A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Semidefinite Progr ams on Sparse Random Graphs and /T_heir Application to Community Detection
16 Pith papers cite this work, alongside 409 external citations. Polarity classification is still indexing.
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Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
Two relational structures are indistinguishable by k-RCR if and only if they receive identical homomorphism counts from every structure of generalised hypertreewidth ≤ k.
Sample complexity for fidelity estimation to a rank-r reference state is O(r²/ε²) with lower bound Ω(r/ε²); O(r²/ε⁴) when unknown state also has rank ≤r.
Random dimension reduction replaces full dimension with max rank in sample complexity for symmetric quantum state properties and connects to but differs from random purification.
Additive εn²-approximation for graph edit distance on VC-dimension-d graphs in n^{O(d/ε²)} time, with extensions to quadratic assignment problems and a Weisfeiler-Leman dimension bound for robust graph isomorphism.
Generalizes homomorphism indistinguishability equivalences induced by orthogonal easy quantum groups, including a classification of (0,0)-intertwiners for graph-theoretic versions.
Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.
Adding loop composition to branching quantum walk models produces a variable-time quantum search algorithm whose complexity matches the best known results.
AC³ isomorphism tests for coprime Abelian extensions and central-radical groups with elementary Abelian radical, plus an AC circuit bound for arbitrary central-radical groups.
A classical agent extracts more work from quantum temporal correlations via adaptive strategies bounded by the new Time-Ordered Free Energy, while reinforcement learning achieves polylogarithmic dissipation when learning unknown states.
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
The paper determines the automorphism groups of Berman codes and associated abelian codes for n ≥ 5 and provides partial results for n = 3.
Presents analogous arguments supporting the Cobham-Edmonds thesis that feasible computation explicates to P.
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Parallel Algorithms for Group Isomorphism via Code Equivalence
AC³ isomorphism tests for coprime Abelian extensions and central-radical groups with elementary Abelian radical, plus an AC circuit bound for arbitrary central-radical groups.