Quantum Co-Design of Inhomogeneous Many-Body Neutrino Fast Flavor Transformation

Abstract: Dense-neutrino flavor evolution is a quantum many-body problem whose fully correlated treatment becomes rapidly more expensive with increasing particle number and spatial structure. We develop a \texttt{QCNO} quantum simulation code that maps a inhomogeneous forward-scattering neutrino Hamiltonian with advection and finite-range interactions to TEBD2 product-formula quantum circuits, and connects ideal many-body simulation, backend-aware execution, and fault-tolerant resource estimation within the same physical model. We reproduce the exact many-body evolution of the suppressed mean-field-like transverse fast flavor instability through $N=30$ and show that even a single open-boundary interaction generates Rënyi entanglement and non-stabilizer magic, although noisy backends still produce polarization RMSEs of order $0.1$--$0.3$. The restricted active interaction graph of this problem allows us to estimate the circuit depth and $T$ gate cost through $N=50$ for both NISQ and fault-tolerant approaches. The measured TEBD2 error in our fiducial ideal simulation of order $10<sup>{-3}$ motivates a synthesis tolerance $\varepsilon_{\rm syn}\sim10<sup>{-7}$, corresponding to about $70$ $T$ gates per $R_Z$ rotation. The generated circuit contains $1.4\times10<sup>4$ $T$ gates per qubit for open boundaries (twice that for closed boundaries), requiring an application-level logical-$T$ error target of order $10<sup>{-7}$ for early fault-tolerant architectures.