Special-Unitary Parameterization for Trainable Variational Quantum Circuits

TL;DR

This paper introduces SUN-VQC, a variational quantum circuit architecture that leverages Lie subgroup parameterization to reduce barren plateaus, improve gradient signals, and enhance convergence in near-term quantum algorithms.

Contribution

The paper presents a novel Lie-subalgebra based parameterization for variational circuits, improving trainability and scalability over existing hardware-efficient ans"atze.

Findings

SUN-VQCs maintain larger gradient signals.

Converge 2-3 times faster than traditional circuits.

Achieve higher fidelities in quantum auto-encoding and classification.

Abstract

We propose SUN-VQC, a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup, $\mathrm{SU}(2^{k}) \subset \mathrm{SU}(2^{n})$ with $k \ll n$. Confining the evolution to this compact subspace reduces the dynamical Lie-algebra dimension from $\mathcal{O}(4^{n})$ to $\mathcal{O}(4^{k})$, ensuring only polynomial suppression of gradient variance and circumventing barren plateaus that plague hardware-efficient ans\"atze. Exact, hardware-compatible gradients are obtained using a generalized parameter-shift rule, avoiding ancillary qubits and finite-difference bias. Numerical experiments on quantum auto-encoding and classification show that SUN-VQCs sustain order-of-magnitude larger gradient signals, converge 2--3$\times$ faster, and reach higher final fidelities than depth-matched Pauli-rotation or hardware-efficient circuits. These results demonstrate that Lie-subalgebra engineering provides a principled, scalable route to barren-plateau-resilient VQAs compatible with near-term quantum processors.