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Title: Witnessing eigenstates for quantum simulation of Hamiltonian spectra

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.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [6]; ORCiD logo [7]; ORCiD logo [1]; ORCiD logo [1]
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  1. Univ. of Bristol (United Kingdom). Quantum Engineering Technology Labs. H. H. Wills Physics Lab. Dept. of Electrical and Electronic Engineering
  2. Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Google Inc., Venice, CA (United States)
  4. Univ. of Bristol (United Kingdom). Quantum Engineering Centre for Doctoral Training. Quantum Engineering Technology Labs. H. H. Wills Physics Lab. Dept. of Electrical and Electronic Engineering
  5. Imperial College London (United Kingdom). Dept. of Physics
  6. Univ. of Bristol (United Kingdom). School of Chemistry; Max Planck Inst. for Solid State Research, Stuttgart (Germany)
  7. Sun Yat-Sen Univ., Guangzhou (China). State Key Lab. of Optoelectronic Materials and Technologies. School of Physics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); LBNL Laboratory Directed Research and Development (LDRD) Program; US Army Research Office (ARO); Royal Society (United Kingdom); Engineering and Physical Sciences Research Council (EPSRC); European Research Council (ERC); National Key Research and Development Program (China); National Young 1000 Talents Plan (China); Natural Science Foundation of Guangdong (China)
OSTI Identifier:
1494079
Grant/Contract Number:  
AC02-05CH11231; W911NF-14-013; UF130574; K033085/1; J017175/1; K02193/1; 648667; 608062; 641039; 640079; EP/L015730/1; 2016YFA0301700; 2017YFA0305200; 2016A030312012
Resource Type:
Accepted Manuscript
Journal Name:
Science Advances
Additional Journal Information:
Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2375-2548
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Santagati, Raffaele, Wang, Jianwei, Gentile, Antonio A., Paesani, Stefano, Wiebe, Nathan, McClean, Jarrod R., Morley-Short, Sam, Shadbolt, Peter J., Bonneau, Damien, Silverstone, Joshua W., Tew, David P., Zhou, Xiaoqi, O’Brien, Jeremy L., and Thompson, Mark G. Witnessing eigenstates for quantum simulation of Hamiltonian spectra. United States: N. p., 2018. Web. doi:10.1126/sciadv.aap9646.
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Santagati, Raffaele, Wang, Jianwei, Gentile, Antonio A., Paesani, Stefano, Wiebe, Nathan, McClean, Jarrod R., Morley-Short, Sam, Shadbolt, Peter J., Bonneau, Damien, Silverstone, Joshua W., Tew, David P., Zhou, Xiaoqi, O’Brien, Jeremy L., & Thompson, Mark G. Witnessing eigenstates for quantum simulation of Hamiltonian spectra. United States. https://doi.org/10.1126/sciadv.aap9646
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Santagati, Raffaele, Wang, Jianwei, Gentile, Antonio A., Paesani, Stefano, Wiebe, Nathan, McClean, Jarrod R., Morley-Short, Sam, Shadbolt, Peter J., Bonneau, Damien, Silverstone, Joshua W., Tew, David P., Zhou, Xiaoqi, O’Brien, Jeremy L., and Thompson, Mark G. Fri . "Witnessing eigenstates for quantum simulation of Hamiltonian spectra". United States. https://doi.org/10.1126/sciadv.aap9646. https://www.osti.gov/servlets/purl/1494079.
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@article{osti_1494079,
title = {Witnessing eigenstates for quantum simulation of Hamiltonian spectra},
author = {Santagati, Raffaele and Wang, Jianwei and Gentile, Antonio A. and Paesani, Stefano and Wiebe, Nathan and McClean, Jarrod R. and Morley-Short, Sam and Shadbolt, Peter J. and Bonneau, Damien and Silverstone, Joshua W. and Tew, David P. and Zhou, Xiaoqi and O’Brien, Jeremy L. and Thompson, Mark G.},
abstractNote = {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.},
doi = {10.1126/sciadv.aap9646},
journal = {Science Advances},
number = 1,
volume = 4,
place = {United States},
year = {2018},
month = {1}
}
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Journal Article:
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https://doi.org/10.1126/sciadv.aap9646
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Figures / Tables:

Fig. 1 Fig. 1: The WAVES protocol. (A) Flowchart describing the protocol. The optimization of $\mathcal{F}$obj($\vec{θ}$) = ε + $\mathcal{TS}$ using the circuit in (B) allows one to variationally find the ground state of the Hamiltonian, preparing trial states via the ansatz Â($\vec{θ}$) with no perturbation (Ê$_{p_{0}}$ = Î). An initial guessmore » for an excited state is given by a perturbation Ê$_{p_{i}}$ on the ground state and then refined using the same circuit by exploiting the eigenstate witness $\mathcal{F}$obj($\vec{θ}$) = $\mathcal{S}$ (high‐T limit). (C) For each target eigenstate found, the eigenvalues are precisely estimated via the IPEA using the quantum logic circuit, where H is the Hadamard gate. The color coding in (B) and (C), blue for the control and red for the target, refers to the difference in wavelength between the photon in the control qubit and the one in the target register in our experimental implementation. (D) Diagram schematically representing the intuition behind the proposed approach, where initial guesses of excited states are variationally refined using the witness and IPEA returns the eigenvalues.« less
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