Letter | Published:

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

Nature volume 549, pages 242246 (14 September 2017) | Download Citation


Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers1. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium2,3,4,5,6,7,8. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians9 and a robust stochastic optimization routine10. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.

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We thank J. Chavez-Garcia, A. D. Córcoles and J. Rozen for experimental contributions, J. Hertzberg and S. Rosenblatt for room temperature characterization, B. Abdo for design and characterization of the Josephson Parametric Converters, S. Brayvi, J. Smolin, E. Magesan, L. Bishop, S. Sheldon, N. Moll, P. Barkoutsos and I. Tavernelli for discussions, and W. Shanks for assistance with the experimental control software. We thank A. D. Córcoles for edits to the manuscript. We acknowledge support from the IBM Research Frontiers Institute. The research is based on work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the Army Research Office contract W911NF-10-1-0324.

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    • Abhinav Kandala
    •  & Antonio Mezzacapo

    These authors contributed equally to this work.


  1. IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA

    • Abhinav Kandala
    • , Antonio Mezzacapo
    • , Kristan Temme
    • , Maika Takita
    • , Markus Brink
    • , Jerry M. Chow
    •  & Jay M. Gambetta


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A.K. and A.M. contributed equally to this work. J.M.G. and K.T. designed the experiments. A.K. and M.T. characterized the device and A.K. performed the experiments. M.B. fabricated the devices. A.M. developed the theory and the numerical simulations. A.K., A.M. and J.M.G. interpreted and analysed the experimental data. A.K., A.M., K.T., J.M.C. and J.M.G. contributed to writing the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Abhinav Kandala or Antonio Mezzacapo.

Reviewer Information Nature thanks N. Linke and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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