Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

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