Matrix manipulations via unitary transformations and ancilla-state measurements

• URL: http://arxiv.org/abs/2311.11329v1
• Date: Sun, 19 Nov 2023 14:06:25 GMT
• Title: Matrix manipulations via unitary transformations and ancilla-state measurements
• Authors: Alexander I. Zenchuk, Wentao Qi, Asutosh Kumar, Junde Wu
• Abstract summary: We propose protocols for calculating inner product, matrix addition and matrix multiplication based on multiqubit Toffoli-type and the simplest one-qubit operations. The depth (runtime) of the addition protocol is $O(1)$ and that of other protocols logarithmically increases with the dimensionality of the considered matrices.
• Score: 49.494595696663524
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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