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Sci Adv. 2018 Jan 26;4(1):eaap9646. doi: 10.1126/sciadv.aap9646. eCollection 2018 Jan.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra.

Author information

1
Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1FD, UK.
2
Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA.
3
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
4
Google Inc., Venice, CA 90291, USA.
5
Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1FD, UK.
6
Department of Physics, Imperial College London, London, SW7 2AZ, UK.
7
School of Chemistry, University of Bristol, Bristol BS8 1TS, UK.
8
Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
9
State Key Laboratory of Optoelectronic Materials and Technologies and School of Physics, Sun Yat-sen University, Guangzhou 510275, China.

Abstract

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.

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