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<p>Quantum computing (QCG) is advancing toward higher-dimensional systems that offer greater efficiency and scalability, moving beyond traditional binary qubit-based architectures. This work presents a novel quaternary (radix-4) quantum full adder (QFA) based on native qudit logic, implemented within the QuTiP framework. The design employs three modular permutation-based gates: SUM1(A, B), SUM2(B, Cin), and Carry-out (A, B, Cin), each realized as a unitary operation on a three-qudit system. The proposed circuit achieves a quantum cost (QC) of only three, representing minimal logic depth when executed on a native qudit processor. In a qubit-equivalent cost model, where each qudit gate is approximately equivalent to three Toffoli gates, the corresponding QC is approximately 9. This is lower than that of standard binary full adders, which typically require 10 to 15 gates under the same model. Building on this efficient adder, we present the first complete implementations of qudit-based quantum multipliers in radix-4, using Wallace, Dadda, and Array architectures. Full simulations were performed using standard benchmarks. Among the three, the Qudit Wallace Multiplier delivers the best performance, achieving a gate count of 38, a quantum cost of 148, and 44 garbage outputs. The array multiplier is more resource-intensive, with a QC of 256 and 80 garbage outputs, while the Dadda variant offers a balanced trade-off, with a QC of 184. All architectures produce fully accurate results. Error detection via a Z-type stabilizer demonstrates the feasibility of fault-aware operation in these systems. The proposed architectures are compatible with emerging multi-level control platforms, including quantum-dot devices, photonic systems, superconducting circuits, and trapped ions. These findings establish qudit-based arithmetic as a practical and effective strategy for scalable quantum processors and advanced Very Large-Scale Integration (VLSI) systems. By leveraging higher-dimensional qudit states, this approach enhances energy efficiency through reduced circuit depth and lower resource requirements.</p>

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Design and analysis of qudit-based quantum arithmetic units: a resource-efficient approach using radix-4 full adders

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Yogeswari Palanisamy,
  • Kathirvelu Murugan,
  • Suresh Muthusamy,
  • Arulmurugan Azhaganantham

摘要

Quantum computing (QCG) is advancing toward higher-dimensional systems that offer greater efficiency and scalability, moving beyond traditional binary qubit-based architectures. This work presents a novel quaternary (radix-4) quantum full adder (QFA) based on native qudit logic, implemented within the QuTiP framework. The design employs three modular permutation-based gates: SUM1(A, B), SUM2(B, Cin), and Carry-out (A, B, Cin), each realized as a unitary operation on a three-qudit system. The proposed circuit achieves a quantum cost (QC) of only three, representing minimal logic depth when executed on a native qudit processor. In a qubit-equivalent cost model, where each qudit gate is approximately equivalent to three Toffoli gates, the corresponding QC is approximately 9. This is lower than that of standard binary full adders, which typically require 10 to 15 gates under the same model. Building on this efficient adder, we present the first complete implementations of qudit-based quantum multipliers in radix-4, using Wallace, Dadda, and Array architectures. Full simulations were performed using standard benchmarks. Among the three, the Qudit Wallace Multiplier delivers the best performance, achieving a gate count of 38, a quantum cost of 148, and 44 garbage outputs. The array multiplier is more resource-intensive, with a QC of 256 and 80 garbage outputs, while the Dadda variant offers a balanced trade-off, with a QC of 184. All architectures produce fully accurate results. Error detection via a Z-type stabilizer demonstrates the feasibility of fault-aware operation in these systems. The proposed architectures are compatible with emerging multi-level control platforms, including quantum-dot devices, photonic systems, superconducting circuits, and trapped ions. These findings establish qudit-based arithmetic as a practical and effective strategy for scalable quantum processors and advanced Very Large-Scale Integration (VLSI) systems. By leveraging higher-dimensional qudit states, this approach enhances energy efficiency through reduced circuit depth and lower resource requirements.