Circuit Complexity across a Topological Phase Transition
arXiv:1902.10720 · doi:10.1103/PhysRevResearch.2.013323
Abstract
We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and non-equilibrium steady states of the Kitaev model exhibit non-analytical behaviors at the critical points, and thus can be used to detect both {\it equilibrium} and {\it dynamical} topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and discuss generalizations to higher dimensions. Our result opens up a new avenue for using circuit complexity as a novel tool to understand quantum many-body systems.
4.5+5 pages, 4+3 figures
References in corpus (60)
- Topological Insulators
- Topological insulators and superconductors
- Unpaired Majorana fermions in quantum wires
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Helical liquids and Majorana bound states in quantum wires
- New directions in the pursuit of Majorana fermions in solid state systems
- A generic new platform for topological quantum computation using semiconductor heterostructures
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- One-Dimensional Fermi liquids
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Complexity Equals Action
- Complexity and Shock Wave Geometries
- Quantum phase transitions
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Decay of Loschmidt Echo Enhanced by Quantum Criticality
- Complexity, action, and black holes
- Quantum Computation as Geometry
- Direct observation of dynamical quantum phase transitions in an interacting many-body system
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Observation of a dynamical topological phase transition
- Kitaev chains with long-range pairing
- Topological classification of dynamical phase transitions
- Circuit Complexity in Fermionic Field Theory
- Complexity and entanglement for thermofield double states
- Quantum Computation as Gravity
- Dynamical preparation of Floquet Chern insulators
- Circuit complexity for free fermions
- Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
- Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
- Measuring Topological Number of a Chern-Insulator from Quench Dynamics
- Quantum Quenches in Chern Insulators
- Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
- Circuit Complexity for Coherent States
- Complexity as a novel probe of quantum quenches: universal scalings and purifications
- Dynamical Topological Quantum Phase Transitions for Mixed States
- Multipartite entanglement in topological quantum phases
- A Complexity for Quantum Field Theory States and Application in Thermofield Double States
- Persistent Hall response in a quantum quench
- Topological Marker Currents in Chern Insulators
- Principles and symmetries of complexity in quantum field theory
- Quantum circuit complexity of one-dimensional topological phases
- Topological Quantum Liquids with Long-Range Couplings
- Adiabatic preparation of many-body states in optical lattices
- Complexity of the AdS Soliton
- Evolution of complexity following a quantum quench in free field theory
- A geometric approach to quantum circuit lower bounds
- Probing ground-state phase transitions through quench dynamics
- The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
- Topological Blocking in Quantum Quench Dynamics
- Optimal control for unitary preparation of many-body states: application to Luttinger liquids
- How difficult is it to prepare a quantum state?
- More on complexity of operators in quantum field theory
- Nonanalyticity of circuit complexity across topological phase transitions
- Circuit complexity for free Fermion with a mass quench
- Locating topological phase transitions using nonequilibrium signatures in local bulk observables
- Extracting entanglement geometry from quantum states
- From Geometry to Quantum Computation
- Complexity of operators generated by quantum mechanical Hamiltonians
Cited by in corpus (38)
- Real- and imaginary-time evolution with compressed quantum circuits
- Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
- Quantum complexity and topological phases of matter
- Complexity for Conformal Field Theories in General Dimensions
- Cosmological Complexity
- Spread Complexity and Topological Transitions in the Kitaev Chain
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
- Quantum complexity in gravity, quantum field theory, and quantum information science
- Quantum state complexity meets many-body scars
- Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
- Nonanalyticity of circuit complexity across topological phase transitions
- Resource theory of quantum uncomplexity
- The Early Universe as an Open Quantum System: Complexity and Decoherence
- Complexity and information geometry in spin chains
- Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
- Complexity in the Lipkin-Meshkov-Glick Model
- Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality
- Complexity and Floquet dynamics: non-equilibrium Ising phase transitions
- Exploring the role of nonlocal Coulomb interactions in perovskite transition metal oxides
- An Operational Definition of Topological Order
- Exploring the optimality of approximate state preparation quantum circuits with a genetic algorithm
- Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
- Circuit Complexity through phase transitions: consequences in quantum state preparation
- Complexity measures in QFT and constrained geometric actions
- Complexity-constrained quantum thermodynamics
- Nielsen complexity of coherent spin state operators
- Circuit complexity in proca theory
- Complexity and quenches in models with three and four spin interactions
- Probabilistic state synthesis based on optimal convex approximation
- Quantum complexity phase transitions in monitored random circuits
- Weighting gates in circuit complexity and holography
- Real space circuit complexity as a probe of phase diagrams
- Time-dependent Hamiltonians and Geometry of Operators Generated by Them
- Probing the self-coherence of primordial quantum fluctuations with complexity
- Quantum circuit complexity and unsupervised machine learning of topological order
- Toward a physically motivated notion of Gaussian complexity geometry
- Comparing quantum complexity and quantum fidelity