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<p>Quantum computers hold the promise of revolutionizing computational paradigms that outperform the largest classical supercomputers. However, decoherence makes the qubit fragile and only permits ab initio calculations over a limited number of qubits. Recent breakthroughs in quantum error correction could pave the way for large-scale quantum computers in Noisy Intermediate Scale Quantum(NISQ) era and inspire a whole new generation of researchers to contribute to the field of quantum computing in the pursuit of quantum supremacy. Noisy near-term quantum computing systems require high-fidelity quantum error correction codes with fault-tolerant architectures at the logical level to explore quantum applications effectively. Furthermore, conventional logic cannot be used due to the limitations imposed by quantum mechanics, necessitating the translation of classical algorithms into quantum algorithms to achieve superior performance. In this work, a fault-tolerant quantum circuit is proposed that employs majority logic to implement a multiplier based on the Nikhilam algorithm. The proposed circuit features (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {O}(n)\)</EquationSource> </InlineEquation>) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T-depth\)</EquationSource> </InlineEquation> and zero garbage and outperforms the current state-of-the-art methods.</p>

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Fault-Tolerant Quantum Realization of Nikhilam Multiplier with Clifford+T-group

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Laxmidhar Biswal,
  • Anirban Bhattacharjee,
  • Chandan Bandyopadhyay,
  • Hafizur Rahaman

摘要

Quantum computers hold the promise of revolutionizing computational paradigms that outperform the largest classical supercomputers. However, decoherence makes the qubit fragile and only permits ab initio calculations over a limited number of qubits. Recent breakthroughs in quantum error correction could pave the way for large-scale quantum computers in Noisy Intermediate Scale Quantum(NISQ) era and inspire a whole new generation of researchers to contribute to the field of quantum computing in the pursuit of quantum supremacy. Noisy near-term quantum computing systems require high-fidelity quantum error correction codes with fault-tolerant architectures at the logical level to explore quantum applications effectively. Furthermore, conventional logic cannot be used due to the limitations imposed by quantum mechanics, necessitating the translation of classical algorithms into quantum algorithms to achieve superior performance. In this work, a fault-tolerant quantum circuit is proposed that employs majority logic to implement a multiplier based on the Nikhilam algorithm. The proposed circuit features ( \(\mathcal {O}(n)\) ) \(T-depth\) and zero garbage and outperforms the current state-of-the-art methods.