ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [Malone et al., J. Chem. Theory Comput. 19(1), 109–121 (2023)]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations of large systems that otherwise would not fit on a single central processing unit node or graphics processing unit (GPU) card. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals with multi-GPUs. Using CUDA and cupy for NVIDIA GPUs, ipie supports GPU-accelerated multi-slater determinant trial wavefunctions [Huang et al. arXiv:2406.08314 (2024)] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu2O2]2+ and [Fe2S2(SCH3)4]2−. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron–phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications.

1.
S.
Zhang
,
J.
Carlson
, and
J. E.
Gubernatis
, “
Constrained path quantum Monte Carlo method for fermion ground states
,”
Phys. Rev. Lett.
74
,
3652
3655
(
1995
).
2.
S.
Zhang
and
H.
Krakauer
, “
Quantum Monte Carlo method using phase-free random walks with slater determinants
,”
Phys. Rev. Lett.
90
,
136401
(
2003
).
3.
J.
Lee
,
H. Q.
Pham
, and
D. R.
Reichman
, “
Twenty years of auxiliary-field quantum Monte Carlo in quantum chemistry: An overview and assessment on main group chemistry and bond-breaking
,”
J. Chem. Theory Comput.
18
,
7024
7042
(
2022
).
4.
M.
Motta
and
S.
Zhang
, “
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
,”
WIREs Comput. Mol. Sci.
8
,
e1364
(
2018
).
5.
W. J.
Huggins
,
B. A.
O’Gorman
,
N. C.
Rubin
,
D. R.
Reichman
,
R.
Babbush
, and
J.
Lee
, “
Unbiasing fermionic quantum Monte Carlo with a quantum computer
,”
Nature
603
,
416
420
(
2022
).
6.
K.
Wan
,
W. J.
Huggins
,
J.
Lee
, and
R.
Babbush
, “
Matchgate shadows for fermionic quantum simulation
,”
Commun. Math. Phys.
404
,
629
700
(
2023
).
7.
M.
Amsler
,
P.
Deglmann
,
M.
Degroote
,
M. P.
Kaicher
,
M.
Kiser
,
M.
Kühn
,
C.
Kumar
,
A.
Maier
,
G.
Samsonidze
,
A.
Schroeder
et al, “
Classical and quantum trial wave functions in auxiliary-field quantum Monte Carlo applied to oxygen allotropes and a CuBr2 model system
,”
J. Chem. Phys.
159
,
044119
(
2023
).
8.
M.
Kiser
,
A.
Schroeder
,
G.-L. R.
Anselmetti
,
C.
Kumar
,
N.
Moll
,
M.
Streif
, and
D.
Vodola
, “
Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum Monte Carlo
,”
New J. Phys.
26
,
033022
(
2024
).
9.
B.
Huang
,
Y.-T.
Chen
,
B.
Gupt
,
M.
Suchara
,
A.
Tran
,
S.
McArdle
, and
G.
Galli
, “
Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
,”
Phys. Rev. Res.
(to be published) (
2024
).
10.
M.
Kiser
,
M.
Beuerle
, and
F.
Simkovic
IV
, “
Contextual subspace auxiliary-field quantum Monte Carlo: Improved bias with reduced quantum resources
,” arXiv:2408.06160v2 (
2024
).
11.
T.
Jiang
,
J.
Zhang
,
M. K. A.
Baumgarten
,
M.-F.
Chen
,
H. Q.
Dinh
,
A.
Ganeshram
,
N.
Maskara
,
A.
Ni
, and
J.
Lee
, “
Walking through Hilbert space with quantum computers
,” arXiv:2407.11672v1 (
2024
).
12.
J.
Lee
,
F. D.
Malone
, and
M. A.
Morales
, “
An auxiliary-field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree–Fock trial wavefunctions
,”
J. Chem. Phys.
151
,
064122
(
2019
).
13.
J.
