An exponentiallygrowing family of universal quantum circuits
Abstract
Quantum machine learning has become an area of growing interest but has certain theoretical and hardwarespecific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits with high qubit counts, imposing a limit on the number of qubits that data scientists can use for solving problems. Independently, angleembedded supervised quantum neural networks were shown to produce truncated Fourier series with a degree directly dependent on two factors: the depth of the encoding and the number of parallel qubits the encoding applied to. The degree of the Fourier series limits the model expressivity. This work introduces two new architectures whose Fourier degrees grow exponentially: the sequential and parallel exponential quantum machine learning architectures. This is done by efficiently using the available Hilbert space when encoding, increasing the expressivity of the quantum encoding. Therefore, the exponential growth allows staying at the lowqubit limit to create highly expressive circuits avoiding barren plateaus. Practically, parallel exponential architecture was shown to outperform the existing linear architectures by reducing their final mean square error value by up to 44.7% in a onedimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.
 Publication:

Machine Learning: Science and Technology
 Pub Date:
 September 2023
 DOI:
 10.1088/26322153/ace757
 arXiv:
 arXiv:2212.00736
 Bibcode:
 2023MLS&T...4c5036K
 Keywords:

 quantum encoding;
 quantum circuits;
 quantum machine learning;
 quantum neural networks;
 machine learning model expressivity;
 quantum algorithms;
 Quantum Physics;
 Computer Science  Machine Learning
 EPrint:
 14 pages, 7 figures