Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

TL;DR

This paper introduces a new floating-point encoding scheme for quantum computers that improves efficiency and reduces ancilla qubit usage, enabling more accurate quantum arithmetic operations.

Contribution

It presents a novel floating-point encoding method based on fixed-point schemes and demonstrates its effectiveness through quantum algorithms and simulations.

Findings

Rapid convergence to exact solutions with more qubits

Significant reduction in ancilla qubits for reciprocation

Effective implementation of fundamental arithmetic operations

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.