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__(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.

static decomp0(target, eps=1e-15)

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)

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)

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)

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)

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.