Classical shadows help quantum computer analyze a complex spin model

Laurin E. Fischer of IBM Quantum and École Polytechnique Fédérale de Lausanne and colleagues have demonstrated a large-scale implementation of quantum subspace expansion, using informationally complete measurements known as classical shadows. The work evaluated O(10^(14)) Pauli traces, representing one of the most significant experimental realizations of classical shadows to date, to probe a quantum phase transition in a spin model featuring complex three-body interactions across systems of up to 80 qubits. By reformulating quantum subspace expansion as a constrained optimization problem, the researchers achieved accurate ground state energy recovery and mitigated local order parameters. This approach addresses the large measurement overhead that has limited the scalability of previous quantum algorithms for spectral calculations. Over 3×104 measurement basis randomizations were performed per circuit in a recent experiment, establishing a new scale for implementations of classical shadows and demanding substantial computational resources. The team’s approach successfully recovered accurate ground state energies and mitigated local order parameters across these varying system sizes, demonstrating the method’s potential for analyzing detailed quantum systems. These Pauli traces were essential for reconstructing the quantum state from the measurement data, a computationally intensive task that required substantial high-performance computing resources. Informationally complete positive operator-valued measurements,…