Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

1.
S.
McArdle
,
S.
Endo
,
A.
Aspuru-Guzik
,
S. C.
Benjamin
, and
X.
Yuan
, “
Quantum computational chemistry
,”
Rev. Mod. Phys.
92
,
015003
(
2020
).
2.
G.
Ortiz
,
J. E.
Gubernatis
,
E.
Knill
, and
R.
Laflamme
, “
Quantum algorithms for fermionic simulations
,”
Phys. Rev. A
64
,
022319
(
2001
).
3.
J.
Tilly
,
H.
Chen
,
S.
Cao
,
D.
Picozzi
,
K.
Setia
,
Y.
Li
,
E.
Grant
,
L.
Wossnig
,
I.
Rungger
,
G. H.
Booth
, and
J.
Tennyson
, “
The variational quantum eigensolver: A review of methods and best practices
,”
Phys. Rep.
986
,
1
128
(
2022
).
4.
D. S.
Abrams
and
S.
Lloyd
, “
Simulation of many-body fermi systems on a universal quantum computer
,”
Phys. Rev. Lett.
79
,
2586
2589
(
1997
).
5.
D. S.
Abrams
and
S.
Lloyd
, “
Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
,”
Phys. Rev. Lett.
83
,
5162
5165
(
1999
).
6.
D.
Halder
,
V. S.
Prasannaa
,
V.
Agarawal
, and
R.
Maitra
, “
Iterative quantum phase estimation with variationally prepared reference state
,”
Int. J. Quantum Chem.
123
,
e27021
(
2023
).
7.
H.
Wang
,
S.
Kais
,
A.
Aspuru-Guzik
, and
M. R.
Hoffmann
, “
Quantum algorithm for obtaining the energy spectrum of molecular systems
,”
Phys. Chem. Chem. Phys.
10
,
5388
5393
(
2008
).
8.
A.
Aspuru-Guzik
,
A. D.
Dutoi
,
P. J.
Love
, and
M.
Head-Gordon
, “
Simulated quantum computation of molecular energies
,”
Science
309
,
1704
1707
(
2005
).
9.
A.
Peruzzo
,
J.
McClean
,
P.
Shadbolt
,
M.-H.
Yung
,
X.-Q.
Zhou
,
P. J.
Love
,
A.
Aspuru-Guzik
, and
J. L.
O’Brien
, “
A variational eigenvalue solver on a photonic quantum processor
,”
Nat. Commun.
5
,
4213
(
2014
).
10.
J. I.
Colless
,
V. V.
Ramasesh
,
D.
Dahlen
,
M. S.
Blok
,
M. E.
Kimchi-Schwartz
,
J. R.
McClean
,
J.
Carter
,
W. A.
de Jong
, and
I.
Siddiqi
, “
Computation of molecular spectra on a quantum processor with an error-resilient algorithm
,”
Phys. Rev. X
8
,
011021
(
2018
).
11.
C.
Hempel
,
C.
Maier
,
J.
Romero
,
J.
McClean
,
T.
Monz
,
H.
Shen
,
P.
Jurcevic
,
B. P.
Lanyon
,
P.
Love
,
R.
Babbush
,
A.
Aspuru-Guzik
,
R.
Blatt
, and
C. F.
Roos
, “
Quantum chemistry calculations on a trapped-ion quantum simulator
,”
Phys. Rev. X
8
,
031022
(
2018
).
12.
M.
Metcalf
,
N. P.
Bauman
,
K.
Kowalski
, and
W. A.
de Jong
, “
Resource-efficient chemistry on quantum computers with the variational quantum eigensolver and the double unitary coupled-cluster approach
,”
J. Chem. Theory Comput.
16
,
6165
6175
(
2020
).
13.
K.
Sugisaki
,
T.
Kato
,
Y.
Minato
,
K.
Okuwaki
, and
Y.
Mochizuki
, “
Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: A case study of the C2v quasi-reaction pathway of beryllium insertion into a H2 molecule
,”
Phys. Chem. Chem. Phys.
24
,
8439
8452
(
2022
).
14.
Y.
Shen
,
X.
Zhang
,
S.
Zhang
,
J.-N.
Zhang
,
M.-H.
Yung
, and
K.
Kim
, “
Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
,”
Phys. Rev. A
95
,
020501
(
2017
).
15.
J.
Romero
,
R.
Babbush
,
J. R.
McClean
,
C.
Hempel
,
P. J.
Love
, and
A.
Aspuru-Guzik
, “
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
,”
Quantum Sci. Technol.
4
,
014008
(
2018
).
16.
F. A.
Evangelista
,
G. K.-L.
Chan
, and
G. E.
Scuseria
, “
Exact parameterization of fermionic wave functions via unitary coupled cluster theory
,”
J. Chem. Phys.
151
,
244112
(
2019
).
17.
I. O.
Sokolov
,
P. K.
Barkoutsos
,
P. J.
Ollitrault
,
D.
Greenberg
,
J.
Rice
,
M.
Pistoia
, and
I.
Tavernelli
, “
Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?
,”
J. Chem. Phys.
152
,
124107
(
2020
).
18.
A.
Anand
,
P.
Schleich
,
S.
Alperin-Lea
,
P. W. K.
Jensen
,
S.
Sim
,
M.
Díaz-Tinoco
,
J. S.
Kottmann
,
M.
Degroote
,
A. F.
Izmaylov
, and
A.
Aspuru-Guzik
, “
A quantum computing view on unitary coupled cluster theory
,”
Chem. Soc. Rev.
51
,
1659
1684
(
2022
).
19.
H.
Nakatsuji
, “
Equation for the direct determination of the density matrix
,”
Phys. Rev. A
14
,
41
50
(
1976
).
20.
M.
Nooijen
, “
Can the eigenstates of a many-body Hamiltonian be represented exactly using a general two-body cluster expansion?
,”
Phys. Rev. Lett.
84
,
2108
2111
(
2000
).
21.
J.
Lee
,
W. J.
Huggins
,
M.
Head-Gordon
, and
K. B.
Whaley
, “
Generalized unitary coupled cluster wave functions for quantum computation
,”
J. Chem. Theory Comput.
15
,
311
324
(
2018
).
22.
D.
Halder
,
V. S.
Prasannaa
, and
R.
Maitra
, “
Dual exponential coupled cluster theory: Unitary adaptation, implementation in the variational quantum eigensolver framework and pilot applications
,”
J. Chem. Phys.
157
,
174117
(
2022
).
23.
R.
Maitra
,
Y.
Akinaga
, and
T.
Nakajima
, “
A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential
,”
J. Chem. Phys.
147
,
074103
(
2017
).
24.
S.
Tribedi
,
A.
Chakraborty
, and
R.
Maitra
, “
Formulation of a dressed coupled-cluster method with implicit triple excitations and benchmark application to hydrogen-bonded systems
,”
J. Chem. Theory Comput.
16
,
6317
6328
(
2020
).
25.
A.
Das
and
B.
Chakrabarti
,
Quantum Annealing and Related Optimization Methods
, edited by
A.
Das
and
B. K.
Chakrabarti
(
Springer
,
Berlin
,
2005
), Vol.
378
, Chap. XIV, p.
124
, ISBN 3-540-27987-3.
26.
K.
Kowalski
and
N. P.
Bauman
, “
Sub-system quantum dynamics using coupled cluster downfolding techniques
,”
J. Chem. Phys.
152
,
244127
(
2020
).
27.
N. P.
Bauman
,
E. J.
Bylaska
,
S.
Krishnamoorthy
,
G. H.
Low
,
N.
Wiebe
,
C. E.
Granade
,
M.
Roetteler
,
M.
Troyer
, and
K.
Kowalski
, “
Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
,”
J. Chem. Phys.
151
,
014107
(
2019
).
28.
Y.
Fan
,
C.
Cao
,
X.
Xu
,
Z.
Li
,
D.
Lv
, and
M.-H.
Yung
, “
Circuit-depth reduction of unitary-coupled-cluster ansatz by energy sorting
,” arXiv:2106.15210 (
2023
).
29.
K.
Kowalski
, “
Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: Classical and quantum computing perspective
,”
Phys. Rev. A
104
,
032804
(
2021
).
30.
K.
Kowalski
and
N. P.
Bauman
, “
Quantum flow algorithms for simulating many-body systems on quantum computers
,” arXiv:2305.05168 (
2023
).
31.
H.
Abraham
et al (
2021
), “
Qiskit: An open-source framework for quantum computing
,” Zenodo. https://zenodo.org/10.5281/zenodo.2562111
32.
Q.
Sun
,
T. C.
Berkelbach
,
N. S.
Blunt
,
G. H.
Booth
,
S.
Guo
,
Z.
Li
,
J.
Liu
,
J. D.
McClain
,
E. R.
Sayfutyarova
,
S.
Sharma
,
S.
Wouters
, and
G. K.-L.
Chan
, “
PySCF: The python-based simulations of chemistry framework
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
,
e1340
(
2018
).
33.
W. J.
Hehre
,
R. F.
Stewart
, and
J. A.
Pople
, “
Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of Slater-type atomic orbitals
,”
J. Chem. Phys.
51
,
2657
2664
(
1969
).
34.
J. T.
Seeley
,
M. J.
Richard
, and
P. J.
Love
, “
The Bravyi-Kitaev transformation for quantum computation of electronic structure
,”
J. Chem. Phys.
137
,
224109
(
2012
).
35.
J. L.
Morales
, “
A numerical study of limited memory BFGS methods
,”
Appl. Math. Lett.
15
,
481
487
(
2002
).
36.
R. H.
Byrd
,
P.
Lu
,
J.
Nocedal
, and
C.
Zhu
, “
A limited memory algorithm for bound constrained optimization
,”
SIAM J. Sci. Comput.
16
,
1190
1208
(
1995
).
37.
O. R.
Meitei
,
B. T.
Gard
,
G. S.
Barron
,
D. P.
Pappas
,
S. E.
Economou
,
E.
Barnes
, and
N. J.
Mayhall
, “
Gate-free state preparation for fast variational quantum eigensolver simulations
,”
npj Quantum Inf.
7
,
155
(
2021
).
38.
N. H.
Stair
and
F. A.
Evangelista
, “
Simulating many-body systems with a projective quantum eigensolver
,”
PRX Quantum
2
,
030301
(
2021
).
39.
H. R.
Grimsley
,
S. E.
Economou
,
E.
Barnes
, and
N. J.
Mayhall
, “
An adaptive variational algorithm for exact molecular simulations on a quantum computer
,”
Nat. Commun.
10
,
3007
(
2019
).
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