From Classical to Quantum: Extending Prometheus to Uncover Quantum Critical Behavior in Disordered Transverse Field Ising Chains

We extend the Prometheus framework from classical to quantum phase transitions, demonstrat- ing unsupervised discovery of quantum critical phenomena in the disordered transverse field Ising model (DTFIM). Building upon our previous work on classical spin systems [1, 2], we develop a quantum-aware variational autoencoder (Q-VAE) architecture that operates directly on quantum ground state wavefunctions obtained via exact diagonalization. The Q-VAE learns latent represen- tations that capture the essential physics of the quantum phase transition between paramagnetic and ferromagnetic phases, achieving detection of the quantum critical point hc = 1.00 ± 0.02 in the clean limit, consistent with the theoretical value hc/J = 1. We introduce disorder through random transverse fields h _i ∼ Uniform[h−W, h+W ] and investigate the disorder-driven infinite-randomness fixed point characteristic of the random TFIM. Our framework successfully identifies the shift in critical behavior with increasing disorder strength and extracts effective critical exponents through finite-size scaling analysis. We formulate and test the hypothesis that the Q-VAE latent space structure reflects the activated dynamical scaling ln ξ ∼ |h − hc| ^−ψ with ψ ≈ 0.5 expected at the infinite-randomness fixed point. The Prometheus quantum discovery pipeline provides a systematic approach to exploring quantum phase diagrams in systems where analytical solutions are unavail- able, with potential applications to quantum materials, cold atom systems, and quantum computing platforms.