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.
Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as our non-stabilizerness monotone, we derive the average and the variance for U(1)-constrained Haar random states. We show that the presence of a conserved charge leads to a substantial suppression of non-stabilizerness (magic) compared to the unconstrained case, and identify a qualitative difference between entanglement and magic response. In the thermodynamic limit, stabilizer entropy exhibits a different leading-order scaling close to a vanishing relative charge density, implying that magic is more robust to charge density fluctuations than entanglement entropy. We test our analytical predictions against midspectrum eigenstates of two chaotic many-body systems with conserved U(1) charge: the complex-fermion Sachdev-Ye-Kitaev (cSYK) model and a Heisenberg XXZ chain with next-to-nearest-neighbour couplings and conserved magnetization. We find an excellent agreement for the non-local cSYK model and systematic deviations for the local XXZ chain, highlighting the role of interaction locality.
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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.
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.
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
Non-local stabilizer entropies of fermionic Gaussian states admit a closed form from reduced Majorana covariance eigenvalues when minimized over local Gaussian unitaries.
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.
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
citing papers explorer
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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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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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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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Non-Gaussianity of random quantum states
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
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Non-Local Magic Resources for Fermionic Gaussian States
Non-local stabilizer entropies of fermionic Gaussian states admit a closed form from reduced Majorana covariance eigenvalues when minimized over local Gaussian unitaries.
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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.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
- Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions
- Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics