mindquantum.algorithm.compiler.kak_decompose

mindquantum.algorithm.compiler.kak_decompose(gate: QuantumGate, return_u3: bool = True)

KAK decomposition (CNOT basis) of an arbitrary two-qubit gate.

For more detail, please refer to An Introduction to Cartan’s KAK Decomposition for QC Programmers.

Parameters

• gate (QuantumGate) – 2-qubit quantum gate.

• return_u3 (bool) – return gates in form of U3 if True, otherwise return UnivMathGate. Default: True.

Returns

Circuit, including at most 3 CNOT gates and 6 single-qubit gates.

Examples

>>> import mindquantum as mq
>>> from mindquantum.algorithm.compiler.decompose import kak_decompose
>>> from scipy.stats import unitary_group
>>> g = mq.UnivMathGate('U', unitary_group.rvs(4, random_state=123)).on([0, 1])
>>> print(mq.Circuit() + g)
      ┏━━━┓
q0: ──┨   ┠───
      ┃   ┃
      ┃ U ┃
q1: ──┨   ┠───
      ┗━━━┛
>>> circ_decomposed = kak_decompose(g)
>>> print(circ_decomposed)
      ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓       ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
q0: ──┨ U3(θ=2.2601, φ=-3.602, λ=2.4907) ┠───■───┨ U3(θ=π/2, φ=-0.2573, λ=-π) ┠───■───↯─
      ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛   ┃   ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛   ┃
      ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━┓  ┏━┻━┓
q1: ──┨ U3(θ=1.846, φ=-2.9209, λ=0.5375) ┠─┨╺╋╸┠─┨ U3(θ=0, φ=-0.19, λ=-0.19) ┠──┨╺╋╸┠─↯─
      ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛ ┗━━━┛ ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━┛  ┗━━━┛
      ┏━━━━━━━━━━━━━━━━━━━━━┓             ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
q0: ──┨ U3(θ=π/2, φ=0, λ=π) ┠─────────■───┨ U3(θ=2.273, φ=-1.8708, λ=0.7431) ┠───
      ┗━━━━━━━━━━━━━━━━━━━━━┛         ┃   ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
      ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
q1: ──┨ U3(θ=0, φ=0.358, λ=0.358) ┠─┨╺╋╸┠─┨ U3(θ=2.7317, φ=1.8583, λ=0.6685) ┠───
      ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━┛ ┗━━━┛ ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