Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

Journal Article · Thu Oct 23 04:00:00 EDT 2025 · No journal information

OSTI ID:3000297

Serrallés, José Cruz ^[1]; Ogunkoya, Oluwadara ^[2]; Kürkçüo{g}lu, Do{g}a Murat; Bornman, Nicholas ^[2]; Tubman, Norm M. ^[3]; Grassellino, Anna ^[3]; Zorzetti, Silvia ^[2]; Lattanzi, Riccardo ^[1]

---

1. Weill Cornell Med. Coll.
2. Fermilab
3. Fermilab; NASA, Ames

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.

• Research Organization: NASA, Ames; Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Weill Cornell Med. Coll.
• Sponsoring Organization: US Department of Energy
• DOE Contract Number: 89243024CSC000002
• OSTI ID: 3000297
• Report Number(s): FERMILAB-PUB-25-0270-SQMS; oai:inspirehep.net:3072660; arXiv:2510.20145
• Journal Information: No journal information, Journal Name: No journal information
• Country of Publication: United States
• Language: English