Circuit Library

qiskit.circuit.library

The circuit library is a collection of well-studied and valuable circuits, directives, and gates. We call them valuable for different reasons, for instance they can serve as building blocks for algorithms or they are circuits that we think are hard to simulate classically.

Each element can be plugged into a circuit using the QuantumCircuit.append() method and so the circuit library allows users to program at higher levels of abstraction. For example, to append a multi-controlled CNOT:

from qiskit.circuit.library import MCXGate
gate = MCXGate(4)
 
from qiskit import QuantumCircuit
circuit = QuantumCircuit(5)
circuit.append(gate, [0, 1, 4, 2, 3])
circuit.draw('mpl')

The library is organized in several sections.

Standard gates

These operations are reversible unitary gates and they all subclass Gate. As a consequence, they all have the methods to_matrix(), power(), and control(), which we can generally only apply to unitary operations.

For example:

from qiskit.circuit.library import XGate
gate = XGate()
print(gate.to_matrix())             # X gate
print(gate.power(1/2).to_matrix())  # √X gate
print(gate.control(1).to_matrix())  # CX (controlled X) gate

[[0.+0.j 1.+0.j]
 [1.+0.j 0.+0.j]]
[[0.5+0.5j 0.5-0.5j]
 [0.5-0.5j 0.5+0.5j]]
[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]
 [0.+0.j 0.+0.j 0.+0.j 1.+0.j]
 [0.+0.j 0.+0.j 1.+0.j 0.+0.j]
 [0.+0.j 1.+0.j 0.+0.j 0.+0.j]]


`C3XGate`(*args[, _force_mutable])	The X gate controlled on 3 qubits.
`C3SXGate`(*args[, _force_mutable])	The 3-qubit controlled sqrt-X gate.
`C4XGate`(*args[, _force_mutable])	The 4-qubit controlled X gate.
`CCXGate`(*args[, _force_mutable])	CCX gate, also known as Toffoli gate.
`DCXGate`(*args[, _force_mutable])	Double-CNOT gate.
`CHGate`(*args[, _force_mutable])	Controlled-Hadamard gate.
`CPhaseGate`(theta[, label, ctrl_state, ...])	Controlled-Phase gate.
`CRXGate`(theta[, label, ctrl_state, ...])	Controlled-RX gate.
`CRYGate`(theta[, label, ctrl_state, ...])	Controlled-RY gate.
`CRZGate`(theta[, label, ctrl_state, ...])	Controlled-RZ gate.
`CSGate`(*args[, _force_mutable])	Controlled-S gate.
`CSdgGate`(*args[, _force_mutable])	Controlled-S^dagger gate.
`CSwapGate`(*args[, _force_mutable])	Controlled-SWAP gate, also known as the Fredkin gate.
`CSXGate`(*args[, _force_mutable])	Controlled-√X gate.
`CUGate`(theta, phi, lam, gamma[, label, ...])	Controlled-U gate (4-parameter two-qubit gate).
`CU1Gate`(theta[, label, ctrl_state, ...])	Controlled-U1 gate.
`CU3Gate`(theta, phi, lam[, label, ...])	Controlled-U3 gate (3-parameter two-qubit gate).
`CXGate`(*args[, _force_mutable])	Controlled-X gate.
`CYGate`(*args[, _force_mutable])	Controlled-Y gate.
`CZGate`(*args[, _force_mutable])	Controlled-Z gate.
`CCZGate`(*args[, _force_mutable])	CCZ gate.
`ECRGate`(*args[, _force_mutable])	An echoed cross-resonance gate.
`HGate`(*args[, _force_mutable])	Single-qubit Hadamard gate.
`IGate`(*args[, _force_mutable])	Identity gate.
`MSGate`(num_qubits, theta[, label])	MSGate has been deprecated.
`PhaseGate`(theta[, label, duration, unit])	Single-qubit rotation about the Z axis.
`RCCXGate`(*args[, _force_mutable])	The simplified Toffoli gate, also referred to as Margolus gate.
`RC3XGate`(*args[, _force_mutable])	The simplified 3-controlled Toffoli gate.
`RGate`(theta, phi[, label, duration, unit])	Rotation θ around the cos(φ)x + sin(φ)y axis.
`RXGate`(theta[, label, duration, unit])	Single-qubit rotation about the X axis.
`RXXGate`(theta[, label, duration, unit])	A parametric 2-qubit $X \otimes X$ interaction (rotation about XX).
`RYGate`(theta[, label, duration, unit])	Single-qubit rotation about the Y axis.
`RYYGate`(theta[, label, duration, unit])	A parametric 2-qubit $Y \otimes Y$ interaction (rotation about YY).
`RZGate`(phi[, label, duration, unit])	Single-qubit rotation about the Z axis.
`RZZGate`(theta[, label, duration, unit])	A parametric 2-qubit $Z \otimes Z$ interaction (rotation about ZZ).
`RZXGate`(theta[, label, duration, unit])	A parametric 2-qubit $Z \otimes X$ interaction (rotation about ZX).
`XXMinusYYGate`(theta[, beta, label, ...])	XX-YY interaction gate.
`XXPlusYYGate`(theta[, beta, label, duration, ...])	XX+YY interaction gate.
`SGate`(*args[, _force_mutable])	Single qubit S gate (Z**0.5).
`SdgGate`(*args[, _force_mutable])	Single qubit S-adjoint gate (~Z**0.5).
`SwapGate`(*args[, _force_mutable])	The SWAP gate.
`iSwapGate`(*args[, _force_mutable])	iSWAP gate.
`SXGate`(*args[, _force_mutable])	The single-qubit Sqrt(X) gate ( $\sqrt{X}$ ).
`SXdgGate`(*args[, _force_mutable])	The inverse single-qubit Sqrt(X) gate.
`TGate`(*args[, _force_mutable])	Single qubit T gate (Z**0.25).
`TdgGate`(*args[, _force_mutable])	Single qubit T-adjoint gate (~Z**0.25).
`UGate`(theta, phi, lam[, label, duration, unit])	Generic single-qubit rotation gate with 3 Euler angles.
`U1Gate`(theta[, label, duration, unit])	Single-qubit rotation about the Z axis.
`U2Gate`(phi, lam[, label, duration, unit])	Single-qubit rotation about the X+Z axis.
`U3Gate`(theta, phi, lam[, label, duration, unit])	Generic single-qubit rotation gate with 3 Euler angles.
`XGate`(*args[, _force_mutable])	The single-qubit Pauli-X gate ( $\sigma_x$ ).
`YGate`(*args[, _force_mutable])	The single-qubit Pauli-Y gate ( $\sigma_y$ ).
`ZGate`(*args[, _force_mutable])	The single-qubit Pauli-Z gate ( $\sigma_z$ ).
`GlobalPhaseGate`(phase[, label, duration, unit])	The global phase gate ( $e^{i\theta}$ ).

