TwoQubitBasisDecomposer

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

GitHub

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. Defaults to 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 (bool(opens in a new tab) | 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 $SU(2)$ using the best approximation given that each basis application has a finite basis_fidelity.

Parameters

unitary (Operator or ndarray) – $4 \times 4$ unitary to synthesize.
basis_fidelity (float(opens in a new tab) or None) – Fidelity to be assumed for applications of KAK Gate. If given, overrides basis_fidelity given at init.
approximate (bool(opens in a new tab)) – Approximates if basis fidelities are less than 1.0.
_num_basis_uses (int(opens in a new tab)) – 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 $\sim U_d(x, y, z)$ with $0$ uses of the basis gate. Result $U_r$ has trace:

\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 $\sim U_d(x, y, z)$ with $1$ use of the basis gate $\sim U_d(a, b, c)$ . Result $U_r$ has trace:

\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 $\sim U_d(x, y, z)$ with $2$ uses of the basis gate.

For supercontrolled basis $\sim U_d(\pi/4, b, 0)$ , all b, result $U_r$ has trace

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

decomp3_supercontrolled

decomp3_supercontrolled(target)

GitHub

Decompose target with $3$ uses of the basis. This is an exact decomposition for supercontrolled basis $\sim U_d(\pi/4, b, 0)$ , 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 $\Big\vert\text{Tr}(U \cdot U_\text{target}^{\dag})\Big\vert$ for a different number of basis gates.

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