Magic-state resource theory for the ground state of the transverse-field Ising model

Abstract

Ground states of quantum many-body systems are both entangled and possess a kind of quantum complexity as their preparation requires universal resources that go beyond the Clifford group and stabilizer states. These resources - sometimes described as magic - are also the crucial ingredient for quantum advantage. We study the behavior of the stabilizer Rényi entropy in the integrable transverse field Ising spin chain. We show that the locality of interactions results in a localized stabilizer Rényi entropy in the gapped phase thus making this quantity computable in terms of local quantities in the gapped phase, while measurements involving $L$ spins are necessary at the critical point to obtain an error scaling with $O(L^{-1})$.

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Cited by in corpus (63)

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• Nonstabilizerness via matrix product states in the Pauli basis
• Measuring nonstabilizerness via multifractal flatness
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Efficient quantum algorithms for stabilizer entropies
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Complexity of frustration: a new source of non-local non-stabilizerness
• Stabilizer entropy dynamics after a quantum quench
• Critical behaviors of non-stabilizerness in quantum spin chains
• Pseudomagic Quantum States
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Magic in generalized Rokhsar-Kivelson wavefunctions
• Nonstabilizerness in U(1) lattice gauge theory
• Stabilizer entropy in non-integrable quantum evolutions
• Retrieving information from a black hole using quantum machine learning
• Nonstabilizerness of Permutationally Invariant Systems
• Phase transition in Stabilizer Entropy and efficient purity estimation
• Magic of quantum hypergraph states
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Efficient mutual magic and magic capacity with matrix product states
• Gravitational back-reaction is magical
• Quantum Non-Local Nonstabilizerness
• Chaos and magic in the dissipative quantum kicked top
• Stabilizer entropy of quantum tetrahedra
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces
• Magic of Random Matrix Product States
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Many-body entropies and entanglement from polynomially-many local measurements
• Magic phase transition and non-local complexity in generalized $W$ State
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Long-range nonstabilizerness and phases of matter
• Nonstabilizerness of a Boundary Time Crystal
• Stabilizer Rényi Entropy and Conformal Field Theory
• Interplay of entanglement structures and stabilizer entropy in spin models
• A nonstabilizerness monotone from stabilizerness asymmetry
• The non-stabilizerness of fermionic Gaussian states
• Efficient witnessing and testing of magic in mixed quantum states
• Maximal Magic for Two-qubit States
• Operational interpretation of the Stabilizer Entropy
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
• Non-stabilizerness of Neural Quantum States
• Unified Framework for Calculating Convex Roof Resource Measures
• Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
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• Rise and fall of nonstabilizerness via random measurements
• Exploiting many-body localization for scalable variational quantum simulation
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Experimental characterization of the hierarchy of quantum correlations in top quark pairs
• Van Hove singularities in stabilizer entropy densities
• Resource complexity of Symmetry Protected Topological phases
• Operator delocalization in disordered spin chains via exact MPO marginals
• An Algorithm for Estimating $\alpha$-Stabilizer Rényi Entropies via Purity
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains