Spectral subspace extraction via incoherent quantum phase estimation

Abstract: Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard form targets individual eigenstates and requires carefully prepared coherent inputs. To overcome these limitations, we adopt an ensemble-based formulation of QPE that estimates the density of states (DOS) of the Hamiltonian generator of the evolution. This approach, which we refer to as DOS-QPE, builds on a prior formulation introduced by one of the authors. In this work, we present DOS-QPE as a circuit primitive, extending it with symmetry-adapted input ensembles and advanced spectrum reconstruction techniques. This variant of QPE enables natural access to thermodynamic properties, symmetry-resolved spectral functions, and features relevant to quantum many-body systems. We demonstrate its performance on fermionic models and nuclear Hamiltonians by casting the spectrum reconstruction problem as a quadratic program solved via compressed sensing. These use cases highlight the potential of DOS-QPE for early fault-tolerant quantum simulations in spectroscopy, electronic structure, and nuclear theory.