MGT protocols encode the input into a measurement-heralded stabilizer code then apply a logical non-Clifford gate; useful resource states are Clifford-equivalent to diagonal states, and feedforward can often be Pauli.
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Stabilizer R\'enyi entropy
Mixed citation behavior. Most common role is background (62%).
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62% of classified citations
abstract
We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" - by considering the R\'enyi entropy of the probability distribution associated to a pure quantum state given by the square of the expectation value of Pauli strings in that state. We show that this is a good measure of nonstabilizerness from the point of view of resource theory and show bounds with other known measures. The stabilizer R\'enyi entropy has the advantage of being easily computable because it does not need a minimization procedure. We present a protocol for an experimental measurement by randomized measurements. We show that the nonstabilizerness is intimately connected to out-of-time-order correlation functions and that maximal levels of nonstabilizerness are necessary for quantum chaos.
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representative citing papers
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
Magic distributions are computed for EW processes (reproducing QED at low energy, new at high energy/Z resonance) and dark-sector scatterings, reaching maximal magic at mass ratios m_f/m_χ → 0 and → 1.83929.
Under Wigner's SU(4) symmetry the neutron-proton scattering amplitude generates no new quantum resources while same-nucleon channels do due to identical-particle constraints.
In a neutrino-gas model, the many-body Hamiltonian yields different evolution timescales and asymptotics than the quantum kinetic approach with collisions, while quantum resources for the full case sit at the low end for HEP problems and mid-to-high for quantum chemistry.
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.
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
In holographic Schwinger pair production, the excess capacity of entanglement is √λ(d−2)/(d−1)³ — positive for d>2, zero for d=2 — so the produced pair carries nonlocal magic for d>2.
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
Transverse polarization in e+e- collisions generates maximally entangled fermion pairs in QED processes and boosts entanglement in electroweak and Bhabha scattering.
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
The linearly polarized gluon distribution enhances entanglement of heavy quark pairs in electron-nucleus collisions when total and relative transverse momenta are orthogonal.
citing papers explorer
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Magic Gate Teleportation: Structure, Useful Resource States, and Simpler Feedforward
MGT protocols encode the input into a measurement-heralded stabilizer code then apply a logical non-Clifford gate; useful resource states are Clifford-equivalent to diagonal states, and feedforward can often be Pauli.
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Analytical Landscape of Maximal Magic for Two-Qutrit States and Beyond
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
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Taming Trotter Errors with Quantum Resources
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
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Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
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Quantum Magic in early FTQC: From Diagonal Clifford Hierarchy No-Go Theorems to Architecture Design Blueprints
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
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The Quantum Complexity of String Breaking in the Schwinger Model
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
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A Framework for Quantum Simulations of Energy-Loss and Hadronization in Non-Abelian Gauge Theories: SU(2) Lattice Gauge Theory in 1+1D
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
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Production of Magic States via $Z$ Bosons and Dark Photons
Magic distributions are computed for EW processes (reproducing QED at low energy, new at high energy/Z resonance) and dark-sector scatterings, reaching maximal magic at mass ratios m_f/m_χ → 0 and → 1.83929.
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Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory
Under Wigner's SU(4) symmetry the neutron-proton scattering amplitude generates no new quantum resources while same-nucleon channels do due to identical-particle constraints.
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Collective neutrino oscillations: Many-body non-forward effects and non-classicality
In a neutrino-gas model, the many-body Hamiltonian yields different evolution timescales and asymptotics than the quantum kinetic approach with collisions, while quantum resources for the full case sit at the low end for HEP problems and mid-to-high for quantum chemistry.
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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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Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
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Nonlocal Nonstabilizerness from Holographic Schwinger Pair Production
In holographic Schwinger pair production, the excess capacity of entanglement is √λ(d−2)/(d−1)³ — positive for d>2, zero for d=2 — so the produced pair carries nonlocal magic for d>2.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
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Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized $e^-e^+$ Collisions
Transverse polarization in e+e- collisions generates maximally entangled fermion pairs in QED processes and boosts entanglement in electroweak and Bhabha scattering.
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Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
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Quantum entanglement in electron-nucleus collisions: Role of the linearly polarized gluon distribution
The linearly polarized gluon distribution enhances entanglement of heavy quark pairs in electron-nucleus collisions when total and relative transverse momenta are orthogonal.