Standard Directives

Directives are operations to the quantum stack that are meant to be interpreted by the backend or the transpiler. In general, the transpiler or backend might optionally ignore them if there is no implementation for them.


`Barrier`(num_qubits[, label])	Barrier instruction.

Standard Operations

Operations are non-reversible changes in the quantum state of the circuit.


`Measure`([label, duration, unit])	Quantum measurement in the computational basis.
`Reset`([label, duration, unit])	Qubit reset.

Generalized Gates

These “gates” (many are QuantumCircuit subclasses) allow to set the amount of qubits involved at instantiation time.

from qiskit.circuit.library import Diagonal
 
diagonal = Diagonal([1, 1])
print(diagonal.num_qubits)
 
diagonal = Diagonal([1, 1, 1, 1])
print(diagonal.num_qubits)

1
2


`Diagonal`(diag)	Diagonal circuit.
`DiagonalGate`(diag)	Gate implementing a diagonal transformation.
`MCMT`(gate, num_ctrl_qubits, num_target_qubits)	The multi-controlled multi-target gate, for an arbitrary singly controlled target gate.
`MCMTVChain`(gate, num_ctrl_qubits, ...)	The MCMT implementation using the CCX V-chain.
`Permutation`(num_qubits[, pattern, seed])	An n_qubit circuit that permutes qubits.
`PermutationGate`(pattern)	A gate that permutes qubits.
`GMS`(num_qubits, theta)	Global Mølmer–Sørensen gate.
`GR`(num_qubits, theta, phi)	Global R gate.
`GRX`(num_qubits, theta)	Global RX gate.
`GRY`(num_qubits, theta)	Global RY gate.
`GRZ`(num_qubits, phi)	Global RZ gate.
`MCPhaseGate`(lam, num_ctrl_qubits[, label, ...])	Multi-controlled-Phase gate.
`MCXGate`([num_ctrl_qubits, label, ...])	The general, multi-controlled X gate.
`MCXGrayCode`([num_ctrl_qubits, label, ...])	Implement the multi-controlled X gate using the Gray code.
`MCXRecursive`([num_ctrl_qubits, label, ...])	Implement the multi-controlled X gate using recursion.
`MCXVChain`([num_ctrl_qubits, dirty_ancillas, ...])	Implement the multi-controlled X gate using a V-chain of CX gates.
`RVGate`(v_x, v_y, v_z[, basis])	Rotation around arbitrary rotation axis $\vec{v}$ where $\\|\vec{v}\\|_2$ is angle of rotation in radians.
`PauliGate`(label)	A multi-qubit Pauli gate.
`LinearFunction`(linear[, validate_input])	A linear reversible circuit on n qubits.
`Isometry`(isometry, num_ancillas_zero, ...[, ...])	Decomposition of arbitrary isometries from $m$ to $n$ qubits.
`UnitaryGate`(data[, label, check_input])	Class quantum gates specified by a unitary matrix.
`UCGate`(gate_list[, up_to_diagonal])	Uniformly controlled gate (also called multiplexed gate).
`UCPauliRotGate`(angle_list, rot_axis)	Uniformly controlled Pauli rotations.
`UCRXGate`(angle_list)	Uniformly controlled Pauli-X rotations.
`UCRYGate`(angle_list)	Uniformly controlled Pauli-Y rotations.
`UCRZGate`(angle_list)	Uniformly controlled Pauli-Z rotations.

