The VQE algorithm uses classical optimization to improve the initial guess of the ground state, and then a quantum computer calculates the expectation value. The final circuit from the simulation is run on a real QPU for comparison.

Solve the XOR problem using a trained quantum neural network (QNN). You use the network to classify the classical data of 2-D coordinates. A QNN is a machine learning model that combines quantum computing layers and classical layers. This example shows how to train such a hybrid network for a classification problem that is nonlinearly separable, such as the exclusive-OR (XOR) problem.

Use Quantum Monte Carlo (QMC) simulation in MATLAB® to compute the mean of a function of a random variable. There are a broad range of tasks in finance and economics that depend on Monte Carlo simulation, from option pricing to macroeconomic stress testing. While this example does not explore computational efficiency, research shows that QMC offers a quadratic speed-up compared to classic Monte Carlo methods.