| Item type |
SIG Technical Reports(1) |
| 公開日 |
2022-03-17 |
| タイトル |
|
|
タイトル |
Cost function gradient for general ansatz in variational quantum algorithm |
| タイトル |
|
|
言語 |
en |
|
タイトル |
Cost function gradient for general ansatz in variational quantum algorithm |
| 言語 |
|
|
言語 |
eng |
| 資源タイプ |
|
|
資源タイプ識別子 |
http://purl.org/coar/resource_type/c_18gh |
|
資源タイプ |
technical report |
| 著者所属 |
|
|
|
Department of Physics, The University of Tokyo |
| 著者所属 |
|
|
|
International Center for Elementary Particle Physics (ICEPP), The University of Tokyo |
| 著者所属(英) |
|
|
|
en |
|
|
Department of Physics, The University of Tokyo |
| 著者所属(英) |
|
|
|
en |
|
|
International Center for Elementary Particle Physics (ICEPP), The University of Tokyo |
| 著者名 |
Ryunosuke, Okubo
Lento, Nagano
|
| 著者名(英) |
Ryunosuke, Okubo
Lento, Nagano
|
| 論文抄録 |
|
|
内容記述タイプ |
Other |
|
内容記述 |
Variational quantum algorithms (VQAs) are expected to be promising strategies to achieve quantum advantages in the near future. However, gradients of some VQA cost functions vanish exponentially with the number of qubits, which requires exponentially large resources for optimizing them. This phenomenon is the so-called barren plateau problem and has been studied in previous works for certain types of ansatzes. We extend the previous works to a more general type of ansatz. Specifically, we calculate the second moment of a cost function gradient for a general ansatz, assuming that it is an unitary 2-design. We also evaluate the second moment without this assumption, which leads to a relation between a metric to quantify ansatz expressibilities and the second moment. This relation implies cost function landscapes for more expressive ansatzes become flatter. Our results hold independently of ansatz structures, so they are applicable to analysis of scalabilities of various VQAs. |
| 論文抄録(英) |
|
|
内容記述タイプ |
Other |
|
内容記述 |
Variational quantum algorithms (VQAs) are expected to be promising strategies to achieve quantum advantages in the near future. However, gradients of some VQA cost functions vanish exponentially with the number of qubits, which requires exponentially large resources for optimizing them. This phenomenon is the so-called barren plateau problem and has been studied in previous works for certain types of ansatzes. We extend the previous works to a more general type of ansatz. Specifically, we calculate the second moment of a cost function gradient for a general ansatz, assuming that it is an unitary 2-design. We also evaluate the second moment without this assumption, which leads to a relation between a metric to quantify ansatz expressibilities and the second moment. This relation implies cost function landscapes for more expressive ansatzes become flatter. Our results hold independently of ansatz structures, so they are applicable to analysis of scalabilities of various VQAs. |
| 書誌レコードID |
|
|
収録物識別子タイプ |
NCID |
|
収録物識別子 |
AA12894105 |
| 書誌情報 |
量子ソフトウェア（QS）
巻 2022-QS-5,
号 29,
p. 1-8,
発行日 2022-03-17
|
| ISSN |
|
|
収録物識別子タイプ |
ISSN |
|
収録物識別子 |
2435-6492 |
| Notice |
|
|
|
SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc. |
| 出版者 |
|
|
言語 |
ja |
|
出版者 |
情報処理学会 |
IPSJ-QS22005029.pdf (791.5 kB)
