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Edit cutting explanation (backport #657) #658

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Aug 20, 2024
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Edit cutting explanation (backport #657) #658

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Edit cutting explanation (#657)
ibrahim-shehzad Aug 20, 2024
df20160
Merge branch 'stable/0.7' into mergify/bp/stable/0.7/pr-657
garrison Aug 20, 2024
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8 changes: 4 additions & 4 deletions docs/circuit_cutting/explanation/index.rst
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Expand Up @@ -60,10 +60,10 @@ As a basic and explicit example, let us consider the decomposition of a cut :cla

As shown in [`2 <https://arxiv.org/abs/1909.07534>`__], a quantum circuit which implements an :class:`~qiskit.circuit.library.RZZGate` can be simulated by performing six subexperiments where the :class:`~qiskit.circuit.library.RZZGate` in the original circuit has been replaced with only local (single-qubit) operations [the :math:`\mathcal{F}_i`\ 's in Eq. :eq:`eq:qpd`]. The result is then reconstructed by combining the subexperiment results with certain coefficients [the :math:`a_i`\ 's in Eq. :eq:`eq:qpd`], which can be either positive or negative. Given the :math:`\theta` parameter of the :class:`~qiskit.circuit.library.RZZGate`, the six subexperiments are as follows:

1. With coefficient :math:`a_1 = \cos^2 \theta`, do nothing (:math:`I \otimes I`, where :math:`I` is the identity operation on a single qubit).
2. With coefficient :math:`a_2 = \sin^2 \theta`, perform a :class:`~qiskit.circuit.library.ZGate` on each qubit (:math:`Z \otimes Z`).
3. With coefficient :math:`a_3 = \sin(2\theta)/2`, perform a projective measurement in the Z basis on the first qubit and an :class:`~qiskit.circuit.library.SGate` gate on the second qubit (denote this as :math:`M_z \otimes S`). If the result of the measurement is 1, flip the sign of that outcome's contribution during reconstruction.
4. With coefficient :math:`a_4 = -\sin(2\theta)/2`, perform a projective measurement in the Z basis on the first qubit and an :class:`~qiskit.circuit.library.SdgGate` gate on the second qubit (denote this as :math:`M_z \otimes S^\dagger`). If the result of the measurement is 1, flip the sign of that outcome's contribution during reconstruction.
1. With coefficient :math:`a_1 = \cos^2 (\theta/2)`, do nothing (:math:`I \otimes I`, where :math:`I` is the identity operation on a single qubit).
2. With coefficient :math:`a_2 = \sin^2 (\theta/2)`, perform a :class:`~qiskit.circuit.library.ZGate` on each qubit (:math:`Z \otimes Z`).
3. With coefficient :math:`a_3 = -\sin(\theta)/2`, perform a projective measurement in the Z basis on the first qubit and an :class:`~qiskit.circuit.library.SGate` gate on the second qubit (denote this as :math:`M_z \otimes S`). If the result of the measurement is 1, flip the sign of that outcome's contribution during reconstruction.
4. With coefficient :math:`a_4 = \sin(\theta)/2`, perform a projective measurement in the Z basis on the first qubit and an :class:`~qiskit.circuit.library.SdgGate` gate on the second qubit (denote this as :math:`M_z \otimes S^\dagger`). If the result of the measurement is 1, flip the sign of that outcome's contribution during reconstruction.
5. Same as term 3 (:math:`a_5 = a_3`), but swap the qubits (:math:`S \otimes M_z`).
6. Same as term 4 (:math:`a_6 = a_4`), but swap the qubits (:math:`S^\dagger \otimes M_z`).

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