Spectral subspace extraction via incoherent quantum phase estimation

• URL: http://arxiv.org/abs/2510.14744v1
• Date: Thu, 16 Oct 2025 14:49:27 GMT
• Title: Spectral subspace extraction via incoherent quantum phase estimation
• Authors: Stefano Scali, Josh Kirsopp, Antonio Márquez Romero, Michał Krompiec,
• Abstract summary: Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues.<n>We adopt an ensemble-based formulation of QPE that estimates the density of states (DOS) of the Hamiltonian generator of the evolution.<n>We present DOS-QPE as a circuit primitive, extending it with symmetry-adapted input ensembles and advanced spectrum reconstruction techniques.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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