g*dZddlmZddlZddlmZddlZddlZddl m Z m Z ddl m Z mZddlmZddlmZdd lmZdd lmZmZdd lmZdd lmZdd lmZ dddddZddddZdZ dZ!dS) zP Quantum Shannon Decomposition. Method is described in arXiv:quant-ph/0406176. ) annotationsN)Callable)QuantumCircuitQuantumRegister)TwoQubitBasisDecomposertwo_qubit_decompose)one_qubit_decompose)is_hermitian_matrix)CXGate)UCPauliRotGate_EPS)UCRYGate)UCRZGate)"two_qubit_decompose_up_to_diagonalT)_depthmat np.ndarrayopt_a1boolopt_a2 decomposer_1q-Callable[[np.ndarray], QuantumCircuit] | None decomposer_2qcB|jd}ttj|}t jt j||rt|S|dkr"|tj }||}n|dkr@|1|r|dkrddl m fd} | }ntt}||}nt|} t| }|dz} tj|d| | \\} } }\}}t%||||| }||| |rt+|}|dz}t-|d|z}||t1|t j| dd|df| dd|df<nLt5d|z}||| d g| dd zt%| | ||| }||| |r|dkr|dkrt7|S|S) u Decomposes a unitary matrix into one and two qubit gates using Quantum Shannon Decomposition, This decomposition is described in Shende et al. [1]. .. code-block:: text ┌───┐ ┌───┐ ┌───┐ ┌───┐ ─┤ ├─ ───────┤ Rz├─────┤ Ry├─────┤ Rz├───── │ │ ≃ ┌───┐└─┬─┘┌───┐└─┬─┘┌───┐└─┬─┘┌───┐ /─┤ ├─ /─┤ ├──□──┤ ├──□──┤ ├──□──┤ ├ └───┘ └───┘ └───┘ └───┘ └───┘ The number of :class:`.CXGate`\ s generated with the decomposition without optimizations is: .. math:: \frac{9}{16} 4^n - \frac{3}{2} 2^n If ``opt_a1 = True``, the default, the CX count is reduced by: .. math:: \frac{1}{3} 4^{n - 2} - 1. If ``opt_a2 = True``, the default, the CX count is reduced by: .. math:: 4^{n-2} - 1. Args: mat: unitary matrix to decompose opt_a1: whether to try optimization A.1 from Shende et al. [1]. This should eliminate 1 ``cx`` per call. If ``True``, :class:`.CZGate`\s are left in the output. If desired these can be further decomposed to :class:`.CXGate`\s. opt_a2: whether to try optimization A.2 from Shende et al. [1]. This decomposes two qubit unitaries into a diagonal gate and a two cx unitary and reduces overall cx count by :math:`4^{n-2} - 1`. decomposer_1q: optional 1Q decomposer. If None, uses :class:`~qiskit.synthesis.OneQubitEulerDecomposer`. decomposer_2q: optional 2Q decomposer. If None, uses :class:`~qiskit.synthesis.TwoQubitBasisDecomposer`. Returns: QuantumCircuit: Decomposed quantum circuit. References: 1. 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A A A " Bqqq)**},= > >Bqqq)**}  QZ//1122D KKr"vhCRC0 1 1 1!"bvVVV  J--//444 &A++#'' Kr(Fc |jd|jdz}ttj|}||jz}t |r#tj |\}} n8tj |d\} } | }tj |} tj| } | | jz|z} t!|}t#| |||dz}||t)|dz dtjtj| z}t/|}|||dz gt3t)|dz zt#| |||dz}||t)|dz |S)u Decompose a generic multiplexer. ────□──── ┌──┴──┐ /─┤ ├─ └─────┘ represented by the block diagonal matrix ┏ ┓ ┃ um0 ┃ ┃ um1 ┃ ┗ ┛ to ┌───┐ ───────┤ Rz├────── ┌───┐└─┬─┘┌───┐ /─┤ w ├──□──┤ v ├─ └───┘ └───┘ where v and w are general unitaries determined from decomposition. Args: um0 (ndarray): applied if MSB is 0 um1 (ndarray): applied if MSB is 1 opt_a1 (bool): whether to try optimization A.1 from Shende. This should eliminate 1 cnot per call. If True CZ gates are left in the output. If desired these can be further decomposed opt_a2 (bool): whether to try optimization A.2 from Shende. 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