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Journal of Optoelectronics·laser

Quantum Binary Searching Algorithm and Circuit Implementation

Daoyi Dong

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Considering the essential difference between quantum bit and classical bit,this paper proposes a quantum binary searching algorithm.Using the quantum parallel process and quantum permutation operations,the circuit implementation of quantum binary searching algorithm is presented.The example shows that the algorithm can greatly reduce the implementation time and steps compared with classical binary search algorithm.This scheme has important applicable potential in quantum information processing within decoherence time.

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Applied Sciences•Oct 27, 2022•6 citations
Considering the essential difference between quantum bit and classical bit,this paper proposes a quantum binary searching algorithm.Using the quantum parallel process and quantum permutation operations,the circuit implementation of quantum binary searching algorithm is presented.The example shows that the algorithm can greatly reduce the implementation time and steps compared with classical binary search algorithm.This scheme has important applicable potential in quantum information processing within decoherence time.
A quantum algorithm provides for the encoding of an exponentially large number of classical data bits by use of a smaller (polynomially large) number of quantum bits (qubits). The development of this algorithm was prompted by the need, heretofore not satisfied, for a means of entering real-world binary data into a quantum computer. The data format provided by this algorithm is suitable for subsequent ultrafast quantum processing of the entered data. Potential applications lie in disciplines (e.g., genomics) in which one needs to search for matches between parts of very long sequences of data. For example, the algorithm could be used to encode the N-bit-long human genome in only log2N qubits. The resulting log2N-qubit state could then be used for subsequent quantum data processing - for example, to perform rapid comparisons of sequences.
Abstract In the coding theory, it is one of the most important research problems to find an efficient algorithm for the decoding process. A quantum computer is an innovative computing device that performs calculations using the principles of quantum mechanics. In this paper, we find a decoding algorithm for binary linear codes using quantum circuits; this is the first time that quantum circuits are used as a main tool for decoding binary linear codes. Our decoding algorithm is mainly based on Grover’s search algorithm. In detail, we study the process of implementing the exhaustive search using quantum circuits for decoding binary linear codes. For our purpose, we design a modified Grover’s algorithm (algorithm 1) using three tools: the matrix multiplier, the Hamming weight counter, and the state indicator. We present algorithm 2, which is a quantum decoding algorithm for binary linear codes. We illustrate algorithm 1 using the [7, 4, 3] Hamming code, and algorithm 2 is implemented by IBM Quantum Composer.
Pattern matching with swaps is a well-known non-standard variant of the string matching problem in which adjacent characters of the pattern may be swapped, under the constraint that each character participates in at most one swap. This problem has received considerable attention in the stringology literature due to its applications in areas such as computational biology, error-tolerant text processing, and pattern discovery. In this paper we investigate the problem in the quantum computing model. Building upon the recently introduced framework of quantum bit-parallelism, which provides a systematic way to translate classical bit-parallel string matching algorithms into quantum circuits, we develop the first quantum algorithm for swap matching based on this paradigm. Our approach adapts the classical cross-sampling technique for swap matching into a reversible quantum procedure that simulates the evolution of two interacting automata configurations using quantum registers and bitwise quantum operations. While the resulting quantum circuit preserves the near-linear behavior of its classical counterpart in terms of circuit depth, its integration with Grover’s search enables a quadratic speedup. By embedding the verification procedure within a quantum search framework and carefully controlling the size of the search space, we obtain a quantum algorithm that solves the swap matching problem in O~(n)\tilde{O}(\sqrt {n})O~(n​) time. This result extends the applicability of quantum bit-parallelism to non-standard string matching problems and provides further evidence that a broad class of classical text searching techniques can be systematically lifted to the quantum setting while preserving their structural efficiency.
The quantum computer has attracted much attention since it can reduce running time of many tasks such as factorization and search compared to classical computers. However, the actual quantum computer is difficult to get access, and the classical computer has a problem of calculation time and computation cost grows exponentially with increasing the number of qubits. In this paper, we address an efficient quantum circuit simulator including quantum circuit emulation hardware and its software framework using classical bit. Also, the proposed quantum circuit simulator operates the same as the conventional quantum software framework and shows a fast operation speed.
Quantum search algorithm, which can search an unsorted database quadratically faster than any known classical algorithms, has become one of the most impressive showcases of quantum computation. It has been implemented using various quantum schemes. Here, we demonstrate both theoretically and experimentally that such a fast search algorithm can also be realized using classical electric circuits. The classical circuit networks to perform such a fast search have been designed. It has been shown that the evolution of electric signals in the circuit networks is analogies of quantum particles randomly walking on graphs described by quantum theory. The searching efficiencies in our designed classical circuits are the same to the quantum schemes. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.
Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To conduct Grover’s search algorithm, the target cipher algorithm should be efficiently implemented in a quantum circuit. Currently, small quantum computers are difficult to operate with large quantum circuits due to limited performance. Therefore, if a large quantum computer that can operate Grover’s algorithm appears, it is expected that a cipher attack will be possible. In this paper, we propose a parallel structure quantum circuit for the Korean hash function standard (i.e., LSH). The proposed quantum circuit designed a parallel operation structure for the message expansion (i.e., MsgExp) function and the mix function, which are the internal structures of the LSH hash function. This approach shows an efficient result for quantum circuit implementation in terms of quantum resources by reducing the depth of the quantum circuit by about 96% through the trade-off of appropriate quantum resources compared to previous work. This result can be a reference for the implementation of a parallel quantum circuit in the future and is expected to advance the attack timing of the search algorithm for Grover’s LSH hash function.