Fredkin Gate Research Articles

A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

Synthesis of energy-conserving quantum circuits with XY interaction

Abstract We study quantum circuits constructed from $\sqrt{iSWAP}$ gates and, more
generally, from the entangling gates that can be realized with the XX+YY
interaction alone. Such gates preserve the Hamming weight of states in the
computational basis, which means they respect the global U(1) symmetry
corresponding to rotations around the z axis. Equivalently, assuming that the
intrinsic Hamiltonian of each qubit in the system is the Pauli Z operator, they
conserve the total energy of the system. We develop efficient methods for
synthesizing circuits realizing any desired energy-conserving unitary using
XX+YY interaction with or without single-qubit rotations around the z-axis.
Interestingly, implementing generic energy-conserving unitaries, such as CCZ
and Fredkin gates, with 2-local energy-conserving gates requires the use of
ancilla qubits. When single-qubit rotations around the z-axis are permitted,
our scheme requires only a single ancilla qubit, whereas with the XX+YY
interaction alone, it requires 2 ancilla qubits. In addition to exact
realizations, we also consider approximate realizations and show how a general
energy-conserving unitary can be synthesized using only a sequence of
$\sqrt{iSWAP}$ gates and 2 ancillary qubits, with arbitrarily small error,
which can be bounded via the Solovay-Kitaev theorem. Our methods are also
applicable for synthesizing energy-conserving unitaries when, rather than the
XX+YY interaction, one has access to any other energy-conserving 2-body
interaction that is not diagonal in the computational basis, such as the
Heisenberg exchange interaction. We briefly discuss the applications of these
circuits in the context of quantum computing, quantum thermodynamics, and
quantum clocks.

Implementation of 4-bit Universal Shift Register using Reversible Logic

The field of digital logic design is increasingly exploring reversible logic due to its potential in minimizing power dissipation, an essential criterion in low-power applications. This paper presents the design and implementation of a 4-bit universal shift register (USR) using reversible logic gates. The design leverages Fredkin gates, multiplexer (MUX), and D flip-flops to achieve functionality with minimal power consumption. Simulation results demonstrate the efficiency and effectiveness of the proposed design. Reversible logic is essential to low-power digital design and quantum computing because it makes it possible to reconstruct input signals from output signals, which reduces heat generation and information loss. The suggested shift register can be used for hold, parallel load, and left and right shift operations. To implement the functions of the shift register, we used a variety of reversible gates, including the Toffoli and Fredkin gates. When the architecture is contrasted with traditional non-reversible shift registers, it shows notable gains in reduced gate count and power efficiency

Quantum-Dot CA-Based Fredkin Gate and Conservative D-Latch for Reliability-Based Information Transmission on Reversible Computing

Reversible computation is very important to minimize energy dissipation and prevent information loss not only in quantum computing but also in digital computing. Therefore, interest in designing efficient universal logic gates has recently increased. In this study, we efficiently design the Fredkin gate (FRG), a well-known conservative reversible operation gate, using quantum-dot cellular automata (QCA), and propose a D-latch using it. The proposed FRG structure can be designed efficiently using the structure of a QCA multiplexer using cell interaction, and a symmetric structure was designed. The proposed structure was simulated using QCADesigner 2.0.3 and QCADesigner-E for accurate comparison of various performance metrics, and the proposed structure clearly shows superiority in most performances and two representative design costs. Therefore, the lightweight design of an efficient reversible gate prevents data loss and increases information reliability.

Design of an Efficient Arithmetic and Logic Unit using Coplanar Reversible Full Adder and Modified Fredkin Gates in Quantum Dots Nanotechnology for Digital Signal Processing

Design of an Efficient Arithmetic and Logic Unit using Coplanar Reversible Full Adder and Modified Fredkin Gates in Quantum Dots Nanotechnology for Digital Signal Processing

Development of a high-performance arithmetic and logic unit for efficient digital signal processing based on reversible logic and quantum dots

Digital Signal Processing (DSP) finds a wide range of applications in various fields, including telecommunications, audio and video processing, biomedical engineering, radar systems, and image processing. Previous DSP designs faced limitations in available processing power and computational resources. Insufficient processing power could result in slower execution times, an inability to handle complex algorithms, or limited capacity to process high-speed or large-scale signals. As the demand for minimal power consumption in DSP circuits continues to grow, reversible logic and quantum-dot cellular automata (QCA) have emerged as promising technologies due to their inherent ability to reduce energy loss. Within this landscape, the arithmetic and logic unit (ALU) plays a vital role in complex circuitry, serving as a key component in digital signal processing applications. However, challenges persist, including high quantum cost and the need to limit the number of cells in the ALU design. To address these challenges, our research aims to develop an efficient ALU by integrating reversible logic and QCA technology. Our focus will be on generating essential components, such as Feynman gates, Fredkin gates, and full adder circuits, which serve as foundational building blocks for reversible logic and QCA designs. These components will be combined to construct a comprehensive ALU capable of performing 20 different operations. Our implementation efforts will be centered around QCADesigner, with a specific emphasis on digital signal processing systems that prioritize energy efficiency and optimal utilization of occupied areas.

