Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

José E. Cruz Serrallés, Oluwadara Ogunkoya, Doğa Murat Kürkçüoğlu, Nicholas Bornman, Norm M. Tubman, Anna Grassellino, Silvia Zorzetti, Riccardo Lattanzi · 2025 · arXiv quant-ph

| 编号 QNF004 | 主题 数值格式 | 链接 arXiv:2510.20145 |

摘要

摘要保留原文（英文）

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We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two’s Complement fixed-point mantissas and Two’s Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

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