Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
arXiv:2507.13437 · doi:10.1103/nk38-ygyq
Abstract
We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We introduce two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and naturally extends to interacting dynamics, and (2) the single-particle transfer matrix (sTM) symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, we show that these two frameworks are equivalent via a novel dynamical bulk-boundary correspondence: the topology of the dynamical system's spacetime bulk determines the topology of the area-law entangled steady-state ensemble living on its temporal boundary. Next, we prove that symmetry-invariant, post-selection-free Gaussian measurements are realizable in only four of the ten mEO classes (A, AI, BDI, D); the remaining six require either post-selection or interacting (non-Gaussian) measurements. Building on these results, we construct general post-selection-free topological adaptive circuits that realize topological dynamical phases in any spatial dimension for the four admissible mEO classes. These circuits simultaneously provide a protocol for preparing and stabilizing free-fermion topological states in all ten symmetry classes. As a concrete demonstration, we construct and simulate 2+1d adaptive circuits that realize mEO-class-A topological dynamics, steering toward a steady-state ensemble of Chern insulators in circuit depth. Finally, we numerically characterize topological phase transitions, dynamical domain-wall modes, and robustness to coherent noise, identifying finite error thresholds at which trajectory-resolved and trajectory-averaged quantities undergo distinct phase transitions.
53 pages, 10 figures
References in corpus (107)
- Topological Insulators
- Topological insulators and superconductors
- Anyons in an exactly solved model and beyond
- Gaussian Quantum Information
- Classification of topological insulators and superconductors in three spatial dimensions
- Maximally localized Wannier functions: Theory and applications
- Classification of topological quantum matter with symmetries
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Periodic table for topological insulators and superconductors
- Symmetry and Topology in Non-Hermitian Physics
- Logical quantum processor based on reconfigurable atom arrays
- Fermionic quantum computation
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Measurement-driven entanglement transition in hybrid quantum circuits
- The effects of interactions on the topological classification of free fermion systems
- Quantum Simulators: Architectures and Opportunities
- Topology by Dissipation in Atomic Quantum Wires
- Theory of the phase transition in random unitary circuits with measurements
- Measurement-induced criticality in random quantum circuits
- Random Quantum Circuits
- Unitary-projective entanglement dynamics
- Non-Markovian Quantum State Diffusion
- Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
- Exponential localization of Wannier functions in insulators
- Dynamical purification phase transitions induced by quantum measurements
- Critical properties of the measurement-induced transition in random quantum circuits
- Fermionic Symmetry Protected Topological Phases and Cobordisms
- Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
- Scalable probes of measurement-induced criticality
- Mapping topological order in coordinate space
- Classification of Topological Insulators and Superconductors
- Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
- Dividing Quantum Channels
- Interacting fermionic topological insulators/superconductors in three dimensions
- Topology by dissipation
- Entanglement phase transitions in measurement-only dynamics
- Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
- Measurement-induced topological entanglement transitions in symmetric random quantum circuits
- Entanglement Transitions from Holographic Random Tensor Networks
- Measurement Protected Quantum Phases
- Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
- Measurement-induced criticality in (2+1)-d hybrid quantum circuits
- Fermionic SPT phases in higher dimensions and bosonization
- Conformal invariance and quantum non-locality in critical hybrid circuits
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Entanglement Transition in the Projective Transverse Field Ising Model
- Operator scaling dimensions and multifractality at measurement-induced transitions
- Symmetry enriched phases of quantum circuits
- Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
- Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond
- Exact Ising model simulation on a quantum computer
- Scalable Dissipative Preparation of Many-Body Entanglement
- Dissipative preparation of Chern insulators
- Topological order and criticality in (2+1)D monitored random quantum circuits
- Symmetry Protected Topological States of Interacting Fermions and Bosons
- Theory of free fermions under random projective measurements
- Entanglement contour
- Measurement-induced steering of quantum systems
- Topological transitions with continuously monitored free fermions
- Quantum error correction for continuously detected errors
- Fermionic quantum processing with programmable neutral atom arrays
- Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
- Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
- Cross Entropy Benchmark for Measurement-Induced Phase Transitions
- Nonlinear sigma models for monitored dynamics of free fermions
- Measurement-induced phase transition for free fermions above one dimension
- Controlling entanglement at absorbing state phase transitions in random circuits
- Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
- Non-Gaussian correlations imprinted by local dephasing in fermionic wires
- A Classification of random Dirac fermions
- Single-ancilla ground state preparation via Lindbladians
- Entanglement transitions with free fermions
- Entanglement Steering in Adaptive Circuits with Feedback
- Constant-depth preparation of matrix product states with adaptive quantum circuits
- Probing post-measurement entanglement without post-selection
- Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
- Triviality of quantum trajectories close to a directed percolation transition
- Dissipation-induced topological insulators: A no-go theorem and a recipe
- Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics
- Majorana Loop Models for Measurement-Only Quantum Circuits
- Orthogonal localized wave functions of an electron in a magnetic field
- Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
- Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
- Measurement-induced transitions for interacting fermions
- Monitored fermions with conserved charge
- Measurement-induced criticality in -symmetric quantum automaton circuits
- Surface codes, quantum circuits, and entanglement phases
- Dissipative Boundary State Preparation
- Quantum state preparation via engineered ancilla resetting
- Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics
- Crystal-symmetry preserving Wannier states for fractional chern insulators
- Designing open quantum systems with known steady states: Davies generators and beyond
- Field theory of monitored, interacting fermion dynamics with charge conservation
- Rapid quantum ground state preparation via dissipative dynamics
- Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage
- A Perturbative Approach to Continuous-Time Quantum Error Correction
- Generalized Real-space Chern Number Formula and Entanglement Hamiltonian
- Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
- Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions
- Accelerating Dissipative State Preparation with Adaptive Open Quantum Dynamics
- Symmetric space description of carbon nanotubes
- Topological Modes in Monitored Quantum Dynamics
- Topology and Spectrum in Measurement-Induced Phase Transitions