Exponential State Preparation
The prepare_exponential_state function
creates a state with exponentially decreasing amplitudes. Namely,
the probability for a state representing an integer \(n\) is
\[P\left(n\right) = \frac{1}{Z} e^{-\lambda n}\]
where \(\lambda\) is the rate, and \(Z\) is a normalization factor. If \(q\) in the number of qubits, then
\[Z = \sum_{n=0} ^{n = 2^q - 1} e^{-\lambda n} = \frac{1 - e^{-\lambda 2^q}}{1 - e^{-\lambda}}\]
Function: prepare_exponential_state
Arguments:
-
rate: CReal -
q: QArray[QBit]
Notice that the function acts inplace on the qubits.
Example
Prepare a state with probabilities:
\[P\left(n\right) = \frac{1}{Z} e^{-0.1 n}\]
where \(n\) is in the range \([0, 31]\).
from classiq import *
@qfunc
def main(x: Output[QArray[QBit]]):
allocate(5, x)
prepare_exponential_state(0.1, x)
qmod = create_model(main, out_file="prepare_exponential_state")
qprog = synthesize(qmod)