Witnessing eigenstates for quantum simulation of Hamiltonian spectra.

Area of Science:

• Quantum computing
• Quantum algorithms
• Computational chemistry

Background:

• Calculating Hamiltonian spectra is crucial for quantum mechanics but often intractable for classical computers.
• Existing quantum methods for eigenvalue approximation have limitations in efficiency and applicability.

Purpose of the Study:

• To introduce a novel quantum approach for efficiently calculating Hamiltonian spectra.
• To experimentally verify this protocol on a programmable quantum photonic chip.

Main Methods:

• Introduced the concept of an "eigenstate witness".
• Combined variational methods and quantum phase estimation for eigenvalue approximation.
• Experimental verification using entangled state generation, controlled unitary operations, and projective measurements on a silicon quantum photonic chip.

Main Results:

• Achieved experimental fidelities >99% for both ground and excited states.
• Estimated eigenvalues with 32 bits of precision.
• Demonstrated the protocol's performance through numerical simulations of complex Hamiltonians.

Conclusions:

• The developed quantum approach offers an efficient and high-precision method for Hamiltonian spectra calculation.
• Experimental validation on a scalable quantum photonic platform shows promising progress for quantum chemistry applications.
• The eigenstate witness concept provides a new avenue for quantum algorithm development.