Efficient Quantum Estimation of Hamiltonian Spectra via Shallow Circuits

Area of Science:

• Quantum Computing
• Quantum Algorithms
• Spectroscopy

Background:

• Noisy Intermediate-Scale Quantum (NISQ) era necessitates resource-efficient quantum algorithms.
• Accurate estimation of Hamiltonian spectra is crucial for quantum simulations.

Purpose of the Study:

• To develop a novel, resource-efficient quantum algorithm for finding eigenstates and eigenvalues.
• To experimentally validate the proposed method on photonic quantum hardware.

Main Methods:

• Development of the variational rodeo eigensolver (VRE) algorithm.
• Experimental demonstration on a programmable photonic chip using a single-qubit exciton transfer Hamiltonian.
• Numerical verification of scalability using a two-qubit Hamiltonian.

Main Results:

• VRE achieved >99% fidelity in searching eigenstates.
• Eigenvalues were estimated with chemical accuracy.
• Ground energies of a hydrogen molecule Hamiltonian were experimentally estimated.
• Scalability was numerically verified for a hydrogen-helium ion Hamiltonian.

Conclusions:

• VRE is a systematic and efficient approach for Hamiltonian spectral estimation.
• The method shows promise for NISQ devices and quantum chemistry applications.