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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For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
Demonstrates a task solvable with 12 qubits but requiring 62-382 classical bits of memory, yielding unconditional quantum information supremacy on a trapped-ion processor.
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.
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
Amplitude damping generates nonstabilizerness in qubit systems unlike depolarizing noise, with local injection washed out collectively after encoding, decoding, and postselection.
Rigorous bounds establish that t = Theta(k^2) non-Clifford gates are necessary and sufficient for frame-potential approximation to unitary k-designs while t = Theta(nk) suffices for relative-error k-designs.
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
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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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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Cloning is as Hard as Learning for Stabilizer States
For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
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Demonstrating an unconditional separation between quantum and classical information resources
Demonstrates a task solvable with 12 qubits but requiring 62-382 classical bits of memory, yielding unconditional quantum information supremacy on a trapped-ion processor.
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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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Geometry of Free Fermion Commutants
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
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Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
Amplitude damping generates nonstabilizerness in qubit systems unlike depolarizing noise, with local injection washed out collectively after encoding, decoding, and postselection.
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Non-Clifford Cost of Random Unitaries
Rigorous bounds establish that t = Theta(k^2) non-Clifford gates are necessary and sufficient for frame-potential approximation to unitary k-designs while t = Theta(nk) suffices for relative-error k-designs.
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Taming Trotter Errors with Quantum Resources
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
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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.