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.
Diffusive Dynamics of Nonstabilizerness
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Symmetries shape the quantum-information dynamics of many-body systems, but their effect on nonstabilizerness, the resource complementary to entanglement, is less understood. We compute the stabilizer R\'enyi entropy, a measure of nonstabilizerness, in $\mathrm{U}(1)$-symmetric one-dimensional random circuits. The disorder-averaged dynamics is captured by a four-replica tensor network, which we evaluate by $S_4$-adapted infinite time-evolving block decimation (iTEBD) directly in the thermodynamic limit. Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value, with the stabilizer R\'enyi entropy gap closing as $1/t$. The same scaling is verified in an energy-conserving nonintegrable Ising chain. More broadly, our framework provides a hydrodynamic perspective on nonstabilizerness generation and offers insight into the design of approximate Haar-random states in Hamiltonian dynamics.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Introduces occupation number entropies (Tsallis) and natural-orbital participation entropies (Renyi) as computable convex resource monotones for fermionic non-Gaussianity from the covariance matrix.
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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Computable measures of fermionic non-Gaussianity from the covariance matrix
Introduces occupation number entropies (Tsallis) and natural-orbital participation entropies (Renyi) as computable convex resource monotones for fermionic non-Gaussianity from the covariance matrix.