Table 3 Resource estimates for uniform electron gas systems with 14, 54, and 114 electrons and Wigner-Seitz radius of 5

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

System

Method

(Electrons, Orbitals)

Logical qubits

Toffolis

Physical qubits

UEG-14

This work (min Qu)

(14, 512)

259

2.01 × 107

6.83 × 105

This work (min T)

 

482

1.32 × 107

1.32 × 106

2nd Q. (DPW)43

 

1127

2.96 × 1010

4.87 × 106

1st Q. (PW)25

(14, 343)

593

2.27 × 107

1.6 × 106

UEG-14

This work (min Qu)

(14, 4096)

330

1.99 × 109

1.23 × 106

This work (min T)

 

1751

2.36 × 108

5.71 × 106

2nd Q. (DPW)43

 

8327

1.27 × 1013

5.69 × 107

1st Q. (PW)25

(14, 3375)

767

8 × 107

2.39 × 106

UEG-54

This work (min-Qu)

(54, 4096)

813

4.21 × 109

3.11 × 106

This work (min-T)

 

2249

6.22 × 108

7.83 × 106

2nd Q. (DPW)43

 

8319

1.93 × 1012

4.88 × 107

1st Q. (PW)25

(54, 3375)

1298

2.94 × 108

4.26 × 106

UEG-114

This work (min-Qu)

(114, 4096)

1535

7.11 × 109

6.15 × 106

This work (min-T)

 

2971

1.33 × 109

1.1 × 107

2nd Q. (DPW)43

 

8314

6.91 × 1011

4.63 × 107

1st Q. (PW)25

(114, 3375)

2023

7.83 × 108

7.55 × 106

  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 resources obtained for algorithms in second quantization with dual plane waves43 and first quantization with plane waves but without the data loading25. Bold font indicates smaller value.
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