For quantum computing applications, the electronic Hamiltonian for the electronic structure problem needs to be unitarily transformed into a qubit form. We found that mean-field procedures on the original electronic Hamiltonian and on its transformed qubit counterpart can give different results. We establish conditions of when fermionic and qubit mean fields provide the same or different energies. In cases when the fermionic mean-field (Hartree–Fock) approach provides an accurate description (electronic correlation effects are small), the choice of molecular orbitals for the electron Hamiltonian representation becomes the determining factor in whether the qubit mean-field energy will be equal to or higher than that of the fermionic counterpart. In strongly correlated cases, the qubit mean-field approach has a higher chance to undergo symmetry breaking and lower its energy below the fermionic counterpart.

1.
B. P.
Lanyon
,
J. D.
Whitfield
,
G. G.
Gillett
,
M. E.
Goggin
,
M. P.
Almeida
,
I.
Kassal
,
J. D.
Biamonte
,
M.
Mohseni
,
B. J.
Powell
,
M.
Barbieri
,
A.
Aspuru-Guzik
, and
A. G.
White
,
Nat. Chem.
2
,
106
(
2010
).
2.
A. Y.
Kitaev
, e-print arXiv:quant-ph/9511026 (
1995
).
3.
D. S.
Abrams
and
S.
Lloyd
,
Phys. Rev. Lett.
79
,
2586
(
1997
).
4.
D. S.
Abrams
and
S.
Lloyd
,
Phys. Rev. Lett.
83
,
5162
(
1999
).
5.
A.
Aspuru-Guzik
,
A. D.
Dutoi
,
P. J.
Love
, and
M.
Head-Gordon
,
Science
309
,
1704
(
2005
).
6.
K. R.
Brown
,
R. J.
Clark
, and
I. L.
Chuang
,
Phys. Rev. Lett.
97
,
050504
(
2006
).
7.
J. D.
Whitfield
,
J.
Biamonte
, and
A.
Aspuru-Guzik
,
Mol. Phys.
109
,
735
(
2011
).
8.
A.
Peruzzo
,
J.
McClean
,
P.
Shadbolt
,
M.-H.
Yung
,
X.-Q.
Zhou
,
P. J.
Love
,
A.
Aspuru-Guzik
, and
J. L.
O’Brien
,
Nat. Commun.
5
,
4213
(
2014
).
9.
J. R.
McClean
,
J.
Romero
,
R.
Babbush
, and
A.
Aspuru-Guzik
,
New J. Phys.
18
,
023023
(
2016
).
10.
P. J. J.
O’Malley
,
R.
Babbush
,
I. D.
Kivlichan
,
J.
Romero
,
J. R.
McClean
,
R.
Barends
,
J.
Kelly
,
P.
Roushan
,
A.
Tranter
,
N.
Ding
,
B.
Campbell
,
Y.
Chen
,
Z.
Chen
,
B.
Chiaro
,
A.
Dunsworth
,
A. G.
Fowler
,
E.
Jeffrey
,
E.
Lucero
,
A.
Megrant
,
J. Y.
Mutus
,
M.
Neeley
,
C.
Neill
,
C.
Quintana
,
D.
Sank
,
A.
Vainsencher
,
J.
Wenner
,
T. C.
White
,
P. V.
Coveney
,
P. J.
Love
,
H.
Neven
,
A.
Aspuru-Guzik
, and
J. M.
Martinis
,
Phys. Rev. X
6
,
031007
(
2016
).
11.
C.
Hempel
,
C.
Maier
,
J.
Romero
,
J.
McClean
,
T.
Monz
,
H.
Shen
,
P.
Jurcevic
,
B.
Lanyon
,
P.
Love
,
R.
Babbush
,
A.
Aspuru-Guzik
,
R.
Blatt
, and
C.
Roos
, e-print arXiv:1803.10238 [quant-ph] (
2018
).
12.
A.
Kandala
,
A.
Mezzacapo
,
K.
Temme
,
M.
Takita
,
M.
Brink
,
J. M.
Chow
, and
J. M.
Gambetta
,
Nature
549
,
242
(
2017
).
13.
P.
Jordan
and
E.
Wigner
,
Z. Phys.
47
,
631
(
1928
).
14.
S. B.
Bravyi
and
A. Y.
Kitaev
,
Ann. Phys.
298
,
210
(
2002
).
15.
J. T.
Seeley
,
M. J.
Richard
, and
P. J.
Love
,
J. Chem. Phys.
137
,
224109
(
2012
).
16.
A.
Tranter
,
S.
Sofia
,
J.
Seeley
,
M.
Kaicher
,
J.
McClean
,
R.
Babbush
,
P. V.
Coveney
,
F.
Mintert
,
F.
Wilhelm
, and
P. J.
Love
,
Int. J. Quantum Chem.
115
,
1431
(
2015
).
17.
K.
Setia
and
J. D.
Whitfield
, e-print arXiv:1712.00446 [quant-ph] (
2017
).
18.
V.
Havlíček
,
M.
Troyer
, and
J. D.
Whitfield
,
Phys. Rev. A
95
,
032332
(
2017
).
19.
T.
Helgaker
,
P.
Jorgensen
, and
J.
Olsen
,
Molecular Electronic-Structure Theory
(
Wiley
,
2000
), Chap. 10, pp.
433
522
.
20.
A.
Perelomov
,
Generalized Coherent States and Their Applications
, Theoretical and Mathematical Physics (
Springer Science & Business Media
,
2012
).
21.
J. M.
Radcliffe
,
J. Phys. A: Gen. Phys.
4
,
313
(
1971
).
22.
F. T.
Arecchi
,
E.
Courtens
,
R.
Gilmore
, and
H.
Thomas
,
Phys. Rev. A
6
,
2211
(
1972
).
23.
E. H.
Lieb
,
Commun. Math. Phys.
31
,
327
(
1973
).
24.

These MSOs were obtained as the HF CMSOs for the singlet LiH2+ cation.

25.
J. R.
McClean
,
I. D.
Kivlichan
,
D. S.
Steiger
,
Y.
Cao
,
E. S.
Fried
,
C.
Gidney
,
T.
Häner
,
V.
Havlíček
,
Z.
Jiang
,
M.
Neeley
,
J.
Romero
,
N.
Rubin
,
N. P. D.
Sawaya
,
K.
Setia
,
S.
Sim
,
W.
Sun
,
K.
Sung
, and
R.
Babbush
, ver. 0.3, e-print arXiv:1710.07629 [quant-ph] (
2017
).
26.

The list of the MSOs is enumerated so that all spin z-projection +1/2 orbits in the ascending order of the orbital energies are followed by the corresponding spin z-projection −1/2 subset.

27.
M. A.
Nielsen
,
The Fermionic Canonical Commutation Relations and the Jordan-Wigner Transform
(
School of Physical Sciences, The University of Queensland
,
2005
).
28.
I. G.
Ryabinkin
,
S. N.
Genin
, and
A. F.
Izmaylov
, e-print arXiv:1806.00461 [physics.chem-ph] (
2018
).
29.
C. A.
Jiménez-Hoyos
,
T. M.
Henderson
,
T.
Tsuchimochi
, and
G. E.
Scuseria
,
J. Chem. Phys.
136
,
164109
(
2012
).
You do not currently have access to this content.