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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Preskill, Quantum computing and the entanglement frontier, arXiv preprint arXiv:1203.5813 (2012)
10 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantum computer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantum computer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state systems, or by combining both methods. Only by challenging the entanglement frontier will we learn whether Nature provides extravagant resources far beyond what the classical world would allow.
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Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.
A classical polynomial-time sampler exists for the output distribution of amplitude-damped IQP circuits with logarithmic depth and arbitrary l-local diagonal gates.
Introduces permutation-agnostic distance measures to quantify non-stabiliserness consumption and shows structured variational methods use it more efficiently than unstructured ones with greater classical optimisation freedom.
kA-QAOA matches MA-QAOA approximation ratios on 3-uniform hypergraphs while using significantly fewer function evaluations.
Quantum neuromorphic kernels outperform parameterized quantum kernels on low-dimensional datasets like Iris but underperform on high-dimensional SDSS data in spectral clustering tasks.
Length asymmetry between counter-propagating chiral edges in a parafermion Josephson junction supplies a spontaneous phase bias that electrically controls Majorana (m=1) or parafermion (m>1) zero modes at Laughlin fillings.
Quantum state evolution in variational algorithms is governed by geometric phase rather than dynamical phase, with entanglement decoupled from evolution in hardware-efficient ansatzes but acting as a dynamical resource in Hamiltonian variational ansatzes.
Consciousness does not directly predict AI existential risk unlike intelligence, though it may indirectly affect risk through alignment or capability requirements.
citing papers explorer
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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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Nonlocal nonstabilizerness in free fermion models
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
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Exponential quantum advantage in processing massive classical data
A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.
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Efficient simulation of noisy IQP circuits with amplitude-damping noise
A classical polynomial-time sampler exists for the output distribution of amplitude-damped IQP circuits with logarithmic depth and arbitrary l-local diagonal gates.
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Geometric and Resource-Theoretic Characterisation of Non-Stabiliserness in Quantum Algorithms
Introduces permutation-agnostic distance measures to quantify non-stabiliserness consumption and shows structured variational methods use it more efficiently than unstructured ones with greater classical optimisation freedom.
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Structured Parameterization and Non-Stabilizerness in Hypergraph QAOA
kA-QAOA matches MA-QAOA approximation ratios on 3-uniform hypergraphs while using significantly fewer function evaluations.
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Quantum Spectral Clustering: Comparing Parameterized and Neuromorphic Quantum Kernels
Quantum neuromorphic kernels outperform parameterized quantum kernels on low-dimensional datasets like Iris but underperform on high-dimensional SDSS data in spectral clustering tasks.
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Spontaneous fractional Josephson current from parafermions
Length asymmetry between counter-propagating chiral edges in a parafermion Josephson junction supplies a spontaneous phase bias that electrically controls Majorana (m=1) or parafermion (m>1) zero modes at Laughlin fillings.
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Calibrating the Role of Entanglement in Variational Quantum Algorithms from a Geometric Perspective
Quantum state evolution in variational algorithms is governed by geometric phase rather than dynamical phase, with entanglement decoupled from evolution in hardware-efficient ansatzes but acting as a dynamical resource in Hamiltonian variational ansatzes.
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AI Consciousness and Existential Risk
Consciousness does not directly predict AI existential risk unlike intelligence, though it may indirectly affect risk through alignment or capability requirements.