Circuit Complexity in Fermionic Field Theory

Abstract

We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying appropriate classes of Bogoliubov-Valatin transformations, and also directly in the continuum by defining squeezing operators and their generalizations. As a closely related problem, we consider cMERA tensor networks for fermions: viewing them as paths in circuit space, we compute their path lengths. Certain ambiguities that arise in some of these results because of cut-off dependence are discussed.

arXiv comment56 pages, 2 figures

References in corpus (42)

• Complexity Equals Action
• Holographic Entanglement Entropy: An Overview
• Complexity and Shock Wave Geometries
• Complexity, action, and black holes
• Quantum Computation as Geometry
• Chaos and complexity by design
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Gravitational action with null boundaries
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• The Second Law of Quantum Complexity
• Comments on Holographic Complexity
• On the Time Dependence of Holographic Complexity
• Holographic Complexity
• Noether charge, black hole volume, and complexity
• Entanglement renormalization for quantum fields
• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• On The Entanglement Entropy For Gauge Theories
• Quantum Complexity and Negative Curvature
• Aspects of Entanglement Entropy for Gauge Theories
• Quantum Chaos and Holographic Tensor Models
• Divergences in Holographic Complexity
• Holographic complexity is nonlocal
• Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• Complexity in de Sitter Space
• Random Matrices and Holographic Tensor Models
• Evolution of Complexity Following a Global Quench
• Action growth of charged black holes with a single horizon
• Quantum Algorithms for Fermionic Quantum Field Theories
• Complexity of the AdS Soliton
• Divergences in the rate of complexification
• Complexity is Simple
• Connecting Fisher information to bulk entanglement in holography
• Boundary and Corner Terms in the Action for General Relativity
• Contrasting SYK-like Models
• Uncomplexity and Black Hole Geometry
• Towards a Finite-$N$ Hologram
• Theory of transformation for the diagonalization of quadratic Hamiltonians
• Comments on Entanglement Entropy in String Theory
• On subregion holographic complexity and renormalization group flows
• Comments on Joint Terms in Gravitational Action

Cited by in corpus (174)

• Complexity and entanglement for thermofield double states
• Quantum Computation as Gravity
• Circuit complexity in interacting QFTs and RG flows
• Holographic Complexity in Vaidya Spacetimes II
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Complexity as a novel probe of quantum quenches: universal scalings and purifications
• Subsystem Complexity and Holography
• Path-Integral Complexity for Perturbed CFTs
• Time Evolution of Complexity: A Critique of Three Methods
• Universal chaotic dynamics from Krylov space
• Chaos and Complexity in Quantum Mechanics
• Complexity of Mixed States in QFT and Holography
• Complexity Growth with Lifshitz Scaling and Hyperscaling Violation
• Holographic Complexity Equals Which Action?
• The Complexity Geometry of a Single Qubit
• The First Law of Complexity
• Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
• Krylov Complexity in Open Quantum Systems
• Path integral optimization as circuit complexity
• Quantum Information in Holographic Duality
• Holographic Subregion Complexity from Kinematic Space
• Random Matrix Theory for Complexity Growth and Black Hole Interiors
• Complexity for Conformal Field Theories in General Dimensions
• Renormalized Circuit Complexity
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
• Cosmological Complexity
• Holographic Complexity for Defects Distinguishes Action from Volume
• Subregion Action and Complexity
• Complexity Growth in Integrable and Chaotic Models
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Circuit Complexity across a Topological Phase Transition
• On the time dependence of holographic complexity in a dynamical Einstein-dilaton model
• Aspects of The First Law of Complexity
• Post-Quench Evolution of Complexity and Entanglement in a Topological System
• Conformal field theory complexity from Euler-Arnold equations
• The Rise of Cosmological Complexity: Saturation of Growth and Chaos
• Complexity of Holographic Superconductors
• Circuit Complexity From Cosmological Islands
• Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Circuit Complexity for Fermionic Thermofield Double states
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Circuit Complexity and 2D Bosonisation
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Holographic complexity of anisotropic black branes
• Spread complexity as classical dilaton solutions
• Quantum state complexity meets many-body scars
• Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Time evolution of the complexity in chaotic systems: concrete examples
• Circuit complexity for generalised coherent states in thermal field dynamics
• Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions
• Thoughts on Holographic Complexity and its Basis-dependence
• Binding Complexity and Multiparty Entanglement
• Complexity of mixed Gaussian states from Fisher information geometry
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Complexity growth rate during phase transitions
• Circuit complexity for free Fermion with a mass quench
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Chaos and Complexity for Inverted Harmonic Oscillators
• Charged Complexity and the Thermofield Double State
• Quantum Complexity as Hydrodynamics
• Holographic Subregion Complexity in Einstein-Born-Infeld theory
• Complexity growth of rotating black holes with a probe string
• Modified "complexity equals action" conjecture
• Subsystem complexity after a global quantum quench
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• A Quantum Complexity Lowerbound from Differential Geometry
• Complexity for Open Quantum System
• Complexity and information geometry in spin chains
• Capacity of Entanglement in Local Operators
• Pseudo complexity of purification for free scalar field theories
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Volume complexity for Janus ${\mathrm{AdS}}_3$ geometries
• Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
• On the time dependence of holographic complexity for charged AdS black holes with scalar hair
• Complexity of warped conformal field theory
• Holographic study of entanglement and complexity for mixed states
• More on Complexity in Finite Cut Off Geometry
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning
• Complexity in the Lipkin-Meshkov-Glick Model
• Holographic complexity growth in a FLRW universe
• Regularizations of Action-Complexity for a Pure BTZ Black Hole Microstate
• Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality
• Action complexity in the presence of defects and boundaries
• Circuit Complexity in Topological Quantum Field Theory
• Complexity of operators generated by quantum mechanical Hamiltonians
• Time dependence of complexity for Lovelock black holes
• Revisit on holographic complexity in two-dimensional gravity
• Knots, links, and long-range magic
• Holographic complexity of charged Taub-NUT-AdS black holes
• Holographic complexity for black branes with momentum relaxation
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Entwinement as a possible alternative to complexity
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• Universality in long-distance geometry and quantum complexity
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Holographic complexity of the electromagnetic black hole
• Chaos and multifold complexity for an inverted harmonic oscillator
• Primordial Gravitational Wave Circuit Complexity
• Circuit complexity near critical points
• Complexity of non-trivial sound speed in inflation
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Holographic Complexity of LST and Single Trace $T\bar{T}$
• Complexity growth in Gubser-Rocha models with momentum relaxation
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Circuit Complexity through phase transitions: consequences in quantum state preparation
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• Complexity growth of massive black hole with a probe string
• Towards the Web of Quantum Chaos Diagnostics
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• Complexity measures in QFT and constrained geometric actions
• Sectional curvatures distribution of complexity geometry
• Quantum Chaos on Complexity Geometry
• Complete Solution of a Gauged Tensor Model
• Subsystem complexity after a local quantum quench
• On the Complexity of a $2+1$--dimensional Holographic Superconductor
• Circuit complexity in proca theory
• Holographic complexity of rotating black holes with conical deficits
• Reparameterization Dependence is Useful for Holographic Complexity
• Nielsen complexity of coherent spin state operators
• Krylov Complexity of Fermionic and Bosonic Gaussian States
• Polynomial Equivalence of Complexity Geometries
• Evolution of circuit complexity in a harmonic chain under multiple quenches
• Complexity and quenches in models with three and four spin interactions
• Complexity and scaling in quantum quench in $1+1$ dimensional fermionic field theories
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Cosmological complexity of the modified dispersion relation
• Geometric quantum complexity of bosonic oscillator systems
• Complexity and Time
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Holographic Complexity of Subregions in the Hyperscaling Violating Theories
• Real space circuit complexity as a probe of phase diagrams
• Circuit Complexity in $U(1)$ Gauge Theory
• Complexity from Spinning Primaries
• Weighting gates in circuit complexity and holography
• Perturbative Complexity of Interacting Theory
• Towards complexity of primary-deformed Virasoro circuits
• The Complexity of Being Entangled
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• Complexity for superconformal primaries from BCH techniques
• Interface in AdS black hole spacetime
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• Information theoretic measures for Lifshitz system
• Complexity of Scalar Collapse in Anti-de Sitter Spacetime
• Non-analyticity in Holographic Complexity near Critical points
• Probing the self-coherence of primordial quantum fluctuations with complexity
• Quantum circuit complexity and unsupervised machine learning of topological order
• HEE and HSC for flavors: perturbative structure in open string geometries
• Operator Approach to Complexity : Excited States
• What kind of "complexity" is dual to holographic complexity?
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Benchmarking quantum chaos from geometric complexity
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them
• Switchback effect of holographic complexity in multiple-horizon black holes
• Holographic and QFT Complexity with angular momentum
• Interface in Kerr-AdS black hole spacetime
• Geometry of quantum complexity
• Purification Complexity without Purifications
• Holographic complexity of rotating black holes
• Holographic complexity of the Klebanov-Strassler background
• Developments in non-relativistic field theory and complexity
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• Geometric measure of quantum complexity in cosmological systems
• Circuit Complexity for Coherent-Thermal States in Bosonic String Theory
• Comparing quantum complexity and quantum fidelity