Large-scale implementation of quantum subspace expansion with classical shadows

Quantum subspace expansion (QSE) offers promising avenues to perform spectral calculations on quantum processors but comes with a large measurement overhead. Informationally complete (IC) measurements, such as classical shadows, were recently proposed to overcome this bottleneck. Here, we report the first large-scale implementation of QSE with IC measurements. In particular, we probe the quantum phase transition of a spin model with three-body interactions, for which we observe accurate ground state energy recovery and mitigation of local order parameters across system sizes of up to 80 qubits. We achieve this by reformulating QSE as a constrained optimization problem, obtaining rigorous statistical error estimates and avoiding numerical ill-conditioning. With over 3 times 10⁴ measurement basis randomizations per circuit and the evaluation of O\(10¹⁴\) Pauli traces, this represents one of the most significant experimental realizations of classical shadows to date.