Energy-selective quantum search with Ising Hamiltonian phase oracles

Abstract:Ising Hamiltonians are basic models of disordered magnets and a standard language for quantum and classical optimization. We study an energy-selective quantum search primitive in which the physical evolution \(\exp(-\mathrm{i} T H)\) is used directly as a Hamiltonian phase oracle. Unlike a Boolean oracle, this oracle marks configurations continuously by their phases and selects a finite resonance band rather than a preassigned marked set. We show that alternating it with the Grover diffusion operator nevertheless produces a Grover-type amplification peak. An exact spectral recurrence and a generating-function representation determine the peak position, width, and height. For an annealed Gaussian density of states, target energies in a high-density tail require \(\Theta(\sqrt{2^n/M})\) oracle calls when the resonance contains \(M\) configurations. For random Ising spectra, overlap-induced correlations shift and distort the peak; spectral symmetrization and iterative calibration remove this detuning for prescribed-energy targeting.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

arXiv:2606.03380 [quant-ph]

(or arXiv:2606.03380v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.03380 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.