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:
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- Univ. of Bristol (United Kingdom). Quantum Engineering Technology Labs. H. H. Wills Physics Lab. Dept. of Electrical and Electronic Engineering
- Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Google Inc., Venice, CA (United States)
- 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
- Imperial College London (United Kingdom). Dept. of Physics
- Univ. of Bristol (United Kingdom). School of Chemistry; Max Planck Inst. for Solid State Research, Stuttgart (Germany)
- 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.
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. doi:10.1126/sciadv.aap9646.
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. doi:10.1126/sciadv.aap9646. https://www.osti.gov/servlets/purl/1494079.
@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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Figures / Tables:
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 »
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