Nonstabilizerness of quantum tensor network states is intractable in two dimensions

arXiv:2609.31459 · quant-ph, cond-mat.str-el · Submitted 2026-09-25 · Read on arXiv

quant-ph, cond-mat.str-el

Submitted: 2026-09-25

Updated: 2026-10-05

Terminology

• Accuracy — 20× in this paper · explained in 1 episode
• Stabilizer States — 18× in this paper · explained in 2 episodes
• BQP — 12× in this paper · explained in 2 episodes
• Entanglement — 6× in this paper · explained in 3 episodes
• Tensor Networks — 4× in this paper
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Projected Entangled Pair States — 3× in this paper
• Core — 2× in this paper · explained in 2 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Matrix Product States (MPS) — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• SYK Model — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

Sources

• The Heisenberg Representation of Quantum Computers
• Quantum complexity across thermal phase transition in the transverse field Ising chain with long-range couplings
• Probes of chaos over the Clifford group and approach to Haar values
• Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
• Magic phase transitions in monitored gaussian fermions
• Non-Local Magic Resources for Fermionic Gaussian States
• Nonlocal nonstabilizerness in free fermion models
• Multipartite Non-local Magic and SYK Model
• Long-range nonstabilizerness of topologically encoded states from mutual information
• Long-range nonstabilizerness and quantum codes, phases, and complexity
• Topological magic response in quantum spin chains
• Stabilizer R'enyi entropy
• Stabilizer entropy is trustworthy for mixed states
• A fast and exact approach for stabilizer R'enyi entropy via the XOR-FWHT algorithm
• The unbearable hardness of deciding about magic
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• An area law and sub-exponential algorithm for 1D systems
• Quantifying nonstabilizerness of matrix product states
• Strengths and Weaknesses of Quantum Computing

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