Lee
and
D. R.
Reichman
, “
Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead
,”
J. Chem. Phys.
153
,
044131
(
2020
).
14.
J.
Lee
,
M. A.
Morales
, and
F. D.
Malone
, “
A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study
,”
J. Chem. Phys.
154
,
064109
(
2021
).
15.
J.
Lee
,
S.
Zhang
, and
D. R.
Reichman
, “
Constrained-path auxiliary-field quantum Monte Carlo for coupled electrons and phonons
,”
Phys. Rev. B
103
,
115123
(
2021
).
16.
J.
Lee
,
F. D.
Malone
,
M. A.
Morales
, and
D. R.
Reichman
, “
Spectral functions from auxiliary-field quantum Monte Carlo without analytic continuation: The extended Koopmans’ theorem approach
,”
J. Chem. Theory Comput.
17
,
3372
3387
(
2021
).
17.
F. D.
Malone
,
A.
Mahajan
,
J. S.
Spencer
, and
J.
Lee
, “
Ipie: A python-based auxiliary-field quantum Monte Carlo program with flexibility and efficiency on CPUs and GPUs
,”
J. Chem. Theory Comput.
19
,
109
121
(
2023
).
18.
S. K.
Lam
,
A.
Pitrou
, and
S.
Seibert
, in
Proceedings of the 2nd Workshop on the LLVM Compiler Infrastructure in HPC. LLVM’15
,
2015
.
19.
C. J.
Cramer
,
M.
Włoch
,
P.
Piecuch
,
C.
Puzzarini
, and
L.
Gagliardi
, “
Theoretical models on the Cu2O2 torture track: Mechanistic implications for oxytyrosinase and small-molecule analogues
,”
J. Phys. Chem. A
110
,
1991
2004
(
2006
).
20.
P. R.
Kent
,
A.
Annaberdiyev
,
A.
Benali
,
M. C.
Bennett
,
E. J.
Landinez Borda
,
P.
Doak
,
H.
Hao
,
K. D.
Jordan
,
J. T.
Krogel
,
I.
Kylänpää
et al, “
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo
,”
J. Chem. Phys.
152
,
174105
(
2020
).
21.
S.
Sharma
,
A. A.
Holmes
,
G.
Jeanmairet
,
A.
Alavi
, and
C. J.
Umrigar
, “
Semistochastic heat-bath configuration interaction method: Selected configuration interaction with semistochastic perturbation theory
,”
J. Chem. Theory Comput.
13
,
1595
1604
(
2017
).
22.
L.
Hehn
,
P.
Deglmann
, and
M.
Kühn
, “
Chelate complexes of 3d transition metal ions—A challenge for electronic-structure methods?
,”
J. Chem. Theory Comput.
20
,
4545
(
2024
).
23.
V. P.
Vysotskiy
,
C.
Filippi
, and
U.
Ryde
, “
Scalar relativistic all-electron and pseudopotential ab initio study of a minimal nitrogenase [Fe(SH)4H] model employing coupled-cluster and auxiliary-field quantum Monte Carlo many-body methods
,”
J. Phys. Chem. A
128
,
1358
(
2024
).
24.
M. S.
Chen
,
J.
Lee
,
H.-Z.
Ye
,
T. C.
Berkelbach
,
D. R.
Reichman
, and
T. E.
Markland
, “
Data-efficient machine learning potentials from transfer learning of periodic correlated electronic structure methods: Liquid water at AFQMC, CCSD, and CCSD(T) accuracy
,”
J. Chem. Theory Comput.
19
,
4510
4519
(
2023
).
25.
T.
Jiang
,
B.
O’Gorman
,
A.
Mahajan
, and
J.
Lee
, “
Unbiasing fermionic auxiliary-field quantum Monte Carlo with matrix product state trial wavefunctions
,” arXiv:2405.05440v1 (
2024
).
26.
