Generators and Relations for Un(Z[1/2,i])
نویسندگان
چکیده
Consider the universal gate set for quantum computing consisting of gates X, CX, CCX, omega^dagger H, and S. All these have matrix entries in ring Z[1/2,i], smallest subring complex numbers containing 1/2 i. Amy, Glaudell, Ross proved converse, i.e., any unitary with Z[1/2,i] can be realized by a circuit over above using at most one ancilla. In this paper, we give finite presentation generators relations U_n(Z[1/2,i]), group nxn-matrices Z[1/2,i].
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ژورنال
عنوان ژورنال: Electronic proceedings in theoretical computer science
سال: 2021
ISSN: ['2075-2180']
DOI: https://doi.org/10.4204/eptcs.343.8