Quantum mechanics: Searching for the master bit

Wenhao He, Zhenduo Wang, Biao Wu

A theoretical model of computation is proposed based on Lorentz quantum mechanics. Besides the standard qubits, this model has an additional bit, which we call hyperbolic bit (or hybit in short). A set of basic logical gates are constructed and their universality is proved. As an application, a search algorithm is designed for this computer model and is found to be exponentially faster than Grover’s search algorithm.

Zhou Lin

Grover′s quantum search algorithm utilizes the parallel properties of quantum mechanics,which has been studied and applied extensively because of its great search efficiency.The principle and performance of Grover′s quantum searching algorithm is researched,especially the quantum algorithm for finding the minimum of a database is deeply researched.Because the search number of the algorithm is high,an improved quantum algorithm which named double threshold for finding a maximum in a database is proposed.The conclusion that the search number of this algorithm is less than the original one through the simulation.The algorithm is applied in multi-user detection,experiment results show that the bit error rate performance of the algorithm is close to the optimal multi-user detection algorithm,and the complexity is less than the optimal one.

Ahmad A. Kamal

Bhupendra Singh, Mohankumar Mylsamy, Thamaraimanalan Thangarajan

“Grover's Algorithm: Quantum Search” explores Grover's Algorithm in the context of quantum search, beginning with an overview of its mechanics. The section includes a literature survey that covers Grover's algorithm, stream ciphers, and the Grover attack, as well as quantum resource estimation. The section then introduces a simplified 4-bit Grain cipher (with a 4-bit key and 4-bit IV), detailing its design, initialization, and key stream generation. Following this, the chapter discusses about key recovery using Grover's algorithm, with an emphasis on quantum circuit development for the simplified Grain 4-bit cipher. It outlines key steps in the circuit, such as executing the Boolean function and XORing the NFSR's fourth bit. Further, the section details the development of a Grover attack quantum circuit, describing both single and double pair methods. Experimental results are provided across multiple cases, with a summary of test cases and classical computation times. Quantum resource estimation, including the costs associated with the simplified Grain 4-bit cipher and the Grover oracle, is analyzed. The section concludes with a discussion on the results, classical and quantum resource estimations, and the potential for future enhancements to the approach.