Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

• URL: http://arxiv.org/abs/2510.20145v1
• Date: Thu, 23 Oct 2025 02:45:41 GMT
• Title: Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers
• Authors: José E. Cruz Serrallés, Oluwadara Ogunkoya, Do{g}a Murat Kürkçüo{g}lu, Nicholas Bornman, Norm M. Tubman, Anna Grassellino, Silvia Zorzetti, Riccardo Lattanzi,
• Abstract summary: We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents.<n>We develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition.
• Score: 0.07026564887314536
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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