OpenAI reports QMA-hardness of continuum Coulomb energy

Approximating the electronic Coulomb spectral infimum in three-dimensional continuum space is QMA-hard when positive integer nuclear charges use binary encoding, nuclei have distinct rational positions and electron count is unary; a deterministic polynomial-time reduction produces a promise gap of at least one.

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OpenAI reports QMA-hardness of continuum Coulomb energy

  • Theoretical Computer Science

Approximating the electronic Coulomb spectral infimum in three-dimensional continuum space is QMA-hard when positive integer nuclear charges use binary encoding, nuclei have distinct rational positions and electron count is unary; a deterministic polynomial-time reduction produces a promise gap of at least one.

AI involvementAI-led
ImportanceNotable
Technical verificationFormal (Lean 4)
Human understandingFew

Understanding the problem

Read the background

Approximating the electronic Coulomb spectral infimum in three-dimensional continuum space is QMA-hard when positive integer nuclear charges use binary encoding, nuclei have distinct rational positions and electron count is unary; a deterministic polynomial-time reduction produces a promise gap of at least one.

Why it matters

If correct, establishes quantum complexity hardness directly for a continuum Coulomb Hamiltonian with unrestricted spin sectors.

What counts as progress

Is full continuum Coulomb ground-energy approximation QMA-hard with binary nuclear charges?

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