Matrix manipulations via unitary transformations and ancilla-state measurements

Abstract

We propose protocols for calculating inner product, matrix addition and matrix multiplication based on multiqubit Toffoli-type and the simplest one-qubit operations and employ ancilla measurements to remove all garbage of calculations. The depth (runtime) of the addition protocol is $O(1)$ and that of other protocols logarithmically increases with the dimensionality of the considered matrices.

6 pages, 1 figure