Table 1 Number of circuits needed to measure the expectation value of the nuclear shell-model for the p, sd and pf shells.

From: Nuclear shell-model simulation in digital quantum computers

Shell

\(N_{qb}\)

\(N_\text {h}\)

\(N_{\text {hh}}\)

\(N_{tot}\)

p

6

2

10 (9)

13 (12)

12

4

109 (44)

114 (49)

sd

12

8

203 (86)

212 (95)

24

16

1389 (518)

1406 (535)

pf

20

20

1507 (570)

1528 (591)

40

40

10,572 (3459)

10,613 (3500)

  1. \(N_{qb}\) indicates the number of qubits for only neutrons or protons (top row for each shell) or both nucleon types (bottom). \(N_{\text {h}}\) and \(N_{\text {hh}}\) are the number of single- and double-hopping terms in the Hamiltonian (related to \(h_{ijki}\) and \(h_{ijkl}\), respectively), defining the number of circuits needed to measure these parts. The last column lists the total number of circuits, \(N_{\text {h}}+N_{\text {hh}}+1\), accounting also for the single circuit needed to measure \(\langle n_i\rangle\) and \(\langle h_{ijij}^{(l)}\rangle\). The values in parenthesis correspond to the minimum number of groups containing \(h_{ijkl}\) terms that commute with each other and thus can be measured with the same circuit.
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