Quantifying non-stabilizerness via information scrambling

Abstract

The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

8 pages, 4 figures, code: https://gitlab.com/QMAI/papers/magicinfoscrambling

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• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Stabilizer Rényi Entropy and Conformal Field Theory
• Bridging Entanglement and Magic Resources within Operator Space
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• Computing quantum magic of state vectors
• Non-stabilizerness in quantum-enhanced metrological protocols
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Towards scalable active steering protocols for genuinely entangled state manifolds
• Optimal quantum reservoir learning in proximity to universality
• A Study on Stabilizer Rényi Entropy Estimation using Machine Learning
• High-expressibility Quantum Neural Networks using only classical resources
• An Algorithm for Estimating $\alpha$-Stabilizer Rényi Entropies via Purity