Boolean Logic Circuits

These are QuantumCircuit subclasses that implement boolean logic operations, such as the logical or of a set of qubit states.


`AND`(num_variable_qubits[, flags, mcx_mode])	A circuit implementing the logical AND operation on a number of qubits.
`OR`(num_variable_qubits[, flags, mcx_mode])	A circuit implementing the logical OR operation on a number of qubits.
`XOR`(num_qubits[, amount, seed])	An n_qubit circuit for bitwise xor-ing the input with some integer `amount`.
`InnerProduct`(num_qubits)	A 2n-qubit Boolean function that computes the inner product of two n-qubit vectors over $F_2$ .

Basis Change Circuits

These circuits allow basis transformations of the qubit states. For example, in the case of the Quantum Fourier Transform (QFT), it transforms between the computational basis and the Fourier basis.


`QFT`([num_qubits, approximation_degree, ...])	Quantum Fourier Transform Circuit.

Arithmetic Circuits

These QuantumCircuits perform classical arithmetic, such as addition or multiplication.

Amplitude Functions


`LinearAmplitudeFunction`(num_state_qubits, ...)	A circuit implementing a (piecewise) linear function on qubit amplitudes.

Functional Pauli Rotations


`FunctionalPauliRotations`([num_state_qubits, ...])	Base class for functional Pauli rotations.
`LinearPauliRotations`([num_state_qubits, ...])	Linearly-controlled X, Y or Z rotation.
`PolynomialPauliRotations`([num_state_qubits, ...])	A circuit implementing polynomial Pauli rotations.
`PiecewiseLinearPauliRotations`([...])	Piecewise-linearly-controlled Pauli rotations.
`PiecewisePolynomialPauliRotations`([...])	Piecewise-polynomially-controlled Pauli rotations.
`PiecewiseChebyshev`(f_x[, degree, ...])	Piecewise Chebyshev approximation to an input function.

Adders


`DraperQFTAdder`(num_state_qubits[, kind, name])	A circuit that uses QFT to perform in-place addition on two qubit registers.
`CDKMRippleCarryAdder`(num_state_qubits[, ...])	A ripple-carry circuit to perform in-place addition on two qubit registers.
`VBERippleCarryAdder`(num_state_qubits[, ...])	The VBE ripple carry adder [1].
`WeightedAdder`([num_state_qubits, weights, name])	A circuit to compute the weighted sum of qubit registers.

Multipliers


`HRSCumulativeMultiplier`(num_state_qubits[, ...])	A multiplication circuit to store product of two input registers out-of-place.
`RGQFTMultiplier`(num_state_qubits[, ...])	A QFT multiplication circuit to store product of two input registers out-of-place.

Comparators


`IntegerComparator`([num_state_qubits, value, ...])	Integer Comparator.

Functions on binary variables


`QuadraticForm`([num_result_qubits, ...])	Implements a quadratic form on binary variables encoded in qubit registers.

Other arithmetic functions


`ExactReciprocal`(num_state_qubits, scaling[, ...])	Exact reciprocal

Particular Quantum Circuits


`FourierChecking`(f, g)	Fourier checking circuit.
`GraphState`(adjacency_matrix)	Circuit to prepare a graph state.
`HiddenLinearFunction`(adjacency_matrix)	Circuit to solve the hidden linear function problem.
`IQP`(interactions)	Instantaneous quantum polynomial (IQP) circuit.
`QuantumVolume`(num_qubits[, depth, seed, ...])	A quantum volume model circuit.
`PhaseEstimation`(num_evaluation_qubits, unitary)	Phase Estimation circuit.
`GroverOperator`(oracle[, state_preparation, ...])	The Grover operator.
`PhaseOracle`(expression[, synthesizer, var_order])	Phase Oracle.
`EvolvedOperatorAnsatz`([operators, reps, ...])	The evolved operator ansatz.
`PauliEvolutionGate`(operator[, time, label, ...])	Time-evolution of an operator consisting of Paulis.
`HamiltonianGate`(data, time[, label])	Class for representing evolution by a Hamiltonian operator as a gate.
`UnitaryOverlap`(unitary1, unitary2[, ...])	Circuit that returns the overlap between two unitaries $U_2^{\dag} U_1$ .

