Generators and Relations for Un(Z[1/2,i])
Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in the ring Z[1/2,i], the smallest subring of the complex numbers containing 1/2 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unita...
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| creator | Bian, Xiaoning Selinger, Peter |
| description | Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in the ring Z[1/2,i], the smallest subring of the complex numbers containing 1/2 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in Z[1/2,i] can be realized by a quantum circuit over the above gate set using at most one ancilla. In this paper, we give a finite presentation by generators and relations of U_n(Z[1/2,i]), the group of unitary nxn-matrices with entries in Z[1/2,i]. |
| doi_str_mv | 10.48550/arxiv.2105.14047 |
| format | Article |
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| subjects | Complex numbers Computer Science - Emerging Technologies Computer Science - Logic in Computer Science Gates (circuits) Generators Physics - Quantum Physics Quantum computing Rings (mathematics) |
| title | Generators and Relations for Un(Z[1/2,i]) |
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