TNO Quantum provides generic software components aimed at facilitating the development of quantum applications.
This package contains implementations of quantum-inspired algorithms for linear regression. It assumes a
linear system of the form Ax=b, where A is the training data, x is a vector of
unknown coefficients, and b is a vector of target values.
The class QILinearEstimator provides three methods:
fit, predict_x, and predict_b. Once the fit method has been called using A and b,
predict_x can be used to sample entries of the estimated coefficient vector. Alternatively,
predict_b can be used to sample entries of predictions corresponding to (un)observed
target values.
Limitations in (end-)use: the content of this software package may solely be used for applications that comply with international export control laws.
Documentation of the linear regression package can be found here.
Easily install the tno.quantum.ml.regression.linear_regression package using pip:
$ python -m pip install tno.quantum.ml.regression.linear_regressionSee example below. More examples can be found in the test directory.
import numpy as np
from sklearn.datasets import make_low_rank_matrix
from sklearn.model_selection import train_test_split
from tno.quantum.ml.regression.linear_regression import QILinearEstimator
rng = np.random.RandomState(7)
# Generate example data
m = 700
n = 100
A = make_low_rank_matrix(n_samples=m, n_features=n, effective_rank=3, random_state=rng, tail_strength=0.1)
x = rng.normal(0, 1, A.shape[1])
b = A @ x
# Create training and test datasets
A_train, A_test, b_train, b_test = train_test_split(A, b, test_size=0.3, random_state=rng)
# Fit quantum-inspired model
rank = 3
r = 100
c = 30
n_samples = 100 # for Monte Carlo methods
qi = QILinearEstimator(r, c, rank, n_samples, rng, sketcher_name="fkv")
qi = qi.fit(A_train, b_train)
# Sample from b (vector of predictions)
n_entries_b = 1000
sampled_indices_b, sampled_b = qi.sample_prediction_b(A_test, n_entries_b)The algorithms found in this repository have been developed in collaboration with the Quantum Application Lab and have been based on:
- https://github.com/QuantumApplicationLab/quantum-inspired-algorithms
- https://github.com/XanaduAI/quantum-inspired-algorithms
- "Quantum-inspired algorithms in practice", by Juan Miguel Arrazola, Alain Delgado, Bhaskar Roy Bardhan, and Seth Lloyd. 2020-08-13, volume 4, page 307. Quantum 4, 307 (2020).
- "Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension", by András Gilyén, Seth Lloyd, Ewin Tang. (2018). ArXiv, abs/1811.04909.
This work was supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme.