Bayesian Retrodiction of quantum phases utilizing weak measurement with explorations into quantum advantages using Metasurfaces

We develop and validate a simulation pipeline that identifies quantum phases directly from weak measurement records using retrodiction, avoiding full state tomography. Using ITensor, we implement Kraus-operator updates on matrix-product density operators (MPDOs) to propagate mixed-state trajectories on spin chains (>10 sites) with noise and finite-strength measurements. The framework targets phase-diagnostic observables—including two-point correlators and nonlocal string order—and quantifies [BS1] identifiability as a function of measurement strength, dephasing, and trajectory length. We report scaling and fidelity/runtime benchmarks demonstrating practical MPDO retrodiction beyond ten qubits/spins, and we show phase classification (e.g., Ising/Haldane indicators) recovered from incomplete, weak measurement data. In parallel, we explore a separate optics/computing track: a compact metasurface-based mini-simulation that leverages programmable phase/amplitude control to sketch routes to quantum advantage in sensing or information processing. Together, these results provide (i) a hardware-aware route to phase discovery “backwards in time” from realistic measurements and (ii) an independent metasurface case study highlighting how reconfigurable nanophotonics could enable resource-efficient quantum tasks.

Keywords: Bayesian retrodiction, weak measurement, MPDO/MPS, ITensor, phase identification, string order, Haldane/Ising models, metasurfaces, quantum advantage

APS topics: Quantum information; Many-body physics; Quantum optics/photonic platforms