Contextuality in the No-Core Shell Model

The Contextual Subspace Method offers an efficient framework for representing

quantum many-body systems. Instead of working in the full Hilbert space, the

method decomposes it into a non-contextual part with fixed degrees of free-

dom, and a contextual part. This contextual Hamiltonian identifies the reduced

subspace in which quantum simulation offers a potential advantage, making it

a powerful tool for lowering the computational cost of many-body problems.

One example of such a many-body system is the No-Core Shell Model (NCSM),

an ab initio description of nuclear structure in which all nucleons are treated

as active degrees of freedom. The NCSM provides a promising framework for

predicting nuclear shells and reaction cross sections from underlying nuclear

interactions, but its exponentially growing Hilbert space poses a major compu-

tational challenge for classical algorithms. We construct the contextual subspace

representation of the Lithium-6 NCSM Hamiltonian. We explore how it captures dom-

inant correlations within the nuclear structure and whether a “core” emerges

from the ab initio Hamiltonian as the non-contextual piece. Implications for

scalable quantum simulations of nuclear systems are discussed.