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<p>Motivated by recent advances in the single-step implementation of <i>n</i>-control-qubit Toffoli gates, we propose a broad class of generalized Toffoli gates with multiple control qubits that can be executed in a single step using a feasible and unified framework based on Ising-type interactions. Unlike the standard Toffoli gate condition, which flips the target qubit only when all control qubits are in the <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(|1\rangle\)</EquationSource><EquationSource Format="MATHML"><math display="inline"><mrow><mo>|</mo></mrow><mn>1</mn><mo>〉</mo></math></EquationSource></InlineEquation> state, our generalized gates allow for diverse, customizable control conditions, including: mixed control, Hamming weight control, weighted Hamming control, multiple-designated configurations, threshold control, multiple-target control, and multiple-option control. Simulation results demonstrate that these gates offer substantial advantages in both feasibility and reliability over decompositions into standard 2-control-qubit Toffoli gates and other primitive gates, significantly reducing circuit depth, execution time, and error rates.</p>

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Generalized Toffoli gates with customizable single-step multiple-qubit control

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月15日

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  • Chung-Kai Wu,
  • Dah-Wei Chiou,
  • Jie-Hong Roland Jiang

摘要

Motivated by recent advances in the single-step implementation of n-control-qubit Toffoli gates, we propose a broad class of generalized Toffoli gates with multiple control qubits that can be executed in a single step using a feasible and unified framework based on Ising-type interactions. Unlike the standard Toffoli gate condition, which flips the target qubit only when all control qubits are in the \(|1\rangle\)|1〉 state, our generalized gates allow for diverse, customizable control conditions, including: mixed control, Hamming weight control, weighted Hamming control, multiple-designated configurations, threshold control, multiple-target control, and multiple-option control. Simulation results demonstrate that these gates offer substantial advantages in both feasibility and reliability over decompositions into standard 2-control-qubit Toffoli gates and other primitive gates, significantly reducing circuit depth, execution time, and error rates.