Quantum Simulation of Cranked Zirconium Isotopes: A Fixed-N Approach with a Structured Number-Conserving Ansatz

We present a methodological study of quantum simulation of cranking in a Nilsson + pairing Hamiltonian on a fixed deformation grid. The many-body Routhian is mapped to qubits via the Jordan--Wigner transformation and minimized using the Variational Quantum Eigensolver (VQE) in a truncated active space (M). We employ a structured, number-conserving singles-and-doubles ansatz: double excitations implement pair transfer, while singles are restricted to the nonzero Coriolis-coupling graph of the active Nilsson basis. For M=8, this yields 42 parameters while preserving particle number exactly. Exact number conservation enforces langle P_k rangle = 0, so the conventional pairing gap Δ_κpropto Gleft|sum_k langle P_k rangleright| vanishes identically. We instead introduce a fixed-N pairing-coherence diagnostic, \[ Δ_{\mathrm{coh}} = G \sqrt{\sum_{k \neq l} \left| \langle P_k^\dagger P_l \rangle \right|}, \] used as a scalar measure of off-diagonal pair coherence rather than a BCS gap. We study even-even ^80,82,84Zr. ⁸⁰Zr shows a stable oblate minimum at δ^ast approx -0.25; ⁸²Zr exhibits the strongest rotational evolution; ⁸⁴Zr retains a robust prolate minimum with the largest neutron pairing coherence. These results reflect the present truncated model rather than converged spectroscopy. A cranked BCS calculation on the same grid serves as a qualitative baseline. Comparisons between M=6 and M=8 show stable trends but visible shifts, so no active-space convergence is claimed. The structured fixed-N ansatz thus captures consistent isotope trends and provides a practical framework to analyze pairing via Δ_coh.