The quantum computing is a giant leap forward in comparison with our common computer models as it allows us to solve some problems with a much smaller number of steps. In this paper, we will demonstrate the design, development, and testing of the DeutschJozsa quantum algorithm using Qiskit. The algorithm can determine whether a Boolean function is identical or evenly divides with a single special query where traditional algorithms may require as many as 2n -1 +1 checks in the worst-case. We simulated the algorithm on an ideal simulator (Qiskit Aer) and IBM Quantum real hardware. Three aspects that we examined were the measurement accuracy, the depth of the quantum circuit, and how the noise of the real world, including decoherence and gate errors as well as readout errors, would influence the outcome of the NISQ devices. The simulator has nearly excellent precision, whereas the actual hardware has some visible disparities due to noise. These findings verify a undeniable quantum efficiency in query complexity and the cost decreases to a constant cost of O(1) quantum versus an exponential cost of O(2n) using a classical computer. Altogether, this paper is an example of quantum parallelism and quantum interference in a practical sense and serves as a good reference point to the capabilities of the current quantum hardware.
The quantum computing is a giant leap forward in comparison with our common computer models as it allows us to solve some problems with a much smaller number of steps. In this paper, we will demonstrate the design, development, and testing of the DeutschJozsa quantum algorithm using Qiskit. The algorithm can determine whether a Boolean function is identical or evenly divides with a single special query where traditional algorithms may require as many as 2n -1 +1 checks in the worst-case. We simulated the algorithm on an ideal simulator (Qiskit Aer) and IBM Quantum real hardware. Three aspects that we examined were the measurement accuracy, the depth of the quantum circuit, and how the noise of the real world, including decoherence and gate errors as well as readout errors, would influence the outcome of the NISQ devices. The simulator has nearly excellent precision, whereas the actual hardware has some visible disparities due to noise. These findings verify a undeniable quantum efficiency in query complexity and the cost decreases to a constant cost of O(1) quantum versus an exponential cost of O(2n) using a classical computer. Altogether, this paper is an example of quantum parallelism and quantum interference in a practical sense and serves as a good reference point to the capabilities of the current quantum hardware.
Abstract This laboratory work presents a practical implementation of the Deutsch–Jozsa algorithm using the Qiskit framework, complemented by the application of artificial intelligence tools such as GPT-based systems to assist in circuit design, debugging, and conceptual analysis. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to bridge theoretical quantum algorithms with executable quantum programs. In Laboratory Work No. 6, participants construct the Deutsch–Jozsa algorithm for n=4n = 4n=4 input qubits within an oracle-based computational model. The circuit includes a quantum register qqq representing the oracle input qubits, an output qubit outoutout, and a classical register ccc for measurement results. The algorithm begins by applying Hadamard (H) gates to all oracle qubits to create a uniform superposition over the input space. The output qubit is prepared using Pauli-X (X) and Hadamard (H) gates to establish the appropriate phase kickback configuration. A visual barrier is introduced in the circuit to clearly separate initialization, oracle evaluation, and interference stages. After the oracle operation, a second layer of Hadamard gates is applied to the input qubits, followed by measurement into classical bits. The resulting measurement pattern allows deterministic distinction between constant and balanced Boolean functions with a single oracle query—demonstrating exponential speedup compared to classical deterministic algorithms. The laboratory exercise emphasizes structured circuit design, oracle modeling, phase interference analysis, and measurement interpretation. Additionally, GPT-based AI tools are used to support code generation, algorithm explanation, and optimization, illustrating how modern artificial intelligence systems can enhance quantum programming workflows. Through simulation and execution on cloud-based quantum hardware, participants gain both theoretical insight and practical experience with one of the foundational quantum algorithms and its implementation in contemporary quantum computing ecosystems.
