Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics

2025/04/15 by Doru Sticlet, Sticlet, Doru, Balázs Dóra +7 · 20 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.2504.11139

openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Magic, or nonstabilizerness, is a crucial quantum resource, yet its dynamics in open quantum systems remain largely unexplored. We investigate magic in the open XXZ spin chain under either boundary gain and loss, or bulk dephasing using the stabilizer Rényi entropy M₂. To enable scalable simulations of large systems, we develop a novel, highly efficient algorithm for computing M₂ within the matrix product states formalism while maintaining constant bond dimension--an advancement over existing methods. For boundary driving, we uncover universal scaling laws, M₂(t) ∼ t^1/z, linked to the dynamical exponent z for several distinct universality classes. We also disentangle classical and quantum contributions to magic by introducing a mean-field approximation for magic, thus emphasizing the prominent role of quantum critical fluctuations in nonstabilizerness. For bulk dephasing, dissipation can transiently enhance magic before suppressing it, and drive it to a nontrivial steady-state value. These findings position magic as a powerful diagnostic tool for probing universality and dynamics in open quantum systems.

Citations

• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Quantum magic dynamics in random circuits
• Magic state cultivation: growing T states as cheap as CNOT gates
• Estimating Non-Stabilizerness Dynamics Without Simulating It
• Extracting randomness from magic quantum states
• Critical behaviors of non-stabilizerness in quantum spin chains
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain
• Benchmarking Quantum Computers and the Impact of Quantum Noise
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum resource theories
• Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
• Relaxation times of dissipative many-body quantum systems
• Matrix product solutions of boundary driven quantum chains
• Open-System Dynamics of Entanglement
• The Resource Theory of Stabilizer Computation
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Heat transport in the XXZ spin chain: from ballistic to diffusive regimes and dephasing enhancement
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
• Stabilizer Formalism for Operator Quantum Error Correction
• OPEN QUANTUM SYSTEMS
• Quantum Computing with Very Noisy Devices
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems

Cited by

• Growth and spreading of quantum resources under random circuit dynamics
• Van Hove singularities in stabilizer entropy densities
• Non-stabilizerness as a Diagnostic of Criticality and Exceptional Points in Non-Hermitian Spin Chains
• Operational interpretation of the Stabilizer Entropy
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Magic Steady State Production: Non-Hermitian and Stochastic pathways
• Magic phase transitions in monitored gaussian fermions
• Quantum Magic in Discrete-Time Quantum Walk
• Universal Spreading of Nonstabilizerness and Quantum Transport
• Non-stabilizerness generation in a multi-particle quantum walk

Related

• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Nonstabilizerness dynamics in many-body localized systems
• Non-stabilizerness as a Diagnostic of Criticality and Exceptional Points in Non-Hermitian Spin Chains
• Critical behaviors of non-stabilizerness in quantum spin chains
• Universal Spreading of Nonstabilizerness and Quantum Transport