Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915356891676672 |
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| author | Smith, Isaac D. Cautrès, Maxime Stephen, David T. Nautrup, Hendrik Poulsen |
| author_facet | Smith, Isaac D. Cautrès, Maxime Stephen, David T. Nautrup, Hendrik Poulsen |
| contents | Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating $\mathfrak{su}(2^{N})$ contains $2N+1$ elements. We provide a number of examples of such generating sets and furthermore provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation, which is shown to have optimal complexity. We also observe that certain sets generate $\mathfrak{su}(2^{N})$ at a faster rate than others, and we show how this rate can be optimized by tuning the fraction of anticommuting pairs of generators. Finally, we briefly comment on implications for measurement-based and trapped ion quantum computation as well as the construction of fault-tolerant gate sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings Smith, Isaac D. Cautrès, Maxime Stephen, David T. Nautrup, Hendrik Poulsen Quantum Physics Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating $\mathfrak{su}(2^{N})$ contains $2N+1$ elements. We provide a number of examples of such generating sets and furthermore provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation, which is shown to have optimal complexity. We also observe that certain sets generate $\mathfrak{su}(2^{N})$ at a faster rate than others, and we show how this rate can be optimized by tuning the fraction of anticommuting pairs of generators. Finally, we briefly comment on implications for measurement-based and trapped ion quantum computation as well as the construction of fault-tolerant gate sets. |
| title | Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.03294 |