The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917029628346368 |
|---|---|
| author | Costa, Pedro C. S. An, Dong Babbush, Ryan Berry, Dominic |
| author_facet | Costa, Pedro C. S. An, Dong Babbush, Ryan Berry, Dominic |
| contents | The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $κ$ and the allowable error $ε$ [PRX Quantum \textbf{3}, 040303 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,200 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is about an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver Costa, Pedro C. S. An, Dong Babbush, Ryan Berry, Dominic Quantum Physics The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $κ$ and the allowable error $ε$ [PRX Quantum \textbf{3}, 040303 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,200 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is about an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient. |
| title | The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.07690 |