Variational Quantum Eigensolver Benchmarking of the Su–Schrieffer–Heeger Model: Ansatz-Conditional Bulk-Spectrum Resolution

Abstract

The Su-Schrieffer-Heeger chain provides a clean benchmark for variational quantum simulation as it breeds topologically non-trivial states, it is analytically transparent & tractable, yet capable enough to expose the central algorithmic question of whether a shallow variational circuit can reproduce physically meaningful low-energy structure when the system size is increased. In this work, we study the Variational Quantum Eigensolver and a deflation-based excited-state extension on the open SSH chain after Jordan-Wigner mapping to qubits. The analysis is carried out in an exact statevector setting so that all expectation values and overlaps are evaluated without sampling noise, allowing the observed performance to be attributed directly to ansatz design and optimizer behavior. We compare three circuit families under matched shallow depth and fixed classical budgets: a number-conserving fermionic circuit, a hardwareefficient ansatz, and a two-local baseline. Across the tested chain lengths, the fermionic circuit tracks the exact diagonalization benchmark most closely for both the ground-state and firstexcited-state bulk energies, whereas the generic baselines exhibit systematic underbinding and a larger excited-state bias. These results establish a compact, physics-informed benchmark for ansatz selection on structured lattice Hamiltonians and provide the starting point for subsequent studies of boundary-localized topological modes and hardware execution.