Nonstabilizerness of permutationally invariant systems
Gianluca Passarelli, Rosario Fazio, Procolo Lucignano
Abstract
Typical measures of nonstabilizerness of a system of $N$ qubits require computing ${4}^{N}$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension ${2}^{N}$. For permutationally invariant systems, this exponential overhead can be reduced to just $O({N}^{3})$ expectation values on a state with a dimension $O(N)$. We exploit this simplification to study the nonstabilizerness phase transitions of systems with hundreds of qubits.
Topics & Concepts
Invariant (physics)Computer scienceMathematicsMathematical physicsAdvanced Differential Equations and Dynamical SystemsMathematical Control Systems and AnalysisQuantum chaos and dynamical systems