Optimizing T and CNOT Gates in Quantum Ripple-Carry Adders and Comparators

• URL: http://arxiv.org/abs/2401.17921v3
• Date: Tue, 28 May 2024 08:02:17 GMT
• Title: Optimizing T and CNOT Gates in Quantum Ripple-Carry Adders and Comparators
• Authors: Maxime Remaud,
• Abstract summary: The ripple-carry strategy for the addition and comparison of two n-bit numbers is presented. In particular, we consider the adders presented by Cuccaro et al. and Takahashi et al.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The state of the art of quantum circuits using the ripple-carry strategy for the addition and comparison of two n-bit numbers is presented, as well as optimizations in the Clifford+T gate set, both in terms of CNOT-depth and T-depth, or CNOT-count and T-count. In particular, we consider the adders presented by Cuccaro et al. and Takahashi et al., and exhibit an adder with a T-depth of 3n and a CNOT-depth of 8n, while without optimization of the original circuits, a T-depth of 6n is expected. Note that we have focused here on quantum ripple-carry adders using at most one ancilla, without any approximation of the 3-qubit gates involved (Toffoli, Peres and TR) or any strategy involving a measurement.

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