@informaq.bsky.socialResolves 25-year-old open problems by proving QIP(2), qq-QAM, QAM, and QMA achieve perfect completeness. Introduces endpoint-inward turn-halving transformation that halves message complexity while preserving completeness guarantees.
@informaq.bsky.socialResearchers proved QMA=QMA1, demonstrating quantum Merlin-Arthur proof systems can achieve perfect completeness without sacrificing computational power using a universal gate set of Hadamard, Toffoli, and X gates.
@informaq.bsky.socialResolving a 20-year-old conjecture: oracle separations proved between all consecutive levels of the Fourier hierarchy, establishing that each additional Hadamard layer strictly increases quantum computational power.
@informaq.bsky.socialProves three quantum complexity classes are equivalent using dimension-free stability bounds for symmetric tensor states, resolving open conjectures about pure-state quantum proof systems and their relationship to standard QMA.
@informaq.bsky.socialNew multiplicative adversary derivation recovers fine-grained quantum query complexity bounds for approximate counting, providing direct analysis of Hamming-weight layer evolution and explicit query-level progress tracking.
@informaq.bsky.socialTheoretical study showing promise problems behave fundamentally differently from languages in relativized settings. Improves upper bound on Quantum-Classical Polynomial Hierarchy and proves self-lowness of PromiseBQP under robust oracle access.
@informaq.bsky.socialWe prove quantum algorithms achieve quadratic speedup for counting positive Bernoulli distributions, establishing near-matching bounds: Õ(√ρ/(Δϵ)) upper and Ω(√ρ/(Δϵ)) lower via novel Boolean-over-average-case composition theorem.
@informaq.bsky.socialQuantitative lower bounds established on semidefinite program complexity for approximating separable quantum state properties, improving previous quasipolynomial bounds and providing insights into entanglement certification hardness.
@informaq.bsky.socialEstablishes upper and lower bounds for sample complexity of the generalized hidden shift problem over arbitrary finite groups using quantum information theory and representation-theoretic techniques.
@informaq.bsky.socialConstant-depth quantum circuits and controlled fanout gates are equivalent for symmetric Boolean functions. The required fanout size is precisely determined by the function's transition radius, unifying prior quantum circuit complexity results.
@informaq.bsky.socialResearchers establish universal bounds linking entanglement spectrum structure to quantum nonstabilizerness, revealing that spectral non-uniformity and entropy distribution independently govern quantum complexity in many-body systems.