Quantum Multiplier Based on Exponent Adder

Quantum multiplication is a fundamental operation in quantum computing. Most existing quantum multipliers require $O(n)$ qubits to multiply two $n$-bit integer numbers, limiting their applicability to multiply large integer numbers using near-term quantum computers. This paper proposes a new approach, the Quantum Multiplier Based on Exponent Adder (QMbead), which addresses this issue by requiring only $log_2(n)$ qubits to multiply two $n$-bit integer numbers. QMbead uses a so-called exponent encoding to represent the two multiplicands as two superposition states, respectively, and then employs a quantum adder to obtain the sum of these two superposition states, and subsequently measures the outputs of the quantum adder to calculate the product of the multiplicands. The paper presents two types of quantum adders based on the quantum Fourier transform (QFT) for use in QMbead. The circuit depth of QMbead is determined by the chosen quantum adder, being $O(log_2^2 n)$ when using the two QFT-based adders. The multiplicand can be either an integer or a decimal number. QMbead has been implemented on quantum simulators to compute products with a bit length of up to 273 bits using only 17 qubits. This establishes QMbead as an efficient solution for multiplying large integer or decimal numbers with many bits.