§ ¹³ÙgC>ãóf—dZddlTddlTddlmZddlmZddlmZddl m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"dd l#m$Z$dd l%m&Z&dd l'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0dd l1m2Z2m3Z3dd l4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;mZ>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHddlImIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXddlYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZaddlbmcZcmbZbddldmeZemdZdddlfmgZgmhZhddlimjZjmiZiddlkmlZlmkZkmmZmddlnmoZomnZnddlpmqZqmpZpddlrmsZsddltmuZumvZvddlmwZwdS)uŸ2 =============================================== Circuit Library (:mod:`qiskit.circuit.library`) =============================================== .. currentmodule:: 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 :meth:`.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: .. plot:: :alt: Circuit diagram output by the previous code. :include-source: 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. The function :func:`.get_standard_gate_name_mapping` allows you to see the available standard gates and operations. .. autofunction:: get_standard_gate_name_mapping Standard gates ============== These operations are reversible unitary gates and they all subclass :class:`~qiskit.circuit.Gate`. As a consequence, they all have the methods :meth:`~qiskit.circuit.Gate.to_matrix`, :meth:`~qiskit.circuit.Gate.power`, and :meth:`~qiskit.circuit.Gate.control`, which we can generally only apply to unitary operations. For example: .. code-block:: 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 .. code-block:: text [[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]] .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst C3XGate C3SXGate C4XGate CCXGate DCXGate CHGate CPhaseGate CRXGate CRYGate CRZGate CSGate CSdgGate CSwapGate CSXGate CUGate CU1Gate CU3Gate CXGate CYGate CZGate CCZGate ECRGate HGate IGate MSGate PhaseGate RCCXGate RC3XGate RGate RXGate RXXGate RYGate RYYGate RZGate RZZGate RZXGate XXMinusYYGate XXPlusYYGate SGate SdgGate SwapGate iSwapGate SXGate SXdgGate TGate TdgGate UGate U1Gate U2Gate U3Gate XGate YGate ZGate GlobalPhaseGate 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. * :class:`qiskit.circuit.Barrier` Standard Operations =================== Operations are non-reversible changes in the quantum state of the circuit. * :class:`qiskit.circuit.Measure` * :class:`qiskit.circuit.Reset` Generalized Gates ================= These "gates" (many are :class:`~qiskit.circuit.QuantumCircuit` subclasses) allow to set the amount of qubits involved at instantiation time. .. code-block:: from qiskit.circuit.library import DiagonalGate diagonal = DiagonalGate([1, 1j]) print(diagonal.num_qubits) diagonal = DiagonalGate([1, 1, 1, -1]) print(diagonal.num_qubits) .. code-block:: text 1 2 .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst Diagonal DiagonalGate MCMT MCMTVChain Permutation PermutationGate GMS GR GRX GRY GRZ MCMTGate MCPhaseGate MCXGate MCXGrayCode MCXRecursive MCXVChain RVGate PauliGate LinearFunction Isometry UnitaryGate UCGate UCPauliRotGate UCRXGate UCRYGate UCRZGate Boolean Logic Circuits ====================== These are :class:`~qiskit.circuit.QuantumCircuit` subclasses that implement boolean logic operations, such as the logical or of a set of qubit states. .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst AND AndGate OR OrGate XOR BitwiseXorGate random_bitwise_xor InnerProduct InnerProductGate 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. .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst QFT QFTGate Arithmetic Circuits =================== These :class:`~qiskit.circuit.QuantumCircuit`\ s perform classical arithmetic, such as addition or multiplication. Amplitude Functions ------------------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst LinearAmplitudeFunction Functional Pauli Rotations -------------------------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst FunctionalPauliRotations LinearPauliRotations PolynomialPauliRotations PiecewiseLinearPauliRotations PiecewisePolynomialPauliRotations PiecewiseChebyshev Adders ------ .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst DraperQFTAdder CDKMRippleCarryAdder VBERippleCarryAdder WeightedAdder ModularAdderGate HalfAdderGate FullAdderGate Multipliers ----------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst HRSCumulativeMultiplier RGQFTMultiplier MultiplierGate Comparators ----------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst IntegerComparator Functions on binary variables ----------------------------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst QuadraticForm Other arithmetic functions -------------------------- .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst ExactReciprocal Particular Quantum Circuits =========================== The following gates and quantum circuits define specific quantum circuits of interest: .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst FourierChecking GraphState GraphStateGate HiddenLinearFunction IQP QuantumVolume PhaseEstimation GroverOperator PhaseOracle PauliEvolutionGate HamiltonianGate UnitaryOverlap For circuits that have a well-defined structure it is preferrable to use the following functions to construct them: .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst fourier_checking hidden_linear_function iqp random_iqp quantum_volume phase_estimation grover_operator unitary_overlap N-local circuits ================ The following functions return a parameterized :class:`.QuantumCircuit` to use as ansatz in a broad set of variational quantum algorithms: .