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.
Magic phase transitions in monitored gaussian fermions
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Monitored quantum systems, where unitary dynamics compete with continuous measurements, exhibit dynamical transitions as the measurement rate is varied. These reflect abrupt changes in the structure of the evolving wavefunction, captured by complementary complexity diagnostics that include and go beyond entanglement aspects. Here, we investigate how monitoring affects magic state resources, the nonstabilizerness, of Gaussian fermionic systems. Using scalable Majorana sampling techniques, we track the evolution of stabilizer R\'enyi entropies in large systems under projective measurements. While the leading extensive (volume-law) scaling of magic remains robust across all measurement rates, we uncover a sharp transition in the subleading logarithmic corrections. This measurement-induced complexity transition, invisible to standard entanglement probes, highlights the power of magic-based diagnostics in revealing hidden features of monitored many-body dynamics.
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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.
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.
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.
Non-local stabilizer entropies of fermionic Gaussian states admit a closed form from reduced Majorana covariance eigenvalues when minimized over local Gaussian unitaries.
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.
Non-Hermitian and dissipative dynamics engineer magic steady states in qubits that attract every initial state to high-magic targets.
citing papers explorer
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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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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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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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Rise and fall of nonstabilizerness via random measurements
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
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The true cost of factoring: Linking magic and number-theoretic complexity in Shor's algorithm
Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.
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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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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.
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Magic Steady State Production: Non-Hermitian, Dissipative, and Stochastic Pathways
Non-Hermitian and dissipative dynamics engineer magic steady states in qubits that attract every initial state to high-magic targets.