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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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 new framework certifies global quantum properties including multipartite entanglement, circuit complexity, and quantum magic on small subsystems with constant sample complexity via local Pauli measurements.
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.
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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 new framework certifies global quantum properties including multipartite entanglement, circuit complexity, and quantum magic on small subsystems with constant sample complexity via local Pauli measurements.
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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.