Stabilizer entropy of quantum tetrahedra
arXiv:2402.07843 · doi:10.1103/PhysRevD.109.126008
Abstract
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts to simulate such models and toward experimental demonstrations of quantum gravity effects. There are, therefore, both a computational and an experimental complexity inherent to this class of models. In this paper, we study this complexity under the lens of stabilizer entropy (SE). We calculate the SE of the gauge-invariant basis states and its average in the SU(2) gauge invariant subspace. We find that the states of definite volume are singled out by the (near) maximal SE and give precise bounds to the verification protocols for experimental demonstrations on available quantum computers.
arXiv comment8 pages, 3 figures, 9 pages supplementary material
References in corpus (47)
- Aspects of Holographic Entanglement Entropy
- Improved Simulation of Stabilizer Circuits
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Black holes as mirrors: quantum information in random subsystems
- Discreteness of area and volume in quantum gravity
- Cool horizons for entangled black holes
- Building up spacetime with quantum entanglement
- Spin Networks and Quantum Gravity
- Roads towards fault-tolerant universal quantum computation
- The Resource Theory of Stabilizer Computation
- Chaos and complexity by design
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Topological Lattice Models in Four Dimensions
- Quantum certification and benchmarking
- Stabilizer Rényi entropy
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- Polyhedra in loop quantum gravity
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
- On The Entanglement Entropy For Gauge Theories
- Entanglement entropy and nonabelian gauge symmetry
- Quantifying nonstabilizerness of matrix product states
- Quantum tetrahedra and simplicial spin networks
- Measuring magic on a quantum processor
- Quantum Chaos is Quantum
- Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
- Magic-state resource theory for the ground state of the transverse-field Ising model
- Entanglement Entropy in Loop Quantum Gravity
- Spin network quantum simulator
- Discreteness of the volume of space from Bohr-Sommerfeld quantization
- Nonstabilizerness determining the hardness of direct fidelity estimation
- Transitions in entanglement complexity in random quantum circuits by measurements
- Transitions in Entanglement Complexity in Random Circuits
- Learning efficient decoders for quasi-chaotic quantum scramblers
- Gravity entanglement, quantum reference systems, degrees of freedom
- Isospectral twirling and quantum chaos
- Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
- Random Matrix Theory of the Isospectral twirling
- Unscrambling Quantum Information with Clifford decoders
- Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
- Retrieving information from a black hole using quantum machine learning
- Quantum entanglement in states generated by bilocal group algebras
- Ising Spin Network States for Loop Quantum Gravity: a Toy Model for Phase Transitions
- Quantum simulations of a qubit of space
- Holographic maps from quantum gravity states as tensor networks
- Inference of gravitational field superposition from quantum measurements
- Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
- Experimental Simulation of Loop Quantum Gravity on a Photonic Chip
Cited by in corpus (11)
- Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
- Stabilizer entropy in non-integrable quantum evolutions
- Spectral Properties Versus Magic Generation in -doped Random Clifford Circuits
- Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces
- Interplay of entanglement structures and stabilizer entropy in spin models
- Maximal Magic for Two-qubit States
- Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
- Magic of discrete lattice gauge theories
- Harvesting stabilizer entropy and non-locality from a quantum field
- Experimental characterization of the hierarchy of quantum correlations in top quark pairs
- Operator Entanglement from Non-Commutative Symmetries