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TwoQubitBasisDecomposer

class qiskit.synthesis.TwoQubitBasisDecomposer(gate, basis_fidelity=1.0, euler_basis='U', pulse_optimize=None)

GitHub

Bases: object

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. Defaults to 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'].
  • pulse_optimize (bool | None) – 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.

__call__

__call__(unitary, basis_fidelity=None, approximate=True, *, _num_basis_uses=None)

GitHub

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

Parameters

  • unitary (Operator or ndarray) – 4×44 \times 4 unitary to synthesize.
  • basis_fidelity (float or None) – Fidelity to be assumed for applications of KAK Gate. If given, overrides basis_fidelity given at init.
  • approximate (bool) – Approximates if basis fidelities are less than 1.0.
  • _num_basis_uses (int) – force a particular approximation by passing a number in [0, 3].

Returns

Synthesized quantum circuit.

Return type

QuantumCircuit

Raises

QiskitError – if pulse_optimize is True but we don’t know how to do it.

Methods

decomp0

static decomp0(target)

GitHub

Decompose target ∼Ud(x,y,z)\sim U_d(x, y, z) with 00 uses of the basis gate. Result UrU_r has trace:

∣Tr(Ur⋅Utarget†)∣=4∣(cos⁡(x)cos⁡(y)cos⁡(z)+jsin⁡(x)sin⁡(y)sin⁡(z)∣\Big\vert\text{Tr}(U_r\cdot U_\text{target}^{\dag})\Big\vert = 4\Big\vert (\cos(x)\cos(y)\cos(z)+ j \sin(x)\sin(y)\sin(z)\Big\vert

which is optimal for all targets and bases

decomp1

decomp1(target)

GitHub

Decompose target ∼Ud(x,y,z)\sim U_d(x, y, z) with 11 use of the basis gate ∼Ud(a,b,c)\sim U_d(a, b, c). Result UrU_r has trace:

∣Tr(Ur⋅Utarget†)∣=4∣cos⁡(x−a)cos⁡(y−b)cos⁡(z−c)+jsin⁡(x−a)sin⁡(y−b)sin⁡(z−c)∣\Big\vert\text{Tr}(U_r \cdot U_\text{target}^{\dag})\Big\vert = 4\Big\vert \cos(x-a)\cos(y-b)\cos(z-c) + j \sin(x-a)\sin(y-b)\sin(z-c)\Big\vert

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

decomp2_supercontrolled

decomp2_supercontrolled(target)

GitHub

Decompose target ∼Ud(x,y,z)\sim U_d(x, y, z) with 22 uses of the basis gate.

For supercontrolled basis ∼Ud(π/4,b,0)\sim U_d(\pi/4, b, 0), all b, result UrU_r has trace

∣Tr(Ur⋅Utarget†)∣=4cos⁡(z)\Big\vert\text{Tr}(U_r \cdot U_\text{target}^\dag) \Big\vert = 4\cos(z)

which is the optimal approximation for basis of CNOT-class ∼Ud(π/4,0,0)\sim U_d(\pi/4, 0, 0) or DCNOT-class ∼Ud(π/4,π/4,0)\sim U_d(\pi/4, \pi/4, 0) and any target. It may be sub-optimal for b≠0b \neq 0 (i.e. there exists an exact decomposition for any target using B∼Ud(π/4,π/8,0)B \sim U_d(\pi/4, \pi/8, 0), but it may not be this decomposition). This is an exact decomposition for supercontrolled basis and target ∼Ud(x,y,0)\sim U_d(x, y, 0). No guarantees for non-supercontrolled basis.

decomp3_supercontrolled

decomp3_supercontrolled(target)

GitHub

Decompose target with 33 uses of the basis. This is an exact decomposition for supercontrolled basis ∼Ud(π/4,b,0)\sim U_d(\pi/4, b, 0), all b, and any target. No guarantees for non-supercontrolled basis.

num_basis_gates

num_basis_gates(unitary)

GitHub

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

traces

traces(target)

GitHub

Give the expected traces ∣Tr(U⋅Utarget†)∣\Big\vert\text{Tr}(U \cdot U_\text{target}^{\dag})\Big\vert for a different number of basis gates.

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