TwoQubitBasisDecomposer

TwoQubitBasisDecomposer.__call__(target, basis_fidelity=None)

Decompose a two-qubit unitary over fixed basis + SU(2) using the best approximation given that each basis application has a finite fidelity.

static TwoQubitBasisDecomposer.decomp0(target)

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

TwoQubitBasisDecomposer.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

TwoQubitBasisDecomposer.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.

TwoQubitBasisDecomposer.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.

TwoQubitBasisDecomposer.num_basis_gates(unitary)

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

TwoQubitBasisDecomposer.traces(target)

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