Nonstabilizerness generation in a multiparticle quantum walk

Abstract

We investigate the generation of non-stabilizerness, or magic, in a multi-particle quantum walk by analyzing the time evolution of the stabilizer Rényi entropy $M_2$. Our study considers both single- and two-particle quantum walks in the framework of the XXZ Heisenberg model with varying interaction strengths. We demonstrate that the spread of magic follows the light-cone structure dictated by the system's dynamics, with distinct behaviors emerging in the easy-plane ($\Delta <1$) and easy-axis ($\Delta >1$) regimes. For $\Delta <1$, magic generation is primarily governed by single-particle dynamics, while for $\Delta >1$, doublon propagation dominates, resulting in a significantly slower growth of $M_2$. Furthermore, the magic exhibits logarithmic growth in time for both one and two-particle dynamics. Additionally, by examining the Pauli spectrum, we show that the statistical distribution of level spacings exhibits Poissonian behavior, independent of interaction strength or particle number. Our results shed light on the role of interactions on magic generation in a many-body system.

7 pages, 5 figures

References in corpus (32)

• Improved Simulation of Stabilizer Circuits
• The ITensor Software Library for Tensor Network Calculations
• Universal computation by quantum walk
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum walks: a comprehensive review
• Universal computation by multi-particle quantum walk
• Stabilizer Formalism for Operator Quantum Error Correction
• Stabilizer Rényi entropy
• Full counting statistics in a propagating quantum front and random matrix spectra
• Quantifying nonstabilizerness of matrix product states
• Measuring magic on a quantum processor
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Nonstabilizerness via matrix product states in the Pauli basis
• Phase transition in magic with random quantum circuits
• Magic spreading in random quantum circuits
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Speed limits and locality in many-body quantum dynamics
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Resource theory of quantum scrambling
• Non-stabilizerness versus entanglement in matrix product states
• Stabilizer entropy dynamics after a quantum quench
• Critical behaviors of non-stabilizerness in quantum spin chains
• Magic in generalized Rokhsar-Kivelson wavefunctions
• Magic-induced computational separation in entanglement theory
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Hybrid Stabilizer Matrix Product Operator
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Magic of Random Matrix Product States
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• Multiparticle quantum walk: a dynamical probe of topological many-body excitations

Cited by in corpus (1)

• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states