Tunable Geometries in Sparse Clifford Circuits
arXiv:2202.11750 · doi:10.3390/sym14040666
Abstract
We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.
arXiv comment19 pages, 11 figures
References in corpus (49)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Area laws for the entanglement entropy - a review
- Aspects of Holographic Entanglement Entropy
- A Covariant Holographic Entanglement Entropy Proposal
- Lectures on holographic methods for condensed matter physics
- Average Entropy of a Subsystem
- Improved Simulation of Stabilizer Circuits
- Black holes as mirrors: quantum information in random subsystems
- Measuring entanglement entropy through the interference of quantum many-body twins
- Quantum thermalization through entanglement in an isolated many-body system
- Entanglement renormalization
- Fast Scramblers
- An Area Law for One Dimensional Quantum Systems
- Entanglement Renormalization and Holography
- Operator Spreading in Random Unitary Circuits
- Chaos in quantum channels
- Baryons And Branes In Anti de Sitter Space
- Probing entanglement entropy via randomized measurements
- Measurement-driven entanglement transition in hybrid quantum circuits
- Spectral Gap and Exponential Decay of Correlations
- Probing entanglement in a many-body-localized system
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Violation of the entropic area law for Fermions
- Towards the fast scrambling conjecture
- Holographic Mutual Information is Monogamous
- Modular Entanglement of Atomic Qubits using both Photons and Phonons
- Lieb-Robinson and the butterfly effect
- Statistical mechanics of quantum error correcting codes
- Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
- Programmable Interactions and Emergent Geometry in an Atomic Array
- The Lieb-Robinson light cone for power-law interactions
- -adic AdS/CFT
- Treelike interactions and fast scrambling with cold atoms
- An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
- Fast scrambling on sparse graphs
- Minimal Model for Fast Scrambling
- Locality in Quantum Systems
- Edge length dynamics on graphs with applications to -adic AdS/CFT
- Measurement-induced purification in large-N hybrid Brownian circuits
- Emergent Replica Conformal Symmetry in Non-Hermitian SYK Chains
- A cavity-QED simulator of slow and fast scrambling
- Generators and relations for n-qubit Clifford operators
- Fast scrambling without appealing to holographic duality
- Measurement-induced phase transitions in sparse nonlocal scramblers
- Deterministic Fast Scrambling with Neutral Atom Arrays
- Continuum limits of sparse coupling patterns
- Mixed field theory
Cited by in corpus (4)
- Transport and entanglement growth in long-range random Clifford circuits
- Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
- Onset of scrambling as a dynamical transition in tunable-range quantum circuits
- Entangled states from sparsely coupled spins for metrology with neutral atoms