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haiqu.distribution_loading() This notebook demonstrates how to use haiqu.distribution_loading() to efficiently prepare a probability distribution in a quantum state. Loading a log-normal distribution on 12 qubits traditionally requires 4083 CNOT gates and a two-qubit gate depth of 4083. With Haiqu, the same distribution is prepared using only 21 CNOT gates (~200x improvement) and a two-qubit gate depth of 11 (>350x improvement). haiqu.distribution_loading() What does it do? Distribution loading prepares a quantum state whose measurement statistics match a desired probability density function. How do I use it? Pass a scipy distribution name, its parameters and intervals, and size of the quantum register to haiqu.distribution_loading(). This will create a data loading job. The results can be retrieve with job.result(). What are the options? num_layers and truncation_cutoff for controling circut synthesis. Which option do you recommend? Start with the default settings. num_layer = 2 is usually more than enought for most distributions. Having a bug or an issue? Submit feedback Initialize the benchmark Import the necessary libraries, initialize the Haiqu SDK. 
import qiskit
import numpy as np
import pandas as pd
from haiqu.sdk import haiqu
import matplotlib.pyplot as plt
from qiskit_finance.circuit.library import LogNormalDistribution

haiqu.login()
haiqu.init("Distribution Loading Tutorial")
Run benchmark scenarios Prepare log-normal distribution with traditional and Haiqu methods. 
# set up the distribution
# support interval to encode
interval_start = 0
interval_end = 10
# amount of qubits to encode, creates 2^num_qubits grid points
num_qubits = 12
# parameters of the corresponding normal distribution
mu = 0  
sigma = 1

# Scenario 1: standard method
# We consider a method proposed in Qiskit, and available for Financial computations
circuit_qiskit = LogNormalDistribution(num_qubits, mu=mu, sigma=sigma**2, bounds=(interval_start, interval_end))
circuit_qiskit.name = "Qiskit"

# Scenario 2: Haiqu distribution loading
circuit_haiqu = qiskit.QuantumCircuit(num_qubits, name="Haiqu")
distribution_gate, fidelity = haiqu.distribution_loading(distribution_name="lognorm", num_qubits=num_qubits, s=sigma, scale=np.exp(mu),
                                                         interval_start=interval_start, interval_end=interval_end).result()
circuit_haiqu.compose(distribution_gate, inplace=True)
print(f"Haiqu distribution is loaded with fidelity: {fidelity:.3f}")

# show the distribution we load
plt.plot(circuit_qiskit.values, circuit_qiskit.probabilities)
plt.title("Log-normal distribution")
plt.xlabel("x")
plt.ylabel("p(x)")
Haiqu’s distribution loading significantly outperforms standard methods as shown in the comparison table below: 
# we consider an ideal device with all-to-all connectivity
device_ideal = haiqu.get_device("aer_simulator")

circuit_qiskit_transpiled = haiqu.transpile(circuit_qiskit, device=device_ideal)

circuit_haiqu_transpiled = haiqu.transpile(circuit_haiqu, device=device_ideal)

haiqu.compare_metrics(circuit_qiskit_transpiled, circuit_haiqu_transpiled)
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