This paper introduces a comprehensive quantum calculator using Qiskit that integrates quantum arithmetic and logic functions into a single calculator. The calculator relies on quantum Fourier transforms (QFT), controlled-phase gates, and quantum modular arithmetic to perform basic arithmetic operations such as addition, subtraction, and multiplication. These arithmetic techniques used quantum parallelism and interference to perform calculations more efficiently, particularly for tasks involving large numerical inputs. Numerical values are stored in qubit registers and processed using QFT-based circuits, which enable efficient and reversible mathematical computations. In addition to arithmetic operations, the calculator also implements quantum logic algorithms, including Grover’s Search and the Deutsch-Jozsa algorithm. Grover’s algorithm is an unstructured search algorithm that operates by constructing an oracle and iteratively amplifying the probability amplitude of the target solution. This amplitude amplification significantly increases the likelihood of measuring the desired outcome. Due to this property, Grover’s algorithm has practical relevance in applications such as database searching and solving combinatorial optimization problems. The Deutsch-Jozsa algorithm determines whether or not a certain Boolean function is constant or balanced and offers an exponential speed up compared to classical methods for this class of problem. A key fundamental function of the calculator is the ability to generate hybrid quantum circuits that support both arithmetic and logical functions. That allows the exploration of simple as well as complex problem-solving strategies that take advantage of both quantum arithmetic and decision-making algorithms. For instance, combining Grover’s amplification with function characterizations from the Deutsch-Jozsa algorithm provides not only interesting circuit configurations but also adds value to the possibilities of the algorithms. This research offers a modular idea and allows exploring the fundamental principles of quantum computing generally speaking and will be a valuable resource for educational as well as research purposes in the rapidly growing field of quantum algorithm development.
Abstract This practical guide explores the use of IBM Quantum cloud simulators for modeling and analyzing quantum circuits under realistic conditions. Using the IBM Q platform and Qiskit Runtime, the work demonstrates how to configure the ibmq_qasm_simulator and map a basic noise model derived from a physical IBM Quantum™ device. The guide focuses on: Setting up the ibmq_qasm_simulator in Qiskit. Extracting and applying a hardware-based noise model from a real IBM Quantum backend. Performing noisy simulations of QuantumCircuits. Using Sampler and Estimator primitives in Qiskit Runtime to analyze circuit outputs. Studying the impact of realistic quantum errors such as decoherence, gate infidelity, and readout noise. By incorporating noise models into simulations, researchers and developers can better understand how quantum circuits behave on real hardware, optimize algorithms before deployment, and design more robust quantum programs. This approach bridges the gap between idealized simulations and physical quantum devices, making it a critical step toward practical quantum application development.
This study examines how noise affects the reliability of quantum circuits through two complementary approaches: a controlled simulation using Qiskit Aer and an execution study on real IBM Quantum hardware. In simulation, five noise models (bit-flip, phase-flip, depolarizing, readout, and thermal-relaxation) were applied to a parameterized benchmark circuit across varying qubit counts, circuit depths, and noise strengths, producing 6,000 experimental observations. Success probability declined substantially as qubit count and circuit depth increased, with bit-flip, phase-flip, and depolarizing noise degrading performance far more severely (mean success probabilities of 0.597, 0.580, and 0.607) than readout noise (0.917) or thermal-relaxation noise (0.982). The same benchmark circuit was then executed on the ibm_marrakesh processor across 150 hardware runs (150,000 shots). Hardware performance remained consistently high (mean success probability 0.992), declining with qubit count (0.998 at two qubits to 0.986 at six) but showing little sensitivity to circuit depth. These results indicate that controlled noise mechanisms and real hardware degrade circuit performance through different dynamics, with implications for interpreting simulated noise models relative to physical device behavior.
This paper represents an accessible overview of quantum program development with IBM's Qiskit. Current quantum computers are still making a lot of mistakes since we are in the NISQ era, where noise is the main problem. Qiskit developers are assisted by means of which they can readily plan their circuits and then the versions which are to be run on the actual hardware are automatically created by the Transpiler. Simulation of the circuit along with the check of how the noise can change the result is done by Qiskit Aer before the program is sent to the real quantum computer. As noise is the cause of the major problem, there is also the provision of error-reduction methods like Readout Error Mitigation and Zero Noise Extrapolation (ZNE) in Qiskit to eliminate the noise. Hybrid algorithms such as VQE and QAOA are increasingly becoming instrumental in solving real problems in chemistry, finance, and machine learning, the paper says, too. The study sums up that Qiskit has become the most popular open-source platform that is leading the way to the next quantum computing era and making the quantum advantage feasible
This study explores how well Grover's Algorithm performs in solving the Boolean Satisfiability Problem (SAT) using quantum circuits. The algorithm is implemented with IBM's Qiskit framework and compared to classical brute-force methods. Experiments focus on 3-SAT, 4-SAT, and 5-SAT problems, using quantum simulators and IBM quantum hardware. The results show that Grover's Algorithm is more efficient, offering a theoretical quadratic speedup over classical methods. However, practical issues like limited qubit availability, hardware noise, and optimization challenges impact its current performance. The data highlights the potential for quantum computing to scale and solve NP-complete problems. This research shows how quantum computing can improve problem-solving and lays the groundwork for future studies on more complex SAT problems and advanced quantum hardware.