Table 3 Simulation costs for energy calculations of seven geometries using the ADAPT approaches on a laptop equipped with an Apple M3 Max chip

From: Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Molecule

ADAPT-

Min # of ADAPT

Total # of Optim-

Total Simulation Time (s)

Ground-State

  

Iterations

ization Rounds

Gradients

Energy Eval.

Energy Error (in a.u.)

H4 (linear)

GCIM

11

0

0.08

0.38

7.11 × 10−15

VQE

11

121

0.10

7.61

7.11 × 10−15

H4 (square)

GCIM

15

0

0.11

0.73

2.89 × 10−15

VQE

11

136

0.09

17.44

4.88 × 10−15

LiH

GCIM

56

0

2.53

30.50

8.88 × 10−15

VQE

27

439

1.24

253.64

6.36 × 10−8

BeH2

GCIM

104

0

10.05

242.14

8.70 × 10−14

VQE

41

1248

3.69

2308.14

1.91 × 10−06

H6 (1.0584 Å)

GCIM

79

0

3.77

77.55

1.33 × 10−15

VQE

70

4792

3.17

4627.37

1.70 × 10−6

GCIM(5,2)

67

28

3.35

85.47

6.66 × 10−15

H6 (1.8521 Å)

GCIM

70

0

3.42

55.85

1.90 × 10−13

VQE

88

9209

3.99

11924.84

9.98 × 10−08

H6 (5.0000 Å)

GCIM

37

0

1.79

12.03

9.57 × 10−8

VQE

84

11313

3.86

12765.16

1.15 × 10−6

GCIM(5,2)

26

12

1.24

13.41

9.61 × 10−8

  1. During the optimization rounds, the default optimizer is the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, implemented in SciPy69. ADAPT-GCIM(5,2) is an extended method introduced in Supplementary Information (Section VIII).
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