PauliBlockEncoding function
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Namespace: Microsoft.Quantum.Simulation
Package: Microsoft.Quantum.Standard
Creates a block-encoding unitary for a Hamiltonian.
The Hamiltonian $H=\sum_{j}\alpha_j P_j$ is described by a sum of Pauli terms $P_j$, each with real coefficient $\alpha_j$.
function PauliBlockEncoding (generatorSystem : Microsoft.Quantum.Simulation.GeneratorSystem) : (Double, Microsoft.Quantum.Simulation.BlockEncodingReflection)
Input
generatorSystem : GeneratorSystem
A GeneratorSystem
that describes $H$ as a sum of Pauli terms
Output : (Double,BlockEncodingReflection)
First parameter
The one-norm of coefficients $\alpha=\sum_{j}|\alpha_j|$.
Second parameter
A BlockEncodingReflection
unitary $U$ of the Hamiltonian $H$. As this unitary
satisfies $U^2 = I$, it is also a reflection.
Remarks
This is obtained by preparing and unpreparing the state $\sum_{j}\sqrt{\alpha_j/\alpha}\ket{j}$, and constructing a multiply-controlled unitary PrepareArbitraryStateD operation and MultiplexOperationsFromGenerator operation.
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