2025
Published
Generalized Hadamard
Efficient Quantum Gradient and Higher-order Derivative Estimation via Generalized Hadamard Test
Quantum gradients.
Higher derivatives.
The example is described below.
Add one control qubit for each derivative. Each control acts on the same system. Multiply the measured outcomes, then average those products to read the derivative.
An exact small circuit with a Y rotation. Angles are in radians. The readout is a mean over repeated runs, not a single-shot derivative.
One test, a wider set of derivatives.
Generalize Hadamard tests to estimate quantum gradients and higher-order derivatives.
How the method works.
A quantum circuit can have adjustable angles. To improve its output, we need to know how the measured result changes with an angle. The gradient gives the slope. Higher derivatives describe how that slope changes.
The paper extends the Hadamard test to estimate these derivatives. It also shows how to choose a gradient method for each circuit parameter. The aim is to use a test that fits the circuit and the measurement, rather than one fixed method for every parameter.
For a teaching example, start a qubit in state 0. Rotate it about the y axis by angle θ in radians, then measure along z. The mean result is f(θ) = cos θ. Its slope is −sin θ, and its second derivative is −cos θ. These exact expressions show what the derivative tests aim to estimate.
This example explains the quantities; it is not a benchmark from the paper. The paper gives the test circuits, their assumptions and the measurement-cost comparisons.
Sources &
citation.
2025 IEEE International Conference on Quantum Computing and Engineering (QCE)
2025 · Published
IEEE QCE2025 · arXiv:2408.05406
View the citation
@inproceedings{generalized-hadamard-2025,
title = {{Efficient Quantum Gradient and Higher-order Derivative Estimation via Generalized Hadamard Test}},
author = {Dantong Li and Dikshant Dulal and Mykhailo Ohorodnikov and Hanrui Wang and Yongshan Ding},
year = {2025},
booktitle = {2025 IEEE International Conference on Quantum Computing and Engineering (QCE)},
doi = {10.1109/QCE65121.2025.00024},
url = {https://arxiv.org/abs/2408.05406}
}