Types of Quantum Gates
Note
Installation Required: This functionality requires MATLAB Support Package for Quantum Computing.
This topic provides a list of functions that you can use to create quantum gates in MATLAB®. Quantum gates are the building blocks of quantum circuits, and they enable you to program algorithms for a quantum computer. Quantum gates are reversible and have unitary matrix representations.
Creation Functions for SimpleGate
Objects
Gates on One Target Qubit
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() hGate
| Hadamard gate | 1 |
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![]() idGate | Identity gate | 1 |
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![]() xGate | Pauli X gate | 1 |
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![]() yGate | Pauli Y gate | 1 |
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![]() zGate | Pauli Z gate | 1 |
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Rotation Gates
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() rxGate | x-axis rotation gate | 1 |
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![]() ryGate | y-axis rotation gate | 1 |
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![]() rzGate | z-axis rotation gate | 1 |
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![]() r1Gate | z-axis rotation gate with global phase | 1 |
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![]() sGate | S gate | 1 | ||
![]() siGate | Inverse S gate | 1 | ||
![]() tGate | T gate | 1 | ||
![]() tiGate | Inverse T gate | 1 |
Gates with One Control Qubit and One Target Qubit
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() chGate
| Controlled Hadamard gate | 2 |
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Controlled X or CNOT gate | 2 |
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![]() cyGate | Controlled Y gate | 2 |
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![]() czGate | Controlled Z gate | 2 |
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Gate That Swap States of Two Qubits
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() swapGate | Swap gate | 2 |
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Controlled Rotation Gates
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() crxGate | Controlled x-axis rotation gate | 2 |
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![]() cryGate | Controlled y-axis rotation gate | 2 |
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![]() crzGate | Controlled z-axis rotation gate | 2 |
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![]() cr1Gate | Controlled z-axis rotation gate with global phase | 2 |
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Controlled Controlled X Gate
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() ccxGate | Controlled controlled X gate (CCNOT or Toffoli gate) | 3 |
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Ising Coupling Gates
Creation Function | Gate Name | No. of Qubits | Matrix Representation | Properties |
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![]() rxxGate | Ising XX coupling gate | 2 |
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![]() ryyGate | Ising YY coupling gate | 2 |
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![]() rzzGate | Ising ZZ coupling gate | 2 |
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Creation Functions for CompositeGate
Objects
Composite and Specialized Gates
Creation Function | Gate Name | No. of Qubits | Gate Symbol | Equivalent Internal Gates | Matrix Representation |
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compositeGate | Composite gate | Varies | Example:
Quantum circuit with two composite gates named | ||
![]() | ![]() |
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qftGate | Quantum Fourier transform (QFT) gate | Varies | Example: Quantum Fourier transform gate on three qubits. The equivalent internal gates are Hadamard gates, R1 gates, and a swap gate. | ||
![]() | ![]() |
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initGate | Initialization gate | Varies | Example: Initialization gate on three target qubits. The equivalent internal gates are inverse uniform controlled y-axis rotation gates. | ||
![]() | ![]() | initGate applies a matrix U such
that , where is the vector representation of the input state. | |||
unitaryGate | Unitary matrix gate | Varies | Example: Unitary matrix gate on three target qubits. The equivalent internal gates are four unitary matrix gates alternating between two uniform controlled z-axis rotation gates and one uniform controlled y-axis rotation gate. | ||
![]() | ![]() | unitaryGate applies the unitary matrix to the target
qubits (up to global phase). | |||
mcxGate | Multi-controlled X gate | Varies | Example: Multi-controlled X gate with three control qubits, one target qubit, and no ancilla qubit. The equivalent internal gates are Hadamard gates, controlled R1 gates, and controlled X gates. | ||
![]() | ![]() |
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Uniformly Controlled Rotation Gates
Creation Function | Gate Name | No. of Qubits | Gate Symbol | Equivalent Internal Gates | Matrix Representation |
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ucrxGate | Uniformly controlled x-axis rotation gate | Varies | Example: Uniformly controlled x-axis rotation gate with one control qubit and one target qubit using rotation angle vector . The equivalent internal gates are x-axis rotation gates and controlled Z gates. | ||
![]() | ![]() |
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ucryGate | Uniformly controlled y-axis rotation gate | Varies | Example: Uniformly controlled y-axis rotation gate with one control qubit and one target qubit using rotation angle vector . The equivalent internal gates are y-axis rotation gates and controlled X gates. | ||
![]() | ![]() |
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ucrzGate | Uniformly controlled z-axis rotation gate | Varies | Example: Uniformly controlled z-axis rotation gate with one control qubit and one target qubit using rotation angle vector . The equivalent internal gates are z-axis rotation gates and controlled X gates. | ||
![]() | ![]() |
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See Also
quantum.gate.SimpleGate
| quantum.gate.CompositeGate