Classical Shadow Tomography for TFIM Phase Transitions
Shadow-estimated Rényi-2 entropy benchmarked against exact diagonalization across the critical point of the transverse-field Ising model.
Classical shadow tomography (Huang et al., 2020) provides an efficient protocol for estimating many properties of a quantum state from a small number of random measurements. Rather than full state tomography, shadows compress measurement outcomes into a compact classical representation from which nonlinear functionals — such as Rényi entropies — can be estimated with polynomial overhead.
This project applies classical shadows to detect the quantum phase transition in the 1D Transverse-Field Ising Model (TFIM):
\[H = -J \sum_i Z_i Z_{i+1} - g \sum_i X_i\]The Rényi-2 entanglement entropy S₂ is estimated via shadow tomography and compared against exact diagonalization across the critical point g/J = 1. The shadow estimator correctly captures the divergence in entanglement at criticality, validating the method on a well-understood benchmark.
DTU Summer School: Scientific Methods for Quantum Information Science (5 ECTS), 2025.
Code: GitHub
Keywords: Classical shadows · Rényi-2 entropy · TFIM · Phase transitions · Exact diagonalization