Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings

• URL: http://arxiv.org/abs/2408.03294v2
• Date: Wed, 28 Aug 2024 10:13:26 GMT
• Title: Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings
• Authors: Isaac D. Smith, Maxime Cautrès, David T. Stephen, Hendrik Poulsen Nautrup,
• Abstract summary: We show that the minimal such set generating $mathfraksu (2N)$ contains $2N+1$ elements. We also provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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