Special-Unitary Parameterization for Trainable Variational Quantum Circuits
This addresses a critical scalability issue for variational quantum algorithms on near-term quantum processors, offering a principled solution to barren plateaus.
The paper tackled the problem of barren plateaus in variational quantum circuits by proposing SUN-VQC, which uses symmetry-restricted Lie subgroups to reduce gradient variance, resulting in order-of-magnitude larger gradient signals, 2-3x faster convergence, and higher final fidelities in numerical experiments.
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 ansätze. 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.