The ipie package (v0.7.1), https://github.com/JoonhoLee-Group/ipie (2024).
27.
A.
Mahajan
and
S.
Sharma
, “
Taming the sign problem in auxiliary-field quantum Monte Carlo using accurate wave functions
,”
J. Chem. Theory Comput.
17
,
4786
4798
(
2021
).
28.
E.
Vitali
,
P.
Rosenberg
, and
S.
Zhang
, “
Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
,”
Phys. Rev. A
100
,
023621
(
2019
).
29.
C.-C.
Chang
,
B. M.
Rubenstein
, and
M. A.
Morales
, “
Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations
,”
Phys. Rev. B
94
,
235144
(
2016
).
30.
Plum: Multiple dispatch in Python
,” https://github.com/beartype/plum.
31.
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
et al, “
PySCF: The python-based simulations of chemistry framework
,”
WIREs Comput. Mol. Sci.
8
,
e1340
(
2018
).
32.
A. A.
Holmes
,
N. M.
Tubman
, and
C.
Umrigar
, “
Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling
,”
J. Chem. Theory Comput.
12
,
3674
3680
(
2016
).
33.
E.
Posenitskiy
,
V. G.
Chilkuri
,
A.
Ammar
,
M.
Hapka
,
K.
Pernal
,
R.
Shinde
,
E. J.
Landinez Borda
,
C.
Filippi
,
K.
Nakano
,
O.
Kohulák
,
S.
Sorella
,
P.
de Oliveira Castro
,
W.
Jalby
,
P. L.
Ríos
,
A.
Alavi
, and
A.
Scemama
, “
TREXIO: A file format and library for quantum chemistry
,”
J. Chem. Phys.
158
,
174801
(
2023
).
34.
N. C.
Rubin
,
K.
Gunst
,
A.
White
,
L.
Freitag
,
K.
Throssell
,
G. K.-L.
Chan
,
R.
Babbush
, and
T.
Shiozaki
, “
The fermionic quantum emulator
,”
Quantum
5
,
568
(
2021
).
35.
Z.
Li
and
G. K.-L.
Chan
, “
Spin-projected matrix product states: Versatile tool for strongly correlated systems
,”
J. Chem. Theory Comput.
13
,
2681
2695
(
2017
).
36.
A.
Mahajan
,
J. S.
Kurian
,
J.
Lee
,
D. R.
Reichman
, and
S.
Sharma
, “
Response properties in phaseless auxiliary field quantum Monte Carlo
,”
J. Chem. Phys.
159
,
184101
(
2023
).
37.
J.
Hubbard
, “
Calculation of partition functions
,”
Phys. Rev. Lett.
3
,
77
(
1959
).
38.
R.
Stratonovich
, “
On a method of calculating quantum distribution functions
,”
Sov. Phys. Dokl.
2
,
416
419
(
1958
), https://zbmath.org/?q=an:0080.19804.
39.
J.
Ren
,
W.
Li
,
T.
Jiang
,
Y.
Wang
, and
Z.
Shuai
, “
Time-dependent density matrix renormalization group method for quantum dynamics in complex systems
,”
WIREs Comput. Mol. Sci.
12
,
e1614
(
2022
).
40.
H.
Flyvbjerg
and
H. G.
Petersen
, “
Error estimates on averages of correlated data
,”
J. Chem. Phys.
91
,
461
466
(
1989
).
41.
A.
Mahajan
,
J.
Lee
, and
S.
Sharma
, “
Selected configuration interaction wave functions in phaseless auxiliary field quantum Monte Carlo
,”
J. Chem. Phys.
156
,
174111
(
2022
).
42.
P.
Jurečka
,
J.
Šponer
,
J.
Černỳ
, and
P.
Hobza
, “
Benchmark database of accurate (MP2 and CCSD (T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs
,”
Phys. Chem. Chem. Phys.
8
,
1985
1993
(
2006
).
43.
F.
Weigend
,
M.
