Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
Coherence dynamics in quantum many-body systems with conservation laws
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
abstract
We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences both globally, via the participation entropy, and locally, via the relative entropy of coherence. Combining exact vector evolution, matrix product state simulations, and replica tensor networks methods, we find that conservation laws replace the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of the global coherence measures. Locally, symmetry-constrained circuits show a clean rise-peak-fall structure whose peak time grows algebraically with subsystem size. In contrast, ergodic Hamiltonians broaden the peak into an extended plateau at larger subsystems, highlighting a qualitatively distinct mechanism. Coherence thus emerges as a sensitive probe of symmetry-constrained thermalization, linking quantum resource dynamics to many-body transport.
citation-role summary
background 3
citation-polarity summary
years
2026 8roles
background 3polarities
background 3representative citing papers
In charge- and dipole-conserving fragmented systems, charge and dipole asymmetries exhibit Mpemba-like crossings on parametrically distinct timescales, driven by frozen sectors retaining asymmetry and active sectors relaxing.
In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
In random quantum automaton ensembles, the subsystem symmetrization scale depends on the initial state's participation entropy, and the onset of U(1) entanglement asymmetry coincides with the onset of subsystem coherence.
In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.
Non-local stabilizer entropies of fermionic Gaussian states admit a closed form from reduced Majorana covariance eigenvalues when minimized over local Gaussian unitaries.
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
citing papers explorer
-
Unitary Designs from Doped Matchgate Circuits
Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
-
Higher-order Symmetric Quantum Mpemba Effect in Fragmented Systems
In charge- and dipole-conserving fragmented systems, charge and dipole asymmetries exhibit Mpemba-like crossings on parametrically distinct timescales, driven by frozen sectors retaining asymmetry and active sectors relaxing.
-
Nonstabilizerness Mpemba Effects
In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
-
Entanglement Asymmetry in Random Quantum Automata
In random quantum automaton ensembles, the subsystem symmetrization scale depends on the initial state's participation entropy, and the onset of U(1) entanglement asymmetry coincides with the onset of subsystem coherence.
-
Diffusive Dynamics of Nonstabilizerness
In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.
-
Non-Local Magic Resources for Fermionic Gaussian States
Non-local stabilizer entropies of fermionic Gaussian states admit a closed form from reduced Majorana covariance eigenvalues when minimized over local Gaussian unitaries.
-
Lecture Notes on Replica Tensor Networks for Random Quantum Circuits
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
- Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics