Optimally generating \mathfraksu(2^N) using Pauli strings

2024/08/06 by Isaac D. Smith, Maxime Cautrès, Smith, Isaac D. +5
Computer Science · #Coding theory and cryptography #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.2408.03294

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 \mathfraksu(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 \mathfraksu(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.

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