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.
Universal spreading of nonstabiliz- erness and quantum transport
11 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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abstract
We investigate how transport properties of $U(1)$-conserving dynamics impact the growth of quantum resources characterizing the complexity of many-body states. We quantify wave-function delocalization using participation entropy (PE), a measure rooted in the coherence theory of pure states, and assess nonstabilizerness through stabilizer R\'enyi entropy (SRE). Focusing on the XXZ spin chain initialized in domain-wall state, we demonstrate universal power-law growth of both PE and SRE, with scaling exponents explicitly reflecting the underlying transport regimes, ballistic, diffusive, or KPZ-type superdiffusive. Our results establish a solid connection between quantum resources and transport, providing insights into the dynamics of complexity within symmetry-constrained quantum systems.
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In U(1)-conserving dynamics the participation entropy deficit after local density decay is dominated by squared connected density correlations, producing diffusive relaxation Delta S(t) ~ t^{-1/2} that crosses over to exp[-O(t/L^2)].
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
Exact results show U(1) symmetry substantially suppresses non-stabilizerness in random states, with different leading scaling from entanglement near zero charge density.
Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.
The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
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.
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
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
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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.
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Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics
In U(1)-conserving dynamics the participation entropy deficit after local density decay is dominated by squared connected density correlations, producing diffusive relaxation Delta S(t) ~ t^{-1/2} that crosses over to exp[-O(t/L^2)].
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Nonlocal nonstabilizerness in free fermion models
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
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Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
Exact results show U(1) symmetry substantially suppresses non-stabilizerness in random states, with different leading scaling from entanglement near zero charge density.
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Computing quantum magic of state vectors
Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.
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Operational interpretation of the Stabilizer Entropy
The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
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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.
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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.
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Coherence dynamics in quantum many-body systems with conservation laws
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
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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.
- Computable fermionic non-Gaussianity from the covariance matrix