Fermionic Gaussian states: an introduction to numerical approaches

Abstract

This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and studying relevant Hamiltonians, such as the transverse field Ising Hamiltonian, in detail. We finish introducing novel algorithms connecting Fermionic Guassian states with matrix product states techniques. All the numerical examples make use of the free Julia package F_utilities.

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Cited by in corpus (61)

• Field Theory of Many-Body Lindbladian Dynamics
• Measurement-altered Ising quantum criticality
• Measurement-induced transitions for interacting fermions
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Entanglement dynamics with string measurement operators
• Measurement induced transitions in non-Markovian free fermion ladders
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• What Can Quantum Information Theory Offer to Quantum Chemistry?
• Rapid quantum ground state preparation via dissipative dynamics
• Efficient learning of quantum states prepared with few fermionic non-Gaussian gates
• Far from equilibrium field theory for strongly coupled light and matter: dynamics of frustrated multi-mode cavity QED
• Learning fermionic correlations by evolving with random translationally invariant Hamiltonians
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• Entanglement enhancement induced by noise in inhomogeneously monitored systems
• Entropy fluctuation formulas of fermionic Gaussian states
• Study of the long-range transverse field Ising model with fermionic Gaussian states
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Quantum and classical contributions to entropy production in fermionic and bosonic Gaussian systems
• Characterization of variational quantum algorithms using free fermions
• Fermionic matter-wave quantum optics with cold-atom impurity models
• The non-stabilizerness of fermionic Gaussian states
• Fermionic Magic Resources of Quantum Many-Body Systems
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Integrability of Goldilocks quantum cellular automata
• Robust Oscillations and Edge Modes in Nonunitary Floquet Systems
• Free fermions under adaptive quantum dynamics
• Matchgate circuits deeply thermalize
• Accuracy of time-dependent GGE under weak dissipation
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Entanglement spectrum of matchgate circuits with universal and non-universal resources
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Hamiltonian Forging of a Thermofield Double
• Erasure conversion in Majorana qubits via local quasiparticle detection
• Simulation of the 1d XY model on a quantum computer
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Tomography of parametrized quantum states
• PAC-learning of free-fermionic states is NP-hard
• The Hilbert-space structure of free fermions in disguise
• Simulation of bilayer Hamiltonians based on monitored quantum trajectories
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Entanglement capacity of fermionic Gaussian states
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity
• Computable measures of non-Markovianity for Gaussian free fermion systems
• Complexity of Fermionic 2-SAT
• Dynamical complexity of non-Gaussian many-body systems with dissipation
• Exact non-Markovian master equations: a generalized derivation for Gaussian systems
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains
• Unveiling hidden features of the Kitaev model through a complex-network analysis
• Critical spin models from holographic disorder
• Optimizing Sparse SYK
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems
• Domain-wall melting in all-to-all QSSEP from random-matrix theory