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Quantum Chaos is Quantum
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Quantum Chaos is Quantum
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It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that $k=O(N)$. This result implies the impossibility of simulating quantum chaos on a classical computer.
Forward citations
Cited by 5 Pith papers
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Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions
A unified Magic Rényi Entropy measure for spins, bosons, and fermions is shown to have a universal critical contribution determined by the Affleck-Ludwig boundary entropy.
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Exponentially Accelerated Sampling of Pauli Strings for Nonstabilizerness
A sampling method combining fast Walsh-Hadamard transform and Clifford-preconditioned Monte Carlo reduces Pauli-string sampling cost from O(2^N) to O(N) with sample count independent of N for stabilizer Rényi entropie...
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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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Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory
Tensor network calculation of magic and entanglement in SU(2) lattice gauge theory ground state shows a crossover from magic-rich to less-magic regime at g_star.
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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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