Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917036012077056 |
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| author | Serrallés, José E. Cruz Ogunkoya, Oluwadara Kürkçüo{g}lu, Do{g}a Murat Bornman, Nicholas Tubman, Norm M. Grassellino, Anna Zorzetti, Silvia Lattanzi, Riccardo |
| author_facet | Serrallés, José E. Cruz Ogunkoya, Oluwadara Kürkçüo{g}lu, Do{g}a Murat Bornman, Nicholas Tubman, Norm M. Grassellino, Anna Zorzetti, Silvia Lattanzi, Riccardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers Serrallés, José E. Cruz Ogunkoya, Oluwadara Kürkçüo{g}lu, Do{g}a Murat Bornman, Nicholas Tubman, Norm M. Grassellino, Anna Zorzetti, Silvia Lattanzi, Riccardo Quantum Physics 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. |
| title | Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.20145 |