Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
Will it glue? on short-depth designs beyond the unitary group
8 Pith papers cite this work. Polarity classification is still indexing.
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Derives improved mode-independent sample complexity bounds O(η log η) for fermionic classical shadows on particle-preserving operators and Slater determinant overlaps.
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.
Classical shadow protocols using uniform sampling over compact symmetric spaces admit a unifying theory and yield slight sample-complexity improvements over standard schemes for certain observable distributions.
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
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.
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
citing papers explorer
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Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
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Particle-preserving fermionic shadows with mode-independent sample complexity
Derives improved mode-independent sample complexity bounds O(η log η) for fermionic classical shadows on particle-preserving operators and Slater determinant overlaps.
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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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Classical shadows over symmetric spaces
Classical shadow protocols using uniform sampling over compact symmetric spaces admit a unifying theory and yield slight sample-complexity improvements over standard schemes for certain observable distributions.
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Arts & crafts: Strong random unitaries and geometric locality
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
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From Pauli Strings to Quantum Dynamics: A Unified Characterization
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
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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.