An unreviewed preprint posted to arXiv describes a quantum algorithm called maximally mixed state spectral sampling, which extracts finite-resolution spectral distributions across the full energy range of a Hamiltonian. The authors show the technique can be steered toward any region of the spectrum — from low-lying energies that reveal quantum criticality to mid-spectrum energies relevant to thermalization — providing what they call a complete "spectral fingerprint" of a quantum model.
As a demonstration, the team applies the algorithm to a (1+1)-dimensional non-Abelian SO(3) gauge theory, a class of model central to high-energy and condensed-matter physics. They report running circuits 78 two-qubit gates deep on superconducting hardware, and show that emerging dynamical circuit capabilities can reduce qubit requirements by roughly half. The paper also introduces a compilation strategy using Pauli-frame optimizations to reduce overhead in the controlled time-evolution steps the algorithm requires, and notes that quantum readout error mitigation is straightforward within this framework.
Two physical applications are illustrated: disordered many-body transitions and mid-spectrum densities of states, each requiring specific postprocessing beyond the raw Fourier outputs. Because this work is a preprint and has not yet undergone peer review, its claims — including the practical near-term viability of the approach and the efficiency gains from dynamical circuits — should be treated as preliminary until independently validated.