N-local circuits

These BlueprintCircuit subclasses are used as parameterized models (a.k.a. ansatzes or variational forms) in variational algorithms. They are heavily used in near-term algorithms in e.g. Chemistry, Physics or Optimization.


`NLocal`([num_qubits, rotation_blocks, ...])	The n-local circuit class.
`TwoLocal`([num_qubits, rotation_blocks, ...])	The two-local circuit.
`PauliTwoDesign`([num_qubits, reps, seed, ...])	The Pauli Two-Design ansatz.
`RealAmplitudes`([num_qubits, entanglement, ...])	The real-amplitudes 2-local circuit.
`EfficientSU2`([num_qubits, su2_gates, ...])	The hardware efficient SU(2) 2-local circuit.
`ExcitationPreserving`([num_qubits, mode, ...])	The heuristic excitation-preserving wave function ansatz.
`QAOAAnsatz`([cost_operator, reps, ...])	A generalized QAOA quantum circuit with a support of custom initial states and mixers.

Data encoding circuits

These BlueprintCircuit encode classical data in quantum states and are used as feature maps for classification.


`PauliFeatureMap`([feature_dimension, reps, ...])	The Pauli Expansion circuit.
`ZFeatureMap`(feature_dimension[, reps, ...])	The first order Pauli Z-evolution circuit.
`ZZFeatureMap`(feature_dimension[, reps, ...])	Second-order Pauli-Z evolution circuit.
`StatePreparation`(params[, num_qubits, ...])	Complex amplitude state preparation.
`Initialize`(params[, num_qubits, normalize])	Complex amplitude initialization.

Template circuits

Templates are functions that return circuits that compute the identity. They are used at circuit optimization where matching part of the template allows the compiler to replace the match with the inverse of the remainder from the template.

In this example, the identity constant in a template is checked:

from qiskit.circuit.library.templates import template_nct_4b_1
from qiskit.quantum_info import Operator
import numpy as np
 
template = template_nct_4b_1()
 
identity = np.identity(2 ** len(template.qubits), dtype=complex)
data = Operator(template).data
np.allclose(data, identity)  # True, template_nct_4b_1 is the identity

NCT (Not-CNOT-Toffoli) template circuits

Template circuits for XGate, CXGate, and CCXGate (Toffoli) gates.

Reference: Maslov, D. and Dueck, G. W. and Miller, D. M., Techniques for the synthesis of reversible Toffoli networks, 2007 http://dx.doi.org/10.1145/1278349.1278355

template_nct_2a_1

qiskit.circuit.library.templates.nct.template_nct_2a_1()

Circuit Library

Standard gates

Standard Directives

Standard Operations

Generalized Gates

Boolean Logic Circuits

Basis Change Circuits

Arithmetic Circuits

Amplitude Functions

Functional Pauli Rotations

Adders

Multipliers

Comparators

Functions on binary variables

Other arithmetic functions

Particular Quantum Circuits

N-local circuits

Data encoding circuits

Template circuits

NCT (Not-CNOT-Toffoli) template circuits

template_nct_2a_1

template_nct_2a_2

template_nct_2a_3

template_nct_4a_1

template_nct_4a_2

template_nct_4a_3

template_nct_4b_1

template_nct_4b_2

template_nct_5a_1

template_nct_5a_2

template_nct_5a_3

template_nct_5a_4

template_nct_6a_1

template_nct_6a_2

template_nct_6a_3

template_nct_6a_4

template_nct_6b_1

template_nct_6b_2

template_nct_6c_1

template_nct_7a_1

template_nct_7b_1

template_nct_7c_1

template_nct_7d_1

template_nct_7e_1

template_nct_9a_1

template_nct_9c_1

template_nct_9c_2

template_nct_9c_3

template_nct_9c_4

template_nct_9c_5

template_nct_9c_6

template_nct_9c_7

template_nct_9c_8

template_nct_9c_9

template_nct_9c_10

template_nct_9c_11

template_nct_9c_12

template_nct_9d_1

template_nct_9d_2

template_nct_9d_3

template_nct_9d_4

template_nct_9d_5

template_nct_9d_6

template_nct_9d_7

template_nct_9d_8

template_nct_9d_9

template_nct_9d_10

Clifford template circuits

clifford_2_1

clifford_2_2

clifford_2_3

clifford_2_4

clifford_3_1

clifford_4_1

clifford_4_2

clifford_4_3

clifford_4_4

clifford_5_1

clifford_6_1

clifford_6_2