Non-local magic equals the fourth Walsh moment of entanglement-spectrum autocorrelations, is bounded by twice the Rényi-2 entropy, and scales as O(1), volume, or log L according to spectral organization.
The Heisenberg representation of quantum computers
12 Pith papers cite this work. Polarity classification is still indexing.
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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.
A hierarchical prefix-tree algorithm identifies the dominant Pauli coefficients of sparse quantum states using Bell sampling on two copies, with sample-complexity bounds tied to the number of coefficients and state purity.
Qutrit Clifford+T gates are realized using two-body angular momentum couplings, rotations, and one-axis-twisting operations, with extensions to bosonic modes via Jordan-Schwinger and cross-Kerr.
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.
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
In U(1)-symmetric monitored random circuits, symmetry-breaking measurements drive the entanglement transition to the non-symmetric universality class and keep the charge correlation length finite at any measurement rate.
Numerical study of SRE in SYK WITP shows structured magic redistribution is required for teleportation fidelity while total magic alone is insufficient, with a transient dip at the fidelity peak.
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
A measurement-only model with fermionic and ancilla chains generates volume-law entanglement and mutual information via local non-random non-commuting measurements, including using only one-body operators.
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.
Pauli and Clifford groups are formulated in complex Geometric Algebra, with Clifford operators generated by π/4-Pauli rotors and a greedy rotor algorithm yielding compact decompositions.
citing papers explorer
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Non-Local Magic from the Entanglement Spectrum
Non-local magic equals the fourth Walsh moment of entanglement-spectrum autocorrelations, is bounded by twice the Rényi-2 entropy, and scales as O(1), volume, or log L according to spectral organization.
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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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Measuring the largest coefficients of a quantum state
A hierarchical prefix-tree algorithm identifies the dominant Pauli coefficients of sparse quantum states using Bell sampling on two copies, with sample-complexity bounds tied to the number of coefficients and state purity.
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Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings
Qutrit Clifford+T gates are realized using two-body angular momentum couplings, rotations, and one-axis-twisting operations, with extensions to bosonic modes via Jordan-Schwinger and cross-Kerr.
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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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Exponential Lindbladian fast forwarding and exponential amplification of certain Gibbs state properties
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
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Universality of Measurement-Induced Criticality under Symmetry-Breaking Measurements
In U(1)-symmetric monitored random circuits, symmetry-breaking measurements drive the entanglement transition to the non-symmetric universality class and keep the charge correlation length finite at any measurement rate.
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Quantum magic is necessary but not sufficient for wormhole-inspired teleportation
Numerical study of SRE in SYK WITP shows structured magic redistribution is required for teleportation fidelity while total magic alone is insufficient, with a transient dip at the fidelity peak.
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Simple slow operators and quantum thermalization
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
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Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
A measurement-only model with fermionic and ancilla chains generates volume-law entanglement and mutual information via local non-random non-commuting measurements, including using only one-body operators.
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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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Geometric Algebra Quantum Gate Decomposition
Pauli and Clifford groups are formulated in complex Geometric Algebra, with Clifford operators generated by π/4-Pauli rotors and a greedy rotor algorithm yielding compact decompositions.