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst n_local efficient_su2 real_amplitudes pauli_two_design excitation_preserving qaoa_ansatz hamiltonian_variational_ansatz evolved_operator_ansatz These :class:`~qiskit.circuit.library.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. .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst NLocal TwoLocal PauliTwoDesign RealAmplitudes EfficientSU2 EvolvedOperatorAnsatz ExcitationPreserving QAOAAnsatz Data encoding circuits ====================== The following functions return a parameterized :class:`.QuantumCircuit` to use as data encoding circuits in a series of variational quantum algorithms: .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst pauli_feature_map z_feature_map zz_feature_map These :class:`~qiskit.circuit.library.BlueprintCircuit` encode classical data in quantum states and are used as feature maps for classification. .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst PauliFeatureMap ZFeatureMap ZZFeatureMap Data preparation circuits ========================= The following operations are used for state preparation: .. autosummary:: :toctree: ../stubs/ :template: autosummary/class_no_inherited_members.rst StatePreparation Initialize 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: .. code-block:: 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 :class:`~qiskit.circuit.library.XGate`, :class:`~qiskit.circuit.library.CXGate`, and :class:`~qiskit.circuit.library.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 .. currentmodule:: qiskit.circuit.library.templates.nct .. autofunction:: template_nct_2a_1 .. autofunction:: template_nct_2a_2 .. autofunction:: template_nct_2a_3 .. autofunction:: template_nct_4a_1 .. autofunction:: template_nct_4a_2 .. autofunction:: template_nct_4a_3 .. autofunction:: template_nct_4b_1 .. autofunction:: template_nct_4b_2 .. autofunction:: template_nct_5a_1 .. autofunction:: template_nct_5a_2 .. autofunction:: template_nct_5a_3 .. autofunction:: template_nct_5a_4 .. autofunction:: template_nct_6a_1 .. autofunction:: template_nct_6a_2 .. autofunction:: template_nct_6a_3 .. autofunction:: template_nct_6a_4 .. autofunction:: template_nct_6b_1 .. autofunction:: template_nct_6b_2 .. autofunction:: template_nct_6c_1 .. autofunction:: template_nct_7a_1 .. autofunction:: template_nct_7b_1 .. autofunction:: template_nct_7c_1 .. autofunction:: template_nct_7d_1 .. autofunction:: template_nct_7e_1 .. autofunction:: template_nct_9a_1 .. autofunction:: template_nct_9c_1 .. autofunction:: template_nct_9c_2 .. autofunction:: template_nct_9c_3 .. autofunction:: template_nct_9c_4 .. autofunction:: template_nct_9c_5 .. autofunction:: template_nct_9c_6 .. autofunction:: template_nct_9c_7 .. autofunction:: template_nct_9c_8 .. autofunction:: template_nct_9c_9 .. autofunction:: template_nct_9c_10 .. autofunction:: template_nct_9c_11 .. autofunction:: template_nct_9c_12 .. autofunction:: template_nct_9d_1 .. autofunction:: template_nct_9d_2 .. autofunction:: template_nct_9d_3 .. autofunction:: template_nct_9d_4 .. autofunction:: template_nct_9d_5 .. autofunction:: template_nct_9d_6 .. autofunction:: template_nct_9d_7 .. autofunction:: template_nct_9d_8 .. autofunction:: template_nct_9d_9 .. autofunction:: template_nct_9d_10 .. currentmodule:: qiskit.circuit.library Clifford template circuits -------------------------- Template circuits over Clifford gates. .. autofunction:: clifford_2_1 .. autofunction:: clifford_2_2 .. autofunction:: clifford_2_3 .. autofunction:: clifford_2_4 .. autofunction:: clifford_3_1 .. autofunction:: clifford_4_1 .. autofunction:: clifford_4_2 .. autofunction:: clifford_4_3 .. autofunction:: clifford_4_4 .. autofunction:: clifford_5_1 .. autofunction:: clifford_6_1 .. autofunction:: clifford_6_2 .. autofunction:: clifford_6_3 .. autofunction:: clifford_6_4 .. autofunction:: clifford_6_5 .. autofunction:: clifford_8_1 .. autofunction:: clifford_8_2 .. autofunction:: clifford_8_3 RZXGate template circuits ------------------------- Template circuits with :class:`~qiskit.circuit.library.RZXGate`. .. autofunction:: rzx_yz .. autofunction:: rzx_xz .. autofunction:: rzx_cy .. autofunction:: rzx_zz1 .. autofunction:: rzx_zz2 .. autofunction:: rzx_zz3 é)Ú*é)ÚBarrier)ÚMeasure)ÚReset)ÚBlueprintCircuit)ÚDiagonalÚ DiagonalGateÚMCMTÚ MCMTVChainÚ PermutationÚPermutationGateÚGMSÚMCMTGateÚMSGateÚGRÚGRXÚGRYÚGRZÚRVGateÚ PauliGateÚLinearFunctionÚIsometryÚ UnitaryGateÚUCGateÚUCPauliRotGateÚUCRXGateÚUCRYGateÚUCRZGate)ÚPauliEvolutionGate)ÚHamiltonianGate) ÚANDÚAndGateÚORÚOrGateÚXORÚBitwiseXorGateÚrandom_bitwise_xorÚ InnerProductÚInnerProductGate)ÚQFTÚQFTGate)ÚModularAdderGateÚ HalfAdderGateÚ FullAdderGateÚMultiplierGateÚFunctionalPauliRotationsÚLinearPauliRotationsÚPiecewiseLinearPauliRotationsÚ!PiecewisePolynomialPauliRotationsÚPolynomialPauliRotationsÚIntegerComparatorÚ WeightedAdderÚ QuadraticFormÚLinearAmplitudeFunctionÚVBERippleCarryAdderÚCDKMRippleCarryAdderÚDraperQFTAdderÚPiecewiseChebyshevÚHRSCumulativeMultiplierÚRGQFTMultiplierÚExactReciprocal)Ún_localÚNLocalÚTwoLocalÚpauli_two_designÚPauliTwoDesignÚreal_amplitudesÚRealAmplitudesÚ efficient_su2Ú EfficientSU2Úhamiltonian_variational_ansatzÚevolved_operator_ansatzÚEvolvedOperatorAnsatzÚexcitation_preservingÚExcitationPreservingÚ qaoa_ansatzÚ QAOAAnsatz)Ú z_feature_mapÚzz_feature_mapÚpauli_feature_mapÚPauliFeatureMapÚ ZFeatureMapÚ 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