Antonio Andreas Gentile

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

We introduce the concept of an eigenstate witness and use it to find energies of quantum systems with quantum computers. The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

Noise resilience of Bayesian quantum phase estimation tested on a Si quantum photonic chip

Quantum Phase Estimation (PE) is a fundamental building block in the framework of Quantum Computing. Accurate estimation of the true eigenphase φ0 of a known eigenstate |φ〉 is fundamental for the implementation of many promising quantum algorithms. The interest in PE is also due to the modest quantum hardware requirements of the Iterative Phase Estimation Algorithm (IPEA) implementation [1], successfully implemented on small-scale devices [2]. However, IPEA makes hard decisions at each step of the algorithm, relying on majority voting schemes for its robustness against noise. It has been observed how non-error-corrected machines may enter a regime where error-rates for IPEA diverge quickly, making this approach impractical [3].