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Most quantum applications start with preparing a state in a quantum register. For example, in finance the state may represent the price distribution of some assets. In chemistry, it may be an initial guess for the ground state of a molecule, and in a quantum machine learning, a feature vector to analyze. The state preparation functions creates a quantum program that outputs either a probability distribution pip_{i} or a real amplitudes vector aia_{i} in the computational basis, with ii denoting the corresponding basis state. The amplitudes take the form of list of float numbers. The probabilities are a list of positive numbers. This is the resulting wave function for probability: ∣ψ⟩=∑ipi∣i⟩,\left|\psi\right\rangle = \sum_{i}\sqrt{p_{i}} \left|i\right\rangle, and this is for amplitude: ∣ψ⟩=∑iai∣i⟩.\left|\psi\right\rangle = \sum_{i}a_{i} \left|i\right\rangle. In general, state preparation is hard. Only a very small portion of the Hilbert space can be prepared efficiently (in O(poly(n))O(poly(n)) steps) on a quantum program. Therefore, in practice, an approximation is often used to lower the complexity. The approximation is specified by an error bound, using the L2L_2 norm. The higher the specified error tolerance, the smaller the output quantum program. For exact state preparation, specify an error bound of 00. The state preparation algorithm can be tuned depending on whether the probability distribution is sparse or dense. The synthesis engine will automatically select the parameterization based on the given constraints and optimization level. Function: prepare_state Parameters:
  • probabilities: CArray[CReal]
  • Probabilities to load.
Should be non-negative and sum to
  • bound: CReal
  • Approximation Error Bound, in the L2L_2 metric (with respect to the given probabilies vector).
  • out: Output[QArray[QBit]]
Function: inplace_prepare_state Parameters:
  • probabilities: CArray[CReal]
  • bound: CReal
  • out: QArray[QBit]
  • Should of size exactly log⁡2\log_2(“probabilities.len`)
The inplace_prepare_state works the same, but for a given allocated QArray. Function: prepare_amplitudes Parameters:
  • amplitudes: CArray[CReal]
  • Amplitudes of the loaded state.
Each should be real and the vector norm should be equal to
  • bound: CReal
  • Approximation Error Bound, in the L2L_2 metric (with respect to the given amplitudes vector).
  • out: Output[QArray[QBit]]
Function: inplace_prepare_amplitudes Parameters:
  • amplitudes: CArray[CReal]
  • Amplitudes of the loaded state.
Each should be real and the vector norm should be equal to
  • bound: CReal
  • Approximation Error Bound, in the L2L_2 metric (with respect to the given amplitudes vector).
  • out: QArray[QBit]
  • Should of size exactly log⁡2\log_2(amplitudes.len)
The inplace_prepare_amplitudes works the same, but for a given allocated QArray.

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Example 1: Loading Point Mass (PMF) Function

This example generates a quantum program whose output state probabilities are an approximation to the PMF given. That is, the probability of measuring the state ∣000⟩|000⟩ is 0.050.05, ∣001⟩|001⟩ is 0.110.11,… , and the probability to measure ∣111⟩|111⟩ is 0.060.06. 
from classiq import *


@qfunc
def main(x: Output[QNum]):
    probabilities = [0.05, 0.11, 0.13, 0.23, 0.27, 0.12, 0.03, 0.06]
    prepare_state(probabilities=probabilities, bound=0.01, out=x)


qmod = create_model(main)


qprog = synthesize(qmod)
Print the resulting probabilities: 
import numpy as np

result = execute(qprog).result_value()

probs = np.zeros(8)
for sample in result.parsed_counts:
    probs[int(sample.state["x"])] = sample.shots / result.num_shots
print("Resulting probabilities:", probs)
Output:

Resulting probabilities: [0.032 0.118 0.141 0.217 0.282 0.107 0.031 0.072]

​
Example 2

  • Preparating Amplitudes
This example loads a normalized linear space between -1 to
  1. The load state has an accuracy of 99 present under the L2 norm.
from classiq.execution import ClassiqBackendPreferences, ExecutionPreferences


@qfunc
def main(x: Output[QNum]):
    amps = np.linspace(-1, 1, 8)
    amps = amps / np.linalg.norm(amps)
    prepare_amplitudes(amplitudes=amps.tolist(), bound=0, out=x)


qmod = create_model(main)
qmod = set_execution_preferences(
    qmod,
    num_shots=1,
    backend_preferences=ClassiqBackendPreferences(backend_name="simulator_statevector"),
)


qprog = synthesize(qmod)
Print the resulting amplitudes: 
import numpy as np

result = execute(qprog).result_value()

amps = np.zeros(8, dtype=complex)
for sample in result.parsed_state_vector:
    amps[int(sample.state["x"])] = sample.amplitude

# remove global phase
global_phase = np.angle(amps[0])
amps = np.real(amps / np.exp(1j * global_phase))

print("Resulting amplitudes:", amps)
Output:

Resulting amplitudes: [ 0.54006172  0.38575837  0.23145502  0.07715167 -0.07715167 -0.23145502
   -0.38575837 -0.54006172]