An exponentially-growing family of universal quantum circuits

TL;DR

This paper introduces two new quantum circuit architectures with exponentially growing Fourier degrees, enhancing expressivity while avoiding barren plateaus, and demonstrates their superior performance and feasibility on quantum hardware.

Contribution

The work presents exponentially-growing quantum circuit architectures that increase expressivity and mitigate barren plateaus, a significant advancement over existing linear models.

Findings

Parallel architecture reduces mean square error by up to 44.7%.

Feasibility demonstrated on a trapped ion quantum processor.

Exponential growth in Fourier degree enhances model expressivity.

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.