Symmetrizing Arithmetic Quantum Computations

This talk begins with an introduction of theoretical and practical notions of quantum computation. Based on their arithmetic realization, we then present a classification of quantum computations and outline how such a partitioning influences algorithmic precision. In contrast with this fault-tolerant and algorithm-error-centric perspective, we examine recent experiments through our arithmetic classification lens. To conclude we introduce a new quantum arithmetic form which combines both arithmetic compositions to further respect symmetries such as (algebraic sub-lattice) inversion and time-reversal.