A new nano-design of configurable logic module based on coplanar reversible adder and modified Fredkin gates using quantum technology

Quantum Dot Cellular Automata (QCA) and reversible logic have emerged as promising alternatives to conventional CMOS technology, offering several advantages, such as ultra-dense structures and ultra-low-power consumption. Among the crucial components of processors, the Arithmetic Logic Unit (ALU) has witnessed significant advancements in reversible computing, leading to energy-efficient and high-speed computing systems, particularly beneficial for Digital Signal Processing (DSP) applications. Conventional ALUs, reliant on irreversible logic, encounter energy inefficiencies due to information loss during computations, resulting in increased power consumption. Moreover, they may face limitations in processing speed, impacting real-time processing capabilities, especially for complex DSP tasks involving intensive arithmetic and logic operations. In response to these challenges, a research paper presents a pioneering approach, proposing a novel reversible ALU design using QCA nanotechnology. The proposed design ingeniously incorporates Modified Fredkin (MF) gates, and a coplanar reversible full adder based on the HNG gate, skillfully leveraging the unique features of QCA nanotechnology to optimize the ALU's energy-efficient and high-speed performance for DSP applications. This revolutionary QCA reversible ALU comprises 330 QCA cells arranged in a compact 0.41 μm2 area, skillfully realized through the coplanar clock-zone-based crossover approach. Its core computational elements, the three MF gates, and the innovative coplanar reversible full adder empower the ALU to execute a remarkable array of 20 distinct arithmetic and logic operations, showcasing its versatility in handling diverse DSP tasks. The proposed structure undergoes extensive simulations utilizing QCADesigner version 2.0.3 to confirm its performance. The evaluation results manifest substantial improvements compared to previous designs, boasting a 30% reduction in area occupancy, a 20% decrement in cell count, a 10% reduction in latency, and a 10% decrease in quantum cost compared to the best-known previous structure. These compelling outcomes solidify the potential of the proposed reversible ALU as a transformative advancement in energy-efficient and high-speed computing for DSP applications.

Efficient design and implementation of a reversible switched network in quantum cellular automata technology

Nano-communication networks have critical roles in future worldwide communications, which provide efficient data transmission at ultra-high speeds employing nano-circuits that operate with ultra-low power. The quantum cellular automata (QCA) paradigm enables designing molecular-scale devices operating at terahertz frequencies with negligible power consumption. Moreover, reversible logic aids in reducing thermodynamic power dissipation significantly. In this paper, we design and implement a single-layer Fredkin gate and use it to implement reversible QCA devices, including the crossbar switch, multiplexer, demultiplexer, transmitter, and receiver. These devices are then used to implement a reversible switched network in QCA technology. The proposed circuits employ standard 90-degree QCA cells and coplanar crossovers. The results show that the area-time complexity and power dissipation of the designed reversible switched network have been reduced significantly compared to previous designs.

Alternative scheme for implementation of 3 qubit Fredkin gate with photonic bandgap crystal

Alternative scheme for implementation of 3 qubit Fredkin gate with photonic bandgap crystal

Review on Reversible Logic Gates

Abstract: Reversible logic gates have emerged as a pivotal area of research in the field of digital circuit design, offering the promise of ultra-low power consumption. This survey paper comprehensively explores the foundations and practical applications of reversible logic gates. Beginning with an introduction to the fundamental principles of reversibility, it delves into the design of reversible gates, covering CNOT, Feynman, Toffoli, Peres, Fredkin gates, and beyond. The paper offers a systematic review of state-of-the-art research in the field, discussing various optimization techniques and quantum-inspired reversible circuits. It also investigates real-world applications, ranging from low-power VLSI design to quantum computing. By summarizing the key findings, challenges, and potential future directions in reversible logic gate design, this survey paper provides a valuable resource for researchers, engineers, and enthusiasts seeking a comprehensive understanding of this transformative technology

Design of Enhanced Reversible 9T SRAM Design for the Reduction in Sub-threshold Leakage Current with14nm FinFET Technology

Power dissipation is considered one of the important issues in low power Very-large-scale integration (VLSI) circuit design and is related to the threshold voltage. Generally, the sub-threshold leakage current and the leakage power dissipation are increased by reducing the threshold voltage. The overall performance of the circuit completely depends on this leakage power dissipation because this leakage and power consumption causes the components that are functioning by the battery for a long period to be washed-out rapidly. In this research, the reversible logic gate-based 9T static random access memory (SRAM) is designed in 14nm FinFET technology to reduce leakage power consumption in memory related applications. The Schmitt-trigger (ST)-based 9T SRAM cell is designed to attain high read-write stability and low power consumption using a single bit line structure. The reversible logic gates of Feynman (FG) and Fredkin gate (FRG) are combined to develop a row and column decoder in an SRAM design to diminish the leakage power. Moreover, the transistor stacking effect is applied to the proposed memory design to reduce the leakage power in active mode. The proposed reversible logic and transistor stacking based SRAM design is implemented in Tanner EDA Tool version 16.0. It also performs both read and write operations using the proposed circuit. The performance measures of read access time (RAT), write access time (WAT), read, write, and static power by varying supply voltage and temperature, delay and stability analysis (read/write static noise margin) are examined and compared with existing SRAM designs.

Two examples of implementation of the if/then/else conditional statement with quantum computers

While quantum algorithms are known to be very powerful, there are also people who think that “quantum computers will never be able to run the if/then/else type of logic”. On the other hand, though many experts know that such a claim is a misconception, in literature there is still lacking of a general description of the procedure for implementing the if/then/else conditional statements in the quantum way. In the current work, we present such a general method in details, explaining how the unitary transformation required for any if/then/else operation can be constructed from simpler unitary transformations and projective operators. Moreover, by using the well-known controlled-NOT gate, Fredkin gate and Toffoli gate as examples, it is elaborated that the structure of the existing conditional quantum operations agrees with our general method. An even more complicated example is also provided, showing that our method is convenient for solving real-world if/then/else problems with quantum computers. Thus the result not only refutes the above claim, but also helps to develop the skill on quantum programming.

Heralded hyperparallel Fredkin gate with robust fidelity

We propose a heralded hyperparallel Fredkin gate for a three-photon system with the help of the optical property of a quantum dot (QD) embedded in a microcavity. This hyper-Fredkin gate performing both on spatial and polarized degrees of freedom (DoFs) of the three-photon