Gate-Based Quantum Computing

Gate-based quantum computing algorithms
Since R2023a

Create quantum gates and circuits, simulate circuits on your local computer, and run circuits on remote hardware using Amazon^® Web Services (AWS^®) or IBM^® Qiskit^® Runtime Services.

Classes

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Quantum Circuits and Gates

`quantumCircuit`	Quantum computing circuit
`quantum.gate.SimpleGate`	Simple gate for quantum computing
`quantum.gate.CompositeGate`	Composite gate for quantum computing

Quantum States and Measurements

`quantum.gate.QuantumState`	State of qubits in quantum circuit
`quantum.gate.QuantumMeasurement`	Measurement result of quantum circuit

Quantum Devices and Tasks

`quantum.backend.QuantumDeviceAWS`	Quantum device available through AWS
`quantum.backend.QuantumTaskAWS`	Task sent to AWS for execution on quantum device
`quantum.backend.QuantumDeviceIBM`	Quantum device available through IBM (Since R2023b)
`quantum.backend.QuantumTaskIBM`	Task sent to IBM for execution on quantum device (Since R2023b)

Properties

QuantumCircuitChart Properties

Quantum circuit plot appearance and behavior (Since R2023b)

Functions

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Gate Creation Functions

Gates on One Target Qubit

`hGate`	Hadamard gate
`idGate`	Identity gate
`xGate`	Pauli X gate
`yGate`	Pauli Y gate
`zGate`	Pauli Z gate

Rotation Gates

`rxGate`	x-axis rotation gate
`ryGate`	y-axis rotation gate
`rzGate`	z-axis rotation gate
`r1Gate`	z-axis rotation gate with global phase
`sGate`	S gate
`siGate`	Inverse S gate
`tGate`	T gate
`tiGate`	Inverse T gate

Gates with One Control Qubit and One Target Qubit

`chGate`	Controlled Hadamard gate
`cnotGate`	CNOT gate (controlled X gate)
`cxGate`	Controlled X gate (CNOT gate)
`cyGate`	Controlled Y gate
`czGate`	Controlled Z gate

Gate That Swap States of Two Qubits

swapGate Swap gate

Controlled Rotation Gates

`crxGate`	Controlled x-axis rotation gate
`cryGate`	Controlled y-axis rotation gate
`crzGate`	Controlled z-axis rotation gate
`cr1Gate`	Controlled z-axis rotation gate with global phase

Controlled Controlled X Gate

ccxGate Controlled controlled X gate (CCNOT or Toffoli gate)

Ising Coupling Gates

`rxxGate`	Ising XX coupling gate
`ryyGate`	Ising YY coupling gate
`rzzGate`	Ising ZZ coupling gate

Composite and Specialized Gates

`compositeGate`	Construct composite gate for quantum computing
`qftGate`	Quantum Fourier transform gate
`initGate`	Initialization gate with specified qubit states (Since R2023b)
`unitaryGate`	Unitary matrix gate (Since R2023b)
`mcxGate`	Multi-controlled X gate

Uniformly Controlled Rotation Gates

`ucrxGate`	Uniformly controlled x-axis rotation gate (Since R2023b)
`ucryGate`	Uniformly controlled y-axis rotation gate (Since R2023b)
`ucrzGate`	Uniformly controlled z-axis rotation gate (Since R2023b)

Topics

Basics and Workflows

Introduction to Quantum Computing
This topic contains background information about qubits, quantum gates, and quantum circuits.
Types of Quantum Gates
This topic describes the different types of quantum gates to build quantum algorithms.
Local Quantum State Simulation
This topic describes how to simulate a quantum circuit locally and analyze the simulation results.
Run Quantum Circuit on Hardware Using AWS
This topic describes how to run quantum circuits on remote hardware using Amazon Web Services.
Run Quantum Circuit on Hardware Using IBM Qiskit Runtime Services
This topic describes how to run quantum circuits on remote hardware using IBM Qiskit Runtime Services.

Related Information

VQE with MATLAB
Quantum Monte Carlo with MATLAB

Featured Examples

Graph Coloring with Grover's Algorithm

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.

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Ground-State Protein Folding Using Variational Quantum Eigensolver (VQE)

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.

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Solve XOR Problem Using Quantum Neural Network (QNN)

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.

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Quantum Monte Carlo (QMC) Simulation

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.

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