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Hartree-Fock on a Superconducting Qubit Quantum Computer

Frank Carlton Arute
Kunal Arya
Rami Barends
Michael Blythe Broughton
Bob Benjamin Buckley
Nicholas Bushnell
Yu Chen
Jimmy Chen
Benjamin Chiaro
Roberto Collins
William Courtney
Andrew Dunsworth
Edward Farhi
Austin Fowler
Brooks Riley Foxen
Rob Graff
Steve Habegger
Alan Ho
Trent Huang
William J. Huggins
Sergei Isakov
Zhang Jiang
Cody Jones
Kostyantyn Kechedzhi
Alexander Korotkov
Fedor Kostritsa
Dave Landhuis
Pavel Laptev
Mike Lindmark
Orion Martin
John Martinis
Anthony Megrant
Xiao Mi
Masoud Mohseni
Wojtek Mruczkiewicz
Josh Mutus
Charles Neill
Thomas E O'Brien
Eric Ostby
Andre Gregory Petukhov
Harry Putterman
Vadim Smelyanskiy
Doug Strain
Kevin Jeffery Sung
Marco Szalay
Tyler Y. Takeshita
Amit Vainsencher
Nathan Wiebe
Jamie Yao
Ping Yeh
Science, vol. 369 (2020), pp. 6507


As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry which involve twice the number of qubits and more than ten times the number of gates as the largest prior experiments. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$, ${\rm H}_{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realize the Givens rotation approach to free fermion evolution, which we variationally optimize to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive corresponds to a rotation of the orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because free fermion evolutions are classically tractable to simulate, yet still generate highly entangled states over the computational basis, we use these experiments to benchmark the performance of our hardware while establishing a foundation for scaling up more complex correlated quantum simulations of chemistry.