Kattannek
, and
R.
Ahlrichs
, “
Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods
,”
J. Chem. Phys.
130
,
164106
(
2009
).
44.
A.
Halkier
,
T.
Helgaker
,
P.
Jørgensen
,
W.
Klopper
,
H.
Koch
,
J.
Olsen
, and
A. K.
Wilson
, “
Basis-set convergence in correlated calculations on Ne, N2, and H2O
,”
Chem. Phys. Lett.
286
,
243
252
(
1998
).
45.
Benchmark data for S22 reaction set,
2024
.
46.
L. A.
Burns
,
M. S.
Marshall
, and
C. D.
Sherrill
, “
Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches
,”
J. Chem. Phys.
141
,
234111
(
2014
).
47.
Y. S.
Al-Hamdani
,
P. R.
Nagy
,
A.
Zen
,
D.
Barton
,
M.
Kállay
,
J. G.
Brandenburg
, and
A.
Tkatchenko
, “
Interactions between large molecules pose a puzzle for reference quantum mechanical methods
,”
Nat. Commun.
12
,
3927
(
2021
).
48.
S. F.
Boys
and
F.
Bernardi
, “
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
,”
Mol. Phys.
19
,
553
566
(
1970
).
49.
S.
Blaschke
and
S.
Stopkowicz
, “
Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields
,”
J. Chem. Phys.
156
,
044115
(
2022
).
50.
M.
Suewattana
,
W.
Purwanto
,
S.
Zhang
,
H.
Krakauer
, and
E. J.
Walter
, “
Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules
,”
Phys. Rev. B
75
,
245123
(
2007
).
51.
Y.
Huang
,
Z.
Guo
,
H. Q.
Pham
, and
D.
Lv
, “
GPU-accelerated auxiliary-field quantum Monte Carlo with multi-slater determinant trial states
,” arXiv:2406.08314v1 (
2024
).
52.
R.
Assaraf
and
M.
Caffarel
, “
Zero-variance principle for Monte Carlo algorithms
,”
Phys. Rev. Lett.
83
,
4682
4685
(
1999
).
53.
Y.
Chen
,
L.
Zhang
,
W.
E
, and
R.
Car
, “
Hybrid auxiliary field quantum Monte Carlo for molecular systems
,”
J. Chem. Theory Comput.
19
,
4484
4493
(
2023
).
54.
Y.-Y.
He
,
M.
Qin
,
H.
Shi
,
Z.-Y.
Lu
, and
S.
Zhang
, “
Finite-temperature auxiliary-field quantum Monte Carlo: Self-consistent constraint and systematic approach to low temperatures
,”
Phys. Rev. B
99
,
045108
(
2019
).
55.
T.
Shen
,
Y.
Liu
,
Y.
Yu
, and
B. M.
Rubenstein
, “
Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble
,”
J. Chem. Phys.
153
,
204108
(
2020
).
56.
R.
Blankenbecler
,
D. J.
Scalapino
, and
R. L.
Sugar
, “
Monte Carlo calculations of coupled boson–fermion systems. I
,”
Phys. Rev. D
24
,
2278
2286
(
1981
).
57.
J. E.
Hirsch
, “
Two-dimensional Hubbard model: Numerical simulation study
,”
Phys. Rev. B
31
,
4403
4419
(
1985
).
58.
R. R. d.
Santos
, “
Introduction to quantum Monte Carlo simulations for fermionic systems
,”
Braz. J. Phys.
33
,
36
54
(
2003
).
59.
A.
Macridin
, “
Phonons, charge and spin in correlated systems
,” Ph.D. thesis,
University of Groningen
,
2003
.
60.
D. J. J.
Marchand
,
P. C. E.
Stamp
, and
M.
Berciu
, “
Dual coupling effective band model for polarons
,”
Phys. Rev. B
95
,
035117
(
2017
).
61.
M. H.
Kalos
,
D.
