In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
Quantum magic dynamics in random circuits
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer, even though they may appear complicated from the perspective of entanglement. In this sense, magic is a crucial resource for unlocking the unique computational power of quantum computers to address problems that are classically intractable. Magic can be quantified by measures such as Wigner negativity and mana that satisfy fundamental properties such as monotonicity under Clifford operations. In this paper, we generalize the statistical mechanical mapping methods of random circuits to the calculation of Renyi Wigner negativity and mana. Based on this, we find: (1) a precise formula describing the competition between magic and entanglement in many-body states prepared under Haar random circuits; (2) a formula describing the the spreading and scrambling of magic in states evolved under random Clifford circuits; (3) a quantitative description of magic "squeezing" and "teleportation" under measurements. Finally, we comment on the relation between coherent information and magic.
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No-cloning theorem for quantum ensembles established information-theoretically, with circumvention for finite evolutions but proven computational intractability.
In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
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.
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 entropies and nullity.
A conditional-fidelity witness on projected small subsystems certifies entanglement, magic, and circuit complexity of generic many-body states with constant sample complexity, with fidelity certification supported by numerics.
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.
Stabilizer Rényi entropies and Pauli spectrum cumulants show universal power-law scaling with driving rate in slow processes across quantum phase transitions, with the logarithmic Pauli spectrum asymptotically Gaussian, demonstrated in the transverse-field Ising model and long-range Kitaev models.
citing papers explorer
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Tuning quantum magic of pure quantum chaotic states with a gravity dual
In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
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No Cloning of Quantum Ensembles
No-cloning theorem for quantum ensembles established information-theoretically, with circumvention for finite evolutions but proven computational intractability.
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Nonstabilizerness Mpemba Effects
In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
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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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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 entropies and nullity.
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Certifying localizable quantum properties with constant sample complexity
A conditional-fidelity witness on projected small subsystems certifies entanglement, magic, and circuit complexity of generic many-body states with constant sample complexity, with fidelity certification supported by numerics.
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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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Universal Non-stabilizerness Dynamics Across Quantum Phase Transitions
Stabilizer Rényi entropies and Pauli spectrum cumulants show universal power-law scaling with driving rate in slow processes across quantum phase transitions, with the logarithmic Pauli spectrum asymptotically Gaussian, demonstrated in the transverse-field Ising model and long-range Kitaev models.