An Improved QFT-Based Quantum Comparator and Extended Modular Arithmetic Using One Ancilla Qubit

• URL: http://arxiv.org/abs/2305.09106v1
• Date: Tue, 16 May 2023 02:09:41 GMT
• Title: An Improved QFT-Based Quantum Comparator and Extended Modular Arithmetic Using One Ancilla Qubit
• Authors: Yewei Yuan, Chao Wang, Bei Wang, Zhao-Yun Chen, Meng-Han Dou, Yu-Chun Wu, and Guo-Ping Guo
• Abstract summary: We propose a quantum-classical comparator based on the quantum Fourier transform (QFT) Proposed operators only require one ancilla qubit, which is optimal for qubit resources. The proposed algorithms reduce computing resources and make them valuable for Noisy Intermediate-Scale Quantum (NISQ) computers.
• Score: 4.314578336989336
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization, option pricing, and risk analysis, commonly require one of the inputs to be classical. It requires many ancillary qubits, especially when subsequent computations are involved. In this paper, we propose a quantum-classical comparator based on the quantum Fourier transform (QFT). Then we extend it to compare two quantum integers and modular arithmetic. Proposed operators only require one ancilla qubit, which is optimal for qubit resources. We analyze limitations in the current modular addition circuit and develop it to process arbitrary quantum states in the entire $n$-qubit space. The proposed algorithms reduce computing resources and make them valuable for Noisy Intermediate-Scale Quantum (NISQ) computers.

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