qiskit.quantum_info.TwoQubitBasisDecomposer
class TwoQubitBasisDecomposer(gate, basis_fidelity=1.0, euler_basis=None)
A class for decomposing 2-qubit unitaries into minimal number of uses of a 2-qubit basis gate.
Parameters
- 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__
__init__(gate, basis_fidelity=1.0, euler_basis=None)
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::. | ||
decomp2_supercontrolled(target) | Decompose target ~Ud(x, y, z) with 2 uses of the basis gate. | ||
decomp3_supercontrolled(target) | 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. |
decomp0
static decomp0(target, eps=1e-15)
Decompose target ~Ud(x, y, z) with 0 uses of the basis gate. Result Ur has trace: , which is optimal for all targets and bases
decomp1
decomp1(target)
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
decomp2_supercontrolled(target)
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
decomp3_supercontrolled(target)
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
num_basis_gates(unitary)
Computes the number of basis gates needed in a decomposition of input unitary
traces
traces(target)
Give the expected traces for different number of basis gates.