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mindquantum.core.gates.U3

class mindquantum.core.gates.U3(theta: ParameterResolver, phi: ParameterResolver, lamda: ParameterResolver)

U3 gate represent arbitrary single qubit gate.

U3 gate with matrix as:

$$\begin{array}{r}\mathrm{U}3(\theta ,\varphi ,\lambda )=\left(\begin{array}{cc}\cos (\theta /2)& -e^{i\lambda }\sin (\theta /2)\\ e^{i\varphi }\sin (\theta /2)& e^{i(\varphi +\lambda )}\cos (\theta /2)\end{array}\right)\end{array}$$

It can be decomposed as:

$$U3(\theta ,\varphi ,\lambda )=RZ(\varphi )RX(-\pi /2)RZ(\theta )RX(\pi /2)RZ(\lambda )$$

Parameters

• theta (Union[numbers.Number, dict, ParameterResolver]) – First parameter for U3 gate.

• phi (Union[numbers.Number, dict, ParameterResolver]) – Second parameter for U3 gate.

• lamda (Union[numbers.Number, dict, ParameterResolver]) – Third parameter for U3 gate.

Examples

>>> from mindquantum.core.gates import U3
>>> U3('theta','phi','lambda').on(0, 1)
U3(θ=theta, φ=phi, λ=lambda|0 <-: 1)

get_cpp_obj()

Construct cpp obj.

hermitian()

Get hermitian form of U3 gate.

Examples

>>> from mindquantum.core.gates import U3
>>> u3 = U3('a', 'b', 0.5).on(0)
>>> u3.hermitian()
U3(θ=-a, φ=-1/2, λ=-b|0)

property lamda: mindquantum.core.parameterresolver.parameterresolver.ParameterResolver

Get lamda parameter of U3 gate.

Returns

ParameterResolver, the lamda.

matrix(pr: ParameterResolver = None, full=False)

Get the matrix of U3 gate.

Parameters

• pr (Union[ParameterResolver, dict]) – The parameter for U3 gate.

• full (bool) – Whether to get the full matrix of this gate (the gate should be acted on some qubits). Default: False.

property phi: mindquantum.core.parameterresolver.parameterresolver.ParameterResolver

Get phi parameter of U3 gate.

Returns

ParameterResolver, the phi.

property theta: mindquantum.core.parameterresolver.parameterresolver.ParameterResolver

Get theta parameter of U3 gate.

Returns

ParameterResolver, the theta.