Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings
| Autor: | Smith, Isaac D., Cautrès, Maxime, Stephen, David T., Nautrup, Hendrik Poulsen |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 6+12 pages, comments welcome! v2: addition example, minor edits throughout |
| Databáze: | arXiv |
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