The present work purports to the proposal and elucidation of a novel kind of logic, where the apparent „practical uncertainty ‟ of chaos is effectively harnessed in the form of S-Bits, or Simultaneous Bits, to achieve quantum computation like effects. Specifically, it is seen that a single NMOSFET possessed the sufficient nonlinearity to generate a signal driven chaos, which is then proposed as similar to the superposed state of a qubit, and hence termed “S-Bits”. The measurement/collapse operations are performed using hysteresis, achieved using back-to-back MOS Varactors. Using these formulations, various quantum and reversible logic gates such as the three Pauli Rotation Gates, Hadamard Gate, CNOT and TOFFOLI gates are implemented in hardware level using extremely simple circuitry. Following this, the phenomenon of entanglement using S-bits is discussed, followed by implementations of quantum teleportation and superdense coding. The results reveal the effective reproduction of quantum computation applications using simple circuitry involving the S-Bit analogue, thus ushering in the golden era of affordable quantum computing. 1.
The present work purports to the proposal and elucidation of a novel kind of logic, where the apparent „practical uncertainty ‟ of chaos is effectively harnessed in the form of S-Bits, or Simultaneous Bits, to achieve quantum computation like effects. Specifically, it is seen that a single NMOSFET possessed the sufficient nonlinearity to generate a signal driven chaos, which is then proposed as similar to the superposed state of a qubit, and hence termed “S-Bits”. The measurement/collapse operations are performed using hysteresis, achieved using back-to-back MOS Varactors. Using these formulations, various quantum and reversible logic gates such as the three Pauli Rotation Gates, Hadamard Gate, CNOT and TOFFOLI gates are implemented in hardware level using extremely simple circuitry. Following this, the phenomenon of entanglement using S-bits is discussed, followed by implementations of quantum teleportation and superdense coding. The results reveal the effective reproduction of quantum computation applications using simple circuitry involving the S-Bit analogue, thus ushering in the golden era of affordable quantum computing. 1.
One of the most successful theories of modern physics, quantum mechanics has undergone rigorous testing and validation, one of the primary motives being fanciful and informative applications of quantum information theory such as teleportation and superdense coding. Over the years, many explanations have been given for the mechanism and interpretation of the various quirks and mysteries of quantum mechanics, the latest entrant being a suggestion of nonlinearity and chaos underlying quantum mechanics. The present work purports to a formulation of quantum bit as a SU(2) Lie Group using a Chua’s chaos generator circuit as the basis. PSPICE simulations of the same are performed. Various basic quantum gates such as the Pauli X, Y, Z, Hadamard and CNOT gates are implemented using this formulation. Finally, the chaos-qubit formulation is validated using a real time application – quantum teleportation. The ability to successfully demonstrate the teleportation of a single qubit numerically suggests that the chaotic interpretation of quantum mechanics has some validity. Furthermore, it ushers in the era of low cost, high capacity, high security information systems using nonlinear electrical circuits.
The present work purports to a radically new perspective towards exploiting the advantages of quantum computation using classical systems. Termed ‘Quantum Tricks’, the technique relies on replacing the inherent probabilistic nature of the qubit with a pseudorandom generator. Using this, extremely simple mathematical operations are developed to implement basic Pauli X, Y and Z gates, using FPGA. Following this, entanglement is implemented and a real life application of quantum computing, namely Quantum Teleportation is implemented using the ‘QTrick Bits’. It is seen that the QTrick Bits are able to implement the teleportation with a remarkable degree of accuracy. Nonlinear characterization of the entangled states reveal the presence of chaos, thus providing subtle hints towards understanding the QTrick signal behavior. The extreme simplicity of the proposed design coupled with its efficacy in implementing quantum teleportation accurately form the highlights of the present work.
A remarkable application of quantum mechanical concepts of coherent superposition and quantum entanglement is a quantum computer which can solve certain problems at speeds unbelievably faster than the conventional computer. In this chapter, the basic principles and the conditions for the implementation of the quantum computer are introduced and the limitations imposed by the probabilistic nature of quantum mechanics and the inevitable decoherence phenomenon are discussed. Next the basic building blocks, the quantum logic gates, are introduced. These include the Hadamard, the CNOT, and the quantum phase gates. After these preliminaries, the implementation of the Deutsch algorithm, quantum teleportation, and quantum dense coding in terms of the quantum logic gates are discussed. It is also shown how the Bell states can be produced and measured using a sequence of quantum logic gates.
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.
This paper investigates the core principles of quantum computation, providing an in-depth understanding of quantum phenomena and illustrating how these principles form the scientific foundation of the field. The pivotal physical concepts, such as properties of subatomic particles, including electrons and photons, as well as their mathematical description through linear algebra are examined. It focuses on the qubit, the quantum analogue of a classical bit, featuring properties like superposition, entanglement, and wave function collapse, which redefine the traditional concept of information processing. The mathematical structures that underlie quantum system modelling—vector spaces, tensor products, and Dirac notation—are also systematically explained. Essential components of quantum computation involve logic gates such as Pauli matrices and Hadamard gates, which demonstrate the novel application of qubits in unique ways. This sets up an important theme of the interdependence and potential for transformation of quantum states through the illustration of advanced ideas of quantum entanglement and teleportation. Quantum circuits serve as an outstanding example of how reversibility and superposition are exploited to solve complex problems at unprecedented levels of efficiency. The paper also highlights the Deutsch-Jozsa algorithm as a compelling example of quantum superiority over traditional computational approaches. Together, these findings emphasize the transformative potential of quantum computing for science and industry.
Quantum computing (Q-computing) is a revolutionary technology that applies quantum mechanics (QM) to implement calculations significantly quicker than traditional computers. Q-computing employs Q-bits (qubits) rather than classical bits, which can take on a superposition state, making it possible to represent both 0 and 1 at once. This distinctive property allows qubits to perform multiple calculations simultaneously, making Q computers exponentially more powerful as more qubits are added, compared to the linear scaling of classical computers. However, challenges such as qubit instability and error rates remain significant obstacles to fully realizing this potential. A vital aspect of this technology is the development of Q arithmetic circuits, which act as the foundational blocks for efficiently executing Q algorithms. Q half-adder and full-adder circuits are integral to performing fundamental arithmetic operations within Q computers. In contrast to classical adders, Q adders rely on Q gates such as Controlled NOT (CNOT) and Toffoli gates. These gates exploit Q phenomena like entanglement and superposition, allowing for more efficient computations. The Q half-adder consists of two qubits and adds two single bits, producing a carry and sum output. It utilizes the CNOT gate to compute the sum and the Toffoli gate (controlled-controlled-NOT [CCNOT]) to compute the carry. The Q full-adder builds on this, adding three qubits to produce a sum and a carry output, further increasing computational capacity. Through the entanglement of qubits, these circuits allow for more parallelism and speed compared to classical adders. Q carry-look-ahead adders (QCLAs) and Q ripple-carry adders (QRCAs) are used to perform more complex arithmetic operations based on these half-adder and full-adder structures. Q arithmetic circuits have broad applications, boosting secure key generation in cryptography, speeding up matrix operations for faster model training in machine learning, and enabling more precise, efficient image transformations in Q image processing, benefiting fields like medical imaging and computer vision.