Entanglement of weighted graphs uncovers transitions in variable-range interacting models
arXiv:2307.11739 · doi:10.1103/PhysRevA.110.022431
Abstract
The cluster state acquired by evolving the nearest-neighbor (NN) Ising model from a completely separable state is the resource for measurement-based quantum computation. Instead of an NN system, a variable-range power law interacting Ising model can generate a genuine multipartite entangled (GME) weighted graph state (WGS) that may reveal intrinsic characteristics of the evolving Hamiltonian. We establish that the pattern of generalized geometric measure (GGM) in the evolved state with an arbitrary number of qubits is sensitive to fall-off rates and the range of interactions of the evolving Hamiltonian. We report that the time-derivative and time-averaged GGM at a particular time can detect the transition points present in the fall-off rates of the interaction strength, separating different regions, namely long-range, quasi-local and local ones in one- and two-dimensional lattices with deformation. Moreover, we illustrate that in the quasi-local and local regimes, there exists a minimum coordination number in the evolving Ising model for a fixed total number of qubits which can mimic the GGM of the long-range model. In order to achieve a finite-size subsystem from the entire system, we design a local measurement strategy that allows a WGS of an arbitrary number of qubits to be reduced to a local unitarily equivalent WGS having fewer qubits with modified weights.
v1: 14 pages, 9 figures, v2: close to publish version
References in corpus (93)
- Quantum entanglement
- Quantum Cryptography
- Fault-tolerant quantum computation by anyons
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Quantum Mechanics helps in searching for a needle in a haystack
- Elementary gates for quantum computation
- Quantum cryptography: Public key distribution and coin tossing
- Introducing Quantum Discord
- Quantum secret sharing
- Quantum algorithm for solving linear systems of equations
- Area laws for the entanglement entropy - a review
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Persistent entanglement in arrays of interacting particles
- Measurement-based quantum computation with cluster states
- The classical-quantum boundary for correlations: discord and related measures
- Improved Simulation of Stabilizer Circuits
- Quantum computing with trapped ions
- Measurement-based quantum computation
- Multi-party entanglement in graph states
- Ground-to-satellite quantum teleportation
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Quantum Cryptography with Entangled Photons
- Effective quantum spin systems with ion traps
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- On the role of entanglement in quantum computational speed-up
- Ultra-Large-Scale Continuous-Variable Cluster States Multiplexed in the Time Domain
- Global entanglement in multiparticle systems
- 10-qubit entanglement and parallel logic operations with a superconducting circuit
- Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator
- High-speed linear optics quantum computing using active feed-forward
- Observation of multi-component atomic Schrödinger cat states of up to 20 qubits
- Valence Bond Solids for Quantum Computation
- Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes
- Entanglement entropy for the long range Ising chain
- Novel schemes for measurement-based quantum computation
- The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
- Measurement-based quantum computation beyond the one-way model
- Kitaev chains with long-range pairing
- Quantum discord and its allies: a review
- Entanglement growth in quench dynamics with variable range interactions
- Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
- Quantum copying: A network
- Distributed quantum dense coding
- Fast simulation of stabilizer circuits using a graph state representation
- Experimental demonstration of graph-state quantum secret sharing
- Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Channel Capacities versus Entanglement Measures in Multiparty Quantum States
- Experimental demonstration of a graph state quantum error-correction code
- Experimental Realization of Deutsch's Algorithm in a One-way Quantum Computer
- Entanglement in spin chains and lattices with long-range Ising-type interactions
- Measurement-based quantum computation with trapped ions
- Universal quantum computation with little entanglement
- A Triangle Governs Genuine Tripartite Entanglement
- Anomalous Behavior of Spin Systems with Dipolar Interactions
- Designer Spin Pseudomolecule Implemented with Trapped Ions in a Magnetic Gradient
- Hierarchies of Geometric Entanglement
- Good dynamics versus bad kinematics. Is entanglement needed for quantum computation?
- Universal geometric entanglement close to quantum phase transitions
- Dipolar Molecules in Optical Lattices
- Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
- Entanglement area laws for long-range interacting systems
- Advances in quantum dense coding
- Causality and quantum criticality in long-range lattice models
- On the Role of Coherence in Shor's Algorithm
- Visualizing elusive phase transitions with geometric entanglement
- Experimental Construction of Optical Multi-qubit Cluster States From Bell States
- Monogamy of entanglement without inequalities
- Criticality of Spin Systems with Weak Long-Range Interactions
- Entanglement entropy in the Long-Range Kitaev chain
- Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems
- Geometric Entanglement in a One-Dimensional Valence Bond Solid State
- Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
- Finite-Size Geometric Entanglement from Tensor Network Algorithms
- Entanglement and coherence in Bernstein-Vazirani algorithm
- Generalized Cluster States Based on Finite Groups
- Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits
- Experimental characterization of universal one-way quantum computing
- A variational method based on weighted graph states
- Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
- Entanglement, fractional magnetization and long-range interactions
- Correlations, long-range entanglement and dynamics in long-range Kitaev chains
- Entanglements and correlations of one-dimensional quantum spin-1/2 chain with anisotropic power-law long range interactions
- Cluster State Generation with Spin-Orbit Coupled Fermionic Atoms in Optical Lattices
- Native three-body interaction in superconducting circuits
- Random circuits by measurements on weighted graph states
- Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity
- Study of the long-range transverse field Ising model with fermionic Gaussian states
- Quantum Information Processing in Disordered and Complex Quantum Systems
- Sublogarithmic behaviour of the entanglement entropy in fermionic chains
- Spin Squeezing Property of Weighted Graph States
- Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
- Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions