The 3-transposition groups that act on a vertex operator algebra in the way described by Miyamoto in [Mi1] are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form. This generalizes and refines the result of Kitazume and Miyamoto [KM]. Application to a similar but different situation is also considered in part by a slight generalization of the argument. √ 2R , where R is a root system. The structure of the Griess algebra of the latter VOA was described by Dong et al. [DLMN].

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This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset confirm the algorithms with more rules can find even better circuit mappings compared with the previously-known best algorithms.

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