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Boosting the Efficiency of Quantum Divider through Effective Design Space Exploration

Siyi Wang, Eugene Lim, Anupam Chattopadhyay

TL;DR

This paper focuses on enhancing the performance of quantum slow dividers by exploring the design choices of its sub-blocks, such as, adders, and emphasizes the importance of adopting a systematic design space exploration approach.

Abstract

Rapid progress in the design of scalable, robust quantum computing necessitates efficient quantum circuit implementation for algorithms with practical relevance. For several algorithms, arithmetic kernels, in particular, division plays an important role. In this manuscript, we focus on enhancing the performance of quantum slow dividers by exploring the design choices of its sub-blocks, such as, adders. Through comprehensive design space exploration of state-of-the-art quantum addition building blocks, our work have resulted in an impressive achievement: a reduction in Toffoli Depth of up to 94.06%, accompanied by substantial reductions in both Toffoli and Qubit Count of up to 91.98% and 99.37%, respectively. This paper offers crucial perspectives on efficient design of quantum dividers, and emphasizes the importance of adopting a systematic design space exploration approach.

Boosting the Efficiency of Quantum Divider through Effective Design Space Exploration

TL;DR

This paper focuses on enhancing the performance of quantum slow dividers by exploring the design choices of its sub-blocks, such as, adders, and emphasizes the importance of adopting a systematic design space exploration approach.

Abstract

Rapid progress in the design of scalable, robust quantum computing necessitates efficient quantum circuit implementation for algorithms with practical relevance. For several algorithms, arithmetic kernels, in particular, division plays an important role. In this manuscript, we focus on enhancing the performance of quantum slow dividers by exploring the design choices of its sub-blocks, such as, adders. Through comprehensive design space exploration of state-of-the-art quantum addition building blocks, our work have resulted in an impressive achievement: a reduction in Toffoli Depth of up to 94.06%, accompanied by substantial reductions in both Toffoli and Qubit Count of up to 91.98% and 99.37%, respectively. This paper offers crucial perspectives on efficient design of quantum dividers, and emphasizes the importance of adopting a systematic design space exploration approach.
Paper Structure (8 sections, 3 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 8 sections, 3 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Quantum Non-restoring Division
  4. An Extension Design: Quantum Restoring Divider
  5. Results and Discussions
  6. Impact of Quantum Adders on Quantum Dividers
  7. Comparison with Existing Quantum Dividers
  8. Conclusion

Figures (3)

  • Figure 1: 3-qubits Quantum Non-restoring Divider.
  • Figure 2: The three essential sub-circuits in the proposed quantum divider.
  • Figure 3: The proposed quantum non-restoring dividers based on different adders. Here, $n$ denotes the qubit-width of the division. Given the identical performance in Toffoli Count between Gayathri RCA and Wang RCA, we use a simplified notation "Gayathri/Wang RCA" to represent their performance. The similar notations are also applied for "Takahashi/Cuccaro RCA" and "Takahashi Low-ancilla /Combination".