This paper addresses the quantum minimum searching algorithm and provides simulation results using qiskit library by IBM Q. We propose a whole procedure to implement the quantum minimum searching algorithm with high accuracy and design a quantum circuit for 5-qubit searching. The circuit consists of several oracles(phase inverter) and Grover operators(amplifier) and a comparator. To implement 5-qubit searching, we suggest three things. Modifying the expected number of iterations described in Section II.C, applying the concept of QRAM as an interface between quantum data and classical data in Section II.D, and designing quantum comparator using constant adder by Thomas in 2017 in Section III.A.
This paper addresses the quantum minimum searching algorithm and provides simulation results using qiskit library by IBM Q. We propose a whole procedure to implement the quantum minimum searching algorithm with high accuracy and design a quantum circuit for 5-qubit searching. The circuit consists of several oracles(phase inverter) and Grover operators(amplifier) and a comparator. To implement 5-qubit searching, we suggest three things. Modifying the expected number of iterations described in Section II.C, applying the concept of QRAM as an interface between quantum data and classical data in Section II.D, and designing quantum comparator using constant adder by Thomas in 2017 in Section III.A.
Abstract This laboratory work presents a practical implementation of Grover’s search algorithm using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is intended to provide hands-on experience with amplitude amplification and oracle-based quantum search. In Laboratory Work No. 7, participants construct Grover’s algorithm step by step. The implementation begins with defining a function that initializes the quantum registers and prepares the initial stage of the circuit. The output qubit associated with the oracle is set to the state ∣1⟩|1\rangle∣1⟩ to enable phase inversion through the phase kickback mechanism. Hadamard gates are then applied to create a uniform superposition over the search space. The oracle is designed to mark the target state by applying a phase shift, effectively flipping the sign of the amplitude corresponding to the solution. This is followed by the diffusion operator (inversion about the mean), which amplifies the probability amplitude of the marked state. The Grover iteration—composed of the oracle and diffusion operator—is repeated an optimal number of times to maximize the probability of measuring the correct result. The laboratory exercise emphasizes the principles of quantum amplitude amplification, circuit modularization, oracle construction, and measurement-based verification. By executing the algorithm on simulators and cloud-accessible quantum hardware, participants observe the quadratic speedup of Grover’s algorithm compared to classical linear search methods. This practical guide bridges theoretical understanding of quantum search with executable quantum circuits, reinforcing the operational aspects of quantum algorithm design within modern quantum computing
Nowadays, quantum computing has emerged as a global technology trend, attracting active research worldwide. One of the most popular quantum algorithms is the quantum search algorithm, commonly known as Grover's algorithm, for unstructured search purposes. This paper presents the implementation of the algorithm with a search space of 3 to 10 qubits using the Python-based Qiskit tool developed by IBM. The implementation results on the IBM QSAM simulator and on the IBM Eagle r3 quantum hardware are analyzed and compared. This paper also provides results with circuits of varying iteration numbers. Finally, the paper discusses the advantages of this quantum search algorithm compared to traditional methods, and the obstacles towards realizing its hardware implementation.
Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential searching algorithm (QESA), which is based on Grover algorithm, is not a sure-success algorithm. Meanwhile, quantum circuits encounter the gate decomposition problem due to variation of the scale of data. In this paper, we propose an optimized quantum algorithm for searching maximum and minimum, based on DHA and the optimal quantum exact search algorithm. Furthermore, we provide the corresponding quantum circuits, together with three equivalent simplifications. In circumstances when we can exactly estimate the ratio of the number of solutions M and the searched space N, our method can improve the successful probability close to 100%. Furthermore, compared with DHA, our algorithm shows an advantage in complexity with large databases and in the gate complexity of constructing oracles. Experiments have been executed on an IBM superconducting processor with two qubits, and a practical problem of finding the minimum from Titanic passengers' age was numerically simulated. Both showed that our optimized maximum or minimum performs more efficiently compared with DHA. Our algorithm can serve as an important subroutine in various quantum algorithms which involves searching maximum or minimum.
Recent advancements in computing speed and capacity of Artificial Intelligence (AI) algorithms have reached a saturation level in performance due to the continuous application of Moore's law which resulted in the memory wall phenomenon. Quantum computing (QC), based on the principles of quantum mechanics which include superposition and entanglement, has the potential to contribute to the advancements of AI by providing exponential speedup. Quantum computers use quantum bits, also known as qubits, as the metric to demonstrate the power of quantum technology. Qubits, the fundamental unit of quantum information can exist in two states, 0 and 1, simultaneously, leveraging the principle of superposition. Quantum gates are the building blocks of quantum circuits, operating on qubits to transform one quantum state into another, and are comparative to classical logic gates. Designing and simulating quantum circuits can be completed using the Qiskit library design by IBM. Qiskit is a cloud-based, open access platform to real quantum computers with 5 to 16 qubits. This paper offers a straightforward tutorial on implementing one, two and three-qubit quantum gates, as well as designing quantum circuits using the Qiskit library, illustrated with an example of a quantum half adder implementation.
Quantum computing is a quickly growing field of research thanks to recent hardware advances. The quantum mechanical properties of quantum computers allow them to solve certain families of problems faster than classical computers. A quantum algorithm solving such a problem is Grover's algorithm, which finds an element in an unordered set faster than any classical search algorithm. In this paper an implementation of a 4-qubit Grover's algorithm for the IBM Q computer ibmqx5 is presented. Executing the implementation on an ibmqx5 simulator yield results in line with the theoretically optimal results. The accuracy of the ibmqx5 simulation results compared to the ibmqx5 execution results suggests that current hardware is not yet suitable,due to required complexity of the circuits for a 4-qubit Grover implementation.
This paper provides an introduction to a quantum search algorithm, known as Grover’s Algorithm, for unsorted search purposes. The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM. While providing detailed proof, the computational complexity of the algorithm is generalized to n qubits. The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared. Finally, the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto. Overall, the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.