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[challenge]: Design and Benchmark a Polynomial-Time Compression Algorithm for Structured Fermionic Sign Problem #290

Description

@JunkaiWang-TheoPhy

Released by

Junkai Wang

Contact email

WangTheoPhys@outlook.com

Method

Variational Monte Carlo / Neural Quantum States

Challenge issue

Fermionic neural quantum states such as FermiNet and PsiFormer represent antisymmetric many-electron wavefunctions. For a real-valued wavefunction, we may write

psi(x) = |psi(x)| s(x),

where s(x) is the sign function. For complex wavefunctions, s(x) is replaced by a phase function.

The generic fermion sign problem is NP-hard, making a generic exact polynomial-time solver unlikely. However, physically structured fermionic states may contain compressible sign or phase patterns. Existing neural-wavefunction and backflow results suggest that antisymmetric structure and correlation-induced nodal/sign structure can sometimes be represented compactly, but low energy or value error alone does not establish polynomial sign compression.

This challenge asks participants to construct and test a representation of the form

s_exact(x) = s_reference(x) s_residual(x),

where the reference sign may be generated by a Slater or Pfaffian structure and the residual sign is learned or analytically modeled.

A successful solution should demonstrate that the representation size and sign-query or local-update cost scale polynomially with system size, while maintaining high sign accuracy on exact-diagonalization or other trusted benchmarks. Participants should also compare raw-sign compression with residual-sign compression.

The issue with the Bosonic version has already been studied. Please refer to ICLR 2026.

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