Quantum Most-Significant Digit-First Addition

In recent years, quantum computers have attracted extensive research interests due to their potential capability of solving problems which are not easily solvable using classical computers. In parallel to the constant research aiming at the physical implementation of quantum processors, there is another branch of research developing quantum algorithms for real-life applications, many of which need to perform arithmetic operations. As one of the most important operations, quantum addition has been adopted in Shor's algorithm, quantum linear algebra algorithms and various quantum machine learning applications. Since precision is always a non-trivial issue to determine during the computation, most-significant digit-first quantum addition can be a fundamental operation for variable precision computing. Therefore, this paper proposes the first quantum adder circuit that is able to compute from the most-significant digits, which demonstrates the advantages over the state-of-the-art quantum adders requiring carry propagation to produce results from least-significant digits. We first present a review of quantum addition circuits design, and then propose a novel method to implement quantum most-significant digit-first adders. Scalability and quantitative comparisons for different quantum full adder, quantum carry-ripple adder and quantum most-significant digit-first adder circuits have been investigated, where all circuits are implemented on IBM Qiskit SDK.