Table 4 Resource estimates for diamond and nickel oxide with different number of atoms in the supercell (8 and 64 atoms)

From: Quantum simulations of chemistry in first quantization with any basis set

System

Method

(Electrons, Orbitals)

Logical qubits

Toffolis

Physical qubits

Diamond-8

This work (min-Qu)

(48, 4096)

759

2.69 × 1011

3.76 × 106

This work (min-T)

 

2285

3.88 × 1010

1.03 × 107

2nd Q. (DPW)43

 

8338

1.78 × 1014

6.27 × 107

1st Q. (PW)25

(48, 3375)

1508

5.35 × 1010

6.87 × 106

Diamond-64

This work (min-Qu)

(384, 32768)

5976

1.51 × 1014

4.51 × 107

This work (min-T)

 

21590

3.35 × 1012

1.33 × 108

2nd Q. (DPW)43

 

65702

3.86 × 1015

6.09 × 108

1st Q. (PW)25

(384, 29791)

6948

2.19 × 1012

4.08 × 107

NiO-8

This work (min-Qu)

(144, 4096)

1919

1.99 × 1012

1.03 × 107

This work (min-T)

 

3475

4.09 × 1011

1.85 × 107

2nd Q. (DPW)43

 

8338

1.43 × 1014

6.27 × 107

1st Q. (PW)25

(144, 3375)

2752

7.52 × 1011

1.47 × 107

NiO-64

This work (min-Qu)

(1152, 32768)

17505

1.16 × 1015

1.43 × 108

This work (min-T)

 

33500

4.15 × 1013

2.5 × 108

2nd Q. (DPW)43

 

65701

3.22 × 1015

5.84 × 108

1st Q. (PW)25

(1152, 29791)

18572

4.56 × 1013

1.39 × 108

  1. Resources are shown for the method developed in this work for two cases: one minimizes the number of logical qubits (min-Qu) and the second case when one minimizes the number of Toffoli gates (min-T). For comparison we also present resource estimates obtained for algorithms in second quantization with dual plane waves43 and first quantization with plane waves but without data loading25. Bold font indicates smaller value.