Knots, links, and long-range magic

Abstract

We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer states are known as "magic states" and play a key role in quantum resource theory. By implementing a particular magic monotone known as the "mana" we quantify the magic of knot and link states. In particular, for $SU(2{)}_k$ Chern-Simons theory we show that knot and link states are generically magical. For link states, we further investigate the mana associated to correlations between separate boundaries which characterizes the state's long-range magic. Our numerical results suggest that the magic of a majority of link states is entirely long-range. We make these statements sharper for torus links.

36 pages; 64 knots; 34 links; v2 to match published version

References in corpus (8)

• Restrictions on Transversal Encoded Quantum Gate Sets
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Black Holes as Effective Geometries
• Conformal field theories are magical
• Holographic Complexity Equals Which Action?
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Qutrit and Ququint Magic States
• Magic State Distillation with the Ternary Golay Code

Cited by in corpus (11)

• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Efficient mutual magic and magic capacity with matrix product states
• Quantum Non-Local Nonstabilizerness
• Circuit Complexity in Topological Quantum Field Theory
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Musings on SVD and pseudo entanglement entropies
• Complexity for link complement States in Chern Simons Theory
• On the stabilizer complexity of Hawking radiation
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Van Hove singularities in stabilizer entropy densities