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T-count and T-depth efficient fault-tolerant quantum arithmetic and logic unit

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Abstract

Quantum circuits are one of the best platforms to implement quantum algorithms. Concerning fault-tolerant quantum circuit, the Clifford + T gate set supports quantum circuits against decoherence error. However, they cause physical resource overheads like many qubits and the use of T gates as a high-cost computing element. This work focuses on low T-cost fault tolerant quantum ALU implementation using Clifford + T gate set. Three new different designs of quantum ALU are proposed by introducing a new quantum logic unit, and new low-cost fault tolerant implementations of full adder and subtractor circuits. We present a novel lemma in synthesizing quantum NCV-based circuits to Clifford + T quantum circuits. This lemma shows how an NCV-based structure with less CNOT layer can lead to an improvement in T-count and T-depth criteria in Clifford + T equivalent circuit. We analyze the effect of applying our proposed lemma in implementing low-cost fault tolerant Clifford + T circuits by some examples on adder and subtractors and ALUs. Comparison of the designs shows 50%, 40%, 36%, and 69% superior functionality of our proposed ALU module in terms of T-count, T-depth, number of qubits, and number of calculated operations compared to the existing counterpart, respectively. The proposed lemma can be used as a simplification step in quantum circuit synthesis algorithms and can be extended to use in quantum synthesis tools.

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  1. Mohammad Reza Reshadinezhad and Shekoofeh Moghimi have contributed equally.

Authors and Affiliations

  1. Faculty of Computer Engineering, University of Isfahan, Isfahan, Iran

    Sarallah Keshavarz, Mohammad Reza Reshadinezhad & Shekoofeh Moghimi

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  1. Sarallah Keshavarz
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Contributions

SK and SM made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work. SK, MRR, and SM involved in drafting the work or revising it critically for important intellectual content. MRR gave final approval of the version to be published. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved by SK, MRR, and SM.

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Correspondence to Mohammad Reza Reshadinezhad.

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Keshavarz, S., Reshadinezhad, M.R. & Moghimi, S. T-count and T-depth efficient fault-tolerant quantum arithmetic and logic unit. Quantum Inf Process 23, 245 (2024). https://doi.org/10.1007/s11128-024-04456-0

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