Levesque
, and
L.
Verlet
, “
Helium at zero temperature with hard-sphere and other forces
,”
Phys. Rev. A
9
,
2178
2195
(
1974
).
62.
T.
Holstein
, “
Studies of polaron motion: Part I. The molecular-crystal model
,”
Ann. Phys.
8
,
325
342
(
1959
).
63.
A.
Paszke
,
S.
Gross
,
F.
Massa
,
A.
Lerer
,
J.
Bradbury
,
G.
Chanan
,
T.
Killeen
,
Z.
Lin
,
N.
Gimelshein
,
L.
Antiga
,
A.
Desmaison
,
A.
Kopf
,
E.
Yang
,
Z.
DeVito
,
M.
Raison
,
A.
Tejani
,
S.
Chilamkurthy
,
B.
Steiner
,
L.
Fang
,
J.
Bai
, and
S.
Chintala
, “
PyTorch: An imperative style, high-performance deep learning library
,” in
Advances in Neural Information Processing Systems
(
Curran Associates, Inc.
,
2019
), Vol.
32
, pp.
8024
8035
.
64.
T.
Chen
,
B.
Xu
,
C.
Zhang
, and
C.
Guestrin
, “
Training deep nets with sublinear memory cost
,” arXiv:1604.06174v2 (
2016
).
65.
T. H.
Dunning
, Jr.
, “
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,”
J. Chem. Phys.
90
,
1007
1023
(
1989
).
66.
S. L.
Shostak
,
W. L.
Ebenstein
, and
J. S.
Muenter
, “
The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states
,”
J. Chem. Phys.
94
,
5875
5882
(
1991
).
67.
F.
Shimizu
, “
Stark spectroscopy of NH3 ν2 band by 10-μ CO2 and N2O lasers
,”
J. Chem. Phys.
52
,
3572
3576
(
1970
).
68.
J.
Muenter
, “
Electric dipole moment of carbon monoxide
,”
J. Mol. Spectrosc.
55
,
490
491
(
1975
).
69.
F.
Lovas
,
E.
Tiemann
,
J.
Coursey
,
S.
Kotochigova
,
J.
Chang
,
K.
Olsen
, and
R.
Dragoset
, “
Diatomic spectral database
,” https://dx.doi.org/10.18434/T4T59X (
2003
).
70.
Y.
Garniron
,
T.
Applencourt
,
K.
Gasperich
,
A.
Benali
,
A.
Ferté
,
J.
Paquier
,
B.
Pradines
,
R.
Assaraf
,
P.
Reinhardt
,
J.
Toulouse
,
P.
Barbaresco
,
N.
Renon
,
G.
David
,
J.-P.
Malrieu
,
M.
Véril
,
M.
Caffarel
,
P.-F.
Loos
,
E.
Giner
, and
A.
Scemama
, “
Quantum package 2.0: An open-source determinant-driven suite of programs
,”
J. Chem. Theory Comput.
15
,
3591
3609
(
2019
).
71.
H. G. A.
Burton
and
P.-F.
Loos
, “
Rationale for the extrapolation procedure in selected configuration interaction
,”
J. Chem. Phys.
160
,
104102
(
2024
).
72.
P.-F.
Loos
,
Y.
Damour
, and
A.
Scemama
, “
The performance of CIPSI on the ground state electronic energy of benzene
,”
J. Chem. Phys.
153
,
176101
(
2020
).
73.
B.-X.
Zheng
,
J. S.
Kretchmer
,
H.
Shi
,
S.
Zhang
, and
G. K.-L.
Chan
, “
Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver
,”
Phys. Rev. B
95
,
045103
(
2017
).
74.
B.
Eskridge
,
H.
Krakauer
, and
S.
Zhang
, “
Local embedding and effective downfolding in the auxiliary-field quantum Monte Carlo method
,”
J. Chem. Theory Comput.
15
,
3949
(
2019
).
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