Automated Unitary Coupled Cluster Circuit Design via Differentiable Quantum Architecture Search

Designing compact and accurate circuits for the variational quantum eigensolver (VQE) is a central challenge in near-term quantum chemistry. Existing adaptive methods such as ADAPT-VQE design circuits by iteratively selecting operators from a predefined pool guided by gradient information and greedy heuristics. In this work, we adopt differentiable quantum architecture search (DQAS) as a circuit design framework based on the UCCSD operator pool, and introduce two complementary strategies: a global mode that simultaneously optimizes all operator selections, and a layerwise mode that constructs circuits incrementally while preserving previously learned structure. By relaxing discrete operator selection into a continuous differentiable optimization, DQAS enables gradient-based exploration over the combinatorial space of UCC circuit architectures. Benchmarks on BeH2, H4, LiH, H6, and H2O (8-14 qubits) show that both strategies achieve higher accuracy and fewer CNOT gates than ADAPT-VQE in the compact circuit regime, with up to 2.7-fold accuracy improvement for H2O and CNOT reductions of 13-17% at equivalent circuit depths. Benchmarks on the qubit-excitation-based (QEB) operator pool confirm that both advantages generalize beyond UCCSD. These results demonstrate that differentiable architecture search provides an effective and generalizable framework for designing accurate and compact VQE circuits in near-term quantum chemistry.