Quantum logic gates differ from classical logic gates as the former involves quantum operators. The conventional gates such as AND, OR, NOT etc., are generally classified as classical gates, however, some of the quantum gates are known as Pauli gates, Toffoli gates and Hadamard gates, respectively. Normally classical states only involve 0 and 1, whereas quantum states involve the superpositions of 0 and 1. Hence, underlying principles of algorithm implementation for classical logic gate and quantum logic gate are indeed different. In this paper, we introduce significant concepts of quantum computations, analyse the discrepancy between classical and quantum gates, compare quantum algorithms using Qiskit against equivalent classical algorithms and analyse their performance in terms of runtime.
Quantum logic gates differ from classical logic gates as the former involves quantum operators. The conventional gates such as AND, OR, NOT etc., are generally classified as classical gates, however, some of the quantum gates are known as Pauli gates, Toffoli gates and Hadamard gates, respectively. Normally classical states only involve 0 and 1, whereas quantum states involve the superpositions of 0 and 1. Hence, underlying principles of algorithm implementation for classical logic gate and quantum logic gate are indeed different. In this paper, we introduce significant concepts of quantum computations, analyse the discrepancy between classical and quantum gates, compare quantum algorithms using Qiskit against equivalent classical algorithms and analyse their performance in terms of runtime.
Quantum computing represents a paradigm shift in computation by leveraging the principles of quantum mechanics such as superposition, entanglement, and interference to perform operations beyond classical limitations. Unlike classical computing systems that rely on irreversible logic operations and suffer from energy dissipation due to information loss, quantum systems utilize reversible unitary transformations that preserve information and improve computational efficiency. This paper presents a comprehensive framework for the design, simulation, and validation of quantum gates and reversible arithmetic circuits, including half adders and half subtractors. The proposed approach systematically maps classical arithmetic logic into quantum circuits using fundamental quantum gates such as Pauli-X, Hadamard, Controlled-NOT (CNOT), and Toffoli gates. The circuits are implemented and simulated using the Qiskit Aer framework, enabling detailed analysis of quantum state evolution and measurement outputs. The results obtained from simulation include program-level outputs, state vector representations, measurement counts, and probability distributions, all of which demonstrate strong agreement with classical truth tables. The analysis confirms the correctness, reversibility, and scalability of the proposed designs. Furthermore, a comparative performance evaluation highlights the advantages of quantum computing over classical approaches in terms of parallelism and energy efficiency. The proposed framework establishes a robust foundation for future implementation of complex Boolean logic and arithmetic operations in quantum systems.
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.
Quantum computing is an emerging field that depends upon the basic properties of quantum physics and principles of classical systems. This leads a way to develop systems to solve complex problems that a classical system cannot do. In this article, we present simple methods to implement logic circuits using quantum gates. Logic gates and circuits are defined with quantum gates using Qiskit in Python. Later, they are verified with quantum circuits created by using IBM Quantum. Moreover, we propose a way of instantiating the basic logic circuits to design high-end logic expressions. As per our knowledge, the proposed simple approach may be helpful to solve the complex logical problems in near future.
The complexity of certain classical computer algorithms can be reduced by a quantum algorithm completing the same task. We examine the implementation of the Bernstein–Vazirani algorithm. It finds the hidden n-bit string s from the function fs(x)=sx that takes an n-bit input string x and outputs one bit, the dot product. This algorithm reduces the complexity from n queries for the best classical algorithm to just one. Though the quantum algorithm theoretically always gives the correct string, in practice, factors such as decoherence of the physical qubits due to external noise reduce the algorithm’s accuracy. By implementing the algorithm on the IBM 5-qubit and 14-qubit quantum computers, we are able to analyze correlations between the accuracy of the results and the properties of the physical qubits used. Not all qubits are pairwise connected, nor do they have the same coherence times. Using Python to build the quantum circuits, we create several implementations of the circuit with different qubits. We establish that 1/T1, 1/T2, and gate errors are positively correlated with calculation errors. Consequently, we observe that the 14-qubit quantum computer, on average, is more prone to errors than the 5-qubit quantum computer.
This lecture continues Lectures One and Two, where we introduced the basic concepts of quantum computing and reviewed the essential linear algebra background for undergraduate students. In this lecture, we focus on the basic computational units of quantum computation, known as quantum gates. Quantum gates play a central role in quantum algorithms, as each quantum algorithm can be implemented as a sequence of quantum gate operations. This idea has a close analogy with classical computing, where computations can be represented by Boolean circuits constructed from elementary logic gates. In principle, classical algorithms can be implemented through combinations of such logic gates. To establish this connection, we first review several fundamental logic gates in classical computing, including the AND, OR, and NOT gates. These elementary Boolean gates provide a useful foundation for understanding quantum gates and how classical computational concepts are extended into the quantum domain. In general, a quantum processing unit (QPU), which executes quantum gate operations, can be viewed as the quantum counterpart of a classical central processing unit (CPU), where computations are carried out through logical operations and circuits. This lecture establishes the foundation for understanding the quantum circuit model and for designing and analyzing quantum algorithms in subsequent lectures. To provide a smooth transition to the topics that follow, we also introduce several tiny quantum algorithms and examples in this lecture. These examples illustrate how quantum gates can be combined to perform meaningful computational tasks and prepare students for the more advanced quantum algorithms discussed later.
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.