An exponentially-growing family of universal quantum circuits

Abstract

Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific 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, angle-embedded 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 low-qubit 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 one-dimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.

Quantum machine learning for image classification

“…A promising area of research within QML for image classification is the hybrid quantum neural network (HQNN) [17,[35][36][37]. HQNNs combine classical deep learning architectures with QML algorithms [38][39][40][41][42], namely parameterized quantum circuits (PQCs), creating a hybrid system that leverages the strengths of both classical and quantum computing. This approach allows for the processing of large datasets with greater efficiency than classical deep learning architectures alone [43,44].…”

Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes

“…For a PINN to provide an accurate solution for a fluid dynamics problem, it is important to have a high expressivity (ability to learn solutions for a large variety of, possibly complex, problems). Fortunately, expressivity is a known strength of quantum computers [47][48][49]. Furthermore, quantum circuits are differentiable, meaning their derivatives can be calculated analytically, which is essential for noisy intermediate-scale quantum (NISQ) devices.…”