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TwoQubitBasisDecomposer

qiskit.quantum_info.TwoQubitBasisDecomposer(gate, basis_fidelity=1.0, euler_basis='U', pulse_optimize=None) GitHub(opens in a new tab)

Bases: object(opens in a new tab)

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(opens in a new tab)) – Fidelity to be assumed for applications of KAK Gate. Default 1.0.
  • euler_basis (str(opens in a new tab)) – Basis string to be provided to OneQubitEulerDecomposer for 1Q synthesis. Valid options are [‘ZYZ’, ‘ZXZ’, ‘XYX’, ‘U’, ‘U3’, ‘U1X’, ‘PSX’, ‘ZSX’, ‘RR’].
  • pulse_optimize (None or bool(opens in a new tab)) – If True, try to do decomposition which minimizes local unitaries in between entangling gates. This will raise an exception if an optimal decomposition is not implemented. Currently, only [{CX, SX, RZ}] is known. If False, don’t attempt optimization. If None, attempt optimization but don’t raise if unknown.

Methods

decomp0

static decomp0(target)

Decompose target ~Ud(x, y, z) with 0 uses of the basis gate. Result Ur has trace: Tr(Ur.Utargetdag)=4(cos(x)cos(y)cos(z)+jsin(x)sin(y)sin(z)|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

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 Tr(UUtargetdag)|Tr(U \cdot Utarget^dag)| for different number of basis gates.

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