Matrix manipulations via unitary transformations and ancilla-state measurements
Alexander Ivanovich Zenchuk, Wentao Qi, Asutosh Kumar, Junde Wu · Quantum Information and Computation · 2024
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 addition protocol is $O(1)$ and that of other protocols logarithmically increases with the dimensionality of the considered matrices.