# qiskit.quantum_info.TwoQubitBasisDecomposer¶

class TwoQubitBasisDecomposer(gate, basis_fidelity=1.0, euler_basis=None)[Quellcode]

A class for decomposing 2-qubit unitaries into minimal number of uses of a 2-qubit basis gate.

Parameter
• gate (Gate) – Two-qubit gate to be used in the KAK decomposition.

• basis_fidelity (float) – Fidelity to be assumed for applications of KAK Gate. Default 1.0.

• euler_basis (str) – Basis string to be provided to OneQubitEulerDecomposer for 1Q synthesis. Valid options are [‚ZYZ‘, ‚ZXZ‘, ‚XYX‘, ‚U‘, ‚U3‘, ‚U1X‘, ‚PSX‘, ‚ZSX‘, ‚RR‘]. Default ‚U3‘.

__init__(gate, basis_fidelity=1.0, euler_basis=None)[Quellcode]

Initialize self. See help(type(self)) for accurate signature.

Methods

 __init__(gate[, basis_fidelity, euler_basis]) Initialize self. decomp0(target[, eps]) Decompose target ~Ud(x, y, z) with 0 uses of the basis gate. decomp1(target) Decompose target ~Ud(x, y, z) with 1 uses of the basis gate ~Ud(a, b, c). Result Ur has trace: .. math::. Decompose target ~Ud(x, y, z) with 2 uses of the basis gate. Decompose target with 3 uses of the basis. num_basis_gates(unitary) Computes the number of basis gates needed in a decomposition of input unitary traces(target) Give the expected traces $$|Tr(U \cdot Utarget^dag)|$$ for different number of basis gates.
static decomp0(target, eps=1e-15)[Quellcode]

Decompose target ~Ud(x, y, z) with 0 uses of the basis gate. Result Ur has trace: $$|Tr(Ur.Utarget^dag)| = 4|(cos(x)cos(y)cos(z)+ j sin(x)sin(y)sin(z)|$$, which is optimal for all targets and bases

decomp1(target)[Quellcode]

Decompose target ~Ud(x, y, z) with 1 uses of the basis gate ~Ud(a, b, c). Result Ur has trace: .. math:

|Tr(Ur.Utarget^dag)| = 4|cos(x-a)cos(y-b)cos(z-c) + j sin(x-a)sin(y-b)sin(z-c)|


which is optimal for all targets and bases with z==0 or c==0

decomp2_supercontrolled(target)[Quellcode]

Decompose target ~Ud(x, y, z) with 2 uses of the basis gate.

For supercontrolled basis ~Ud(pi/4, b, 0), all b, result Ur has trace .. math:

|Tr(Ur.Utarget^dag)| = 4cos(z)


which is the optimal approximation for basis of CNOT-class ~Ud(pi/4, 0, 0) or DCNOT-class ~Ud(pi/4, pi/4, 0) and any target. May be sub-optimal for b!=0 (e.g. there exists exact decomposition for any target using B B~Ud(pi/4, pi/8, 0), but not this decomposition.) This is an exact decomposition for supercontrolled basis and target ~Ud(x, y, 0). No guarantees for non-supercontrolled basis.

decomp3_supercontrolled(target)[Quellcode]

Decompose target with 3 uses of the basis. This is an exact decomposition for supercontrolled basis ~Ud(pi/4, b, 0), all b, and any target. No guarantees for non-supercontrolled basis.

num_basis_gates(unitary)[Quellcode]

Computes the number of basis gates needed in a decomposition of input unitary

traces(target)[Quellcode]

Give the expected traces $$|Tr(U \cdot Utarget^dag)|$$ for different number of basis gates.