qml.labs.estimator_beta.ops.ch_resource_decomp

ch_resource_decomp()

Returns a list of GateCount objects representing the resources of the CH operator.

Resources:

The resources are derived from the following identities:

\[\begin{split}\begin{align} \hat{H} &= \hat{R}_{y}(\frac{\pi}{4}) \cdot \hat{Z} \cdot \hat{R}_{y}(\frac{-\pi}{4}), \\ \hat{Z} &= \hat{H} \cdot \hat{X} \cdot \hat{H}. \end{align}\end{split}\]

Specifically, the resources are defined as two RY, two Hadamard and one CNOT gates.

Decomposing the \(\hat{R}_y(\pm\frac{\pi}{4})\) rotations into the Clifford+T basis and substituting yields:

\[\begin{split}\begin{align} \hat{H} &= (S H T H S^\dagger) \cdot \hat{Z} \cdot (S H T^\dagger H S^\dagger) \\ &= S H T \cdot (\hat{H} \hat{Z} \hat{H}) \cdot T^\dagger H S^\dagger \\ &= S H T \cdot \hat{X} \cdot T^\dagger H S^\dagger \end{align}\end{split}\]

The final resources are: 2 Hadamard, 1 T, 1 Adjoint(T), 1 S, 1 Adjoint(S), and 1 CNOT.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

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