Figure 1.
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Figure 9.
Summary of our results and comparison with previous work_ Note that we report here worst-case values, corresponding to k ∼ sn and k→∼(n/d,…,n/d)\vec k \sim (n/d, \ldots ,n/d) for |Dn,k(s)〉|D_{n,k}^{(s)}\rangle and |Dn(k→)〉|{D^n}(\vec k)\rangle , respectively; see the respective sections for more comprehensive discussions_
| Dicke state | Reference | Depth | Ancillas [Dimension] | Repetitions |
|---|---|---|---|---|
| SU(2) spin-s | NRR [22] | 𝒪(skn) | 0 | 1 |
| Result 1 | 𝒪(skn) | 1 [k + 1] | 1 | |
| Result 2 | 𝒪 (log(sn)) | 𝒪(log(sn) + n) [2] | ||
| Result 3 | 𝒪(1) | 𝒪(n) [2sn + 1] | ||
| Result 4 | 𝒪(1) | 𝒪(log(sn)) [2], 𝒪(n log(sn)) [2s + 1] | ||
| SU(d) | NR [23] | 𝒪(nd) | 0 | 1 |
| LCG [9] | 𝒪(log n) | 𝒪(n log n + log d) [2] | 𝒪(1) | |
| Result 5 | 𝒪((n/d)d) | 1 [2], 1[𝒪((n/d)d)] | 1 | |
| Result 6 | 𝒪(d log n) | 𝒪(d log n + n) [2] | 𝒪(n(d−1)/2) | |
| Result 7 | 𝒪(d) | 𝒪(n + d) [n + 1] | 𝒪(n(d−1)/2) | |
| Result 8 | 𝒪(1) | 𝒪(d log n) [2], 𝒪(nd log n) [d] | 𝒪(n(d−1)/2) |