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Partial Uniform State Preparations

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The functions prepare_uniform_trimmed_state and prepare_uniform_interval_state create states with uniform superposition over a discrete interval of the possible states. Both scale polynomially with the number of qubits.

Uniform Trimmed State

Function: prepare_uniform_trimmed_state

Arguments:

  • m: CInt - number of states to load.

  • q: QArray[QBit] - quantum variable to load the state into.

The function loads the following superposition:

\[|\psi\rangle = \frac{1}{\sqrt{m}}\sum_{i=0}^{m-1}{|i\rangle}\]

Example

Prepare the following state on a variable of size 4 qubits.:

\[|\psi\rangle = \frac{1}{\sqrt{3}}\sum_{i=0}^{2}{|i\rangle}\]
import matplotlib.pyplot as plt

from classiq import *


@qfunc
def main(x: Output[QNum]):
    allocate(4, x)
    prepare_uniform_trimmed_state(3, x)


qmod = create_model(main, out_file="prepare_uniform_trimmed_state")
qprog = synthesize(qmod)

result = execute(qprog).result_value()
counts = result.parsed_counts

plt.figure(figsize=(4, 3))
plt.bar(
    [c.state["x"] for c in counts],
    [c.shots for c in counts],
    color="skyblue",
    edgecolor="black",
)
plt.xlabel("state")
plt.ylabel("shots")

Text(0, 0.5, 'shots')

png

Uniform Interval State

Function: prepare_uniform_interval_state

Arguments:

  • start: CInt - first state to be loaded.

  • end: CInt - boundary of the loaded states (not including).

  • q: QArray[QBit] - quantum variable to load the state into.

The function loads the following superposition:

\[|\psi\rangle = \frac{1}{\sqrt{end-start}}\sum_{i=start}^{end-1}{|i\rangle}\]

Example

Prepare the following state on a variable of size 5 qubits.:

\[|\psi\rangle = \frac{1}{\sqrt{6}}\sum_{i=2}^{7}{|i\rangle}\]
@qfunc
def main(x: Output[QNum]):
    allocate(5, x)
    prepare_uniform_interval_state(2, 8, x)


qmod = create_model(main, out_file="prepare_uniform_interval_state")
qprog = synthesize(qmod)

result = execute(qprog).result_value()
counts = result.parsed_counts

plt.figure(figsize=(5, 3))
plt.bar(
    [c.state["x"] for c in counts],
    [c.shots for c in counts],
    color="skyblue",
    edgecolor="black",
)
plt.xlabel("state")
plt.ylabel("shots")

Text(0, 0.5, 'shots')

png