The paper proposes a novel quantum adder design based on the Sklansky prefix tree structure, which is verified as the optimal depth structure among all quantum adders. The authors faced challenges in directly applying classical prefix tree adders in the quantum world due to the inability to copy qubits. To address this, they developed a quantum repeat gate that enables the efficient incorporation of different prefix tree structures, such as Sklansky, into quantum circuits.
The primary contribution is the development of an optimal-depth quantum adder that achieves a Toffoli-Depth of log(n) + O(1) for n-bit additions, marking a significant improvement over previous quantum carry-lookahead adders based on the Brent-Kung tree, which required a minimum of 2 log(n) + O(1) Toffoli-Depth. The authors conducted a thorough assessment involving Toffoli-Depth, Qubit Count, and Toffoli-Count, providing insights into the strengths and constraints of the quantum optimal-depth adder.
The paper also explores alternative designs, including an optimal Toffoli-Depth Ling adder and an optimal Toffoli-Depth modular adder, further enhancing the performance of quantum addition circuits.
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by Siyi Wang,Su... alle arxiv.org 05-07-2024
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