Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916411272593408 |
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| author | Mao, Rui Tian, Guojing Sun, Xiaoming |
| author_facet | Mao, Rui Tian, Guojing Sun, Xiaoming |
| contents | In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ansätze and relaxed Trotterized UCC ansätze, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ansätze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs' ability to surpass classical methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08105 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms Mao, Rui Tian, Guojing Sun, Xiaoming Quantum Physics In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ansätze and relaxed Trotterized UCC ansätze, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ansätze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs' ability to surpass classical methods. |
| title | Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.08105 |