A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
Quantum lower bounds by polynomials
5 Pith papers cite this work. Polarity classification is still indexing.
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For every Boolean f, bounded-error quantum and classical deterministic communication complexity of f ∘ AND₂ are polynomially related up to polylog n, both characterized by log of De Morgan sparsity of f.
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.
Identifies conditions and explicit constructions allowing polynomial-size quantum circuits to implement geometry oracles for pseudorandom textured materials, in contrast to Grover-hard unstructured cases.
A hybrid quantum-classical variational method using polynomial approximations to the energy functional enables finite element analysis of a 1D Neo-Hookean hyperelastic model on near-term quantum hardware.
citing papers explorer
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Quantum Time Lower Bounds by Permutation Invariance
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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Quantum-Classical Equivalence for AND-Functions
For every Boolean f, bounded-error quantum and classical deterministic communication complexity of f ∘ AND₂ are polynomially related up to polylog n, both characterized by log of De Morgan sparsity of f.
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Estimating Fidelity to a Reference Quantum State
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.
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How to make quantum cheese: efficient geometry oracles for exponentially many pseudorandom microstructures
Identifies conditions and explicit constructions allowing polynomial-size quantum circuits to implement geometry oracles for pseudorandom textured materials, in contrast to Grover-hard unstructured cases.
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A Variational Quantum Algorithm for Nonlinear Finite Element Analysis of Hyperelastic Materials
A hybrid quantum-classical variational method using polynomial approximations to the energy functional enables finite element analysis of a 1D Neo-Hookean hyperelastic model on near-term quantum hardware.