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

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.

The issue names no repository files, tests, or benchmark entry points. Start by reviewing the challenge statement and the linked ICLR 2026 Bosonic study, then establish trusted exact-diagonalization benchmarks and compare raw-sign with residual-sign representations. Done means demonstrating polynomial representation and query or local-update scaling with high sign accuracy; confirm the scope with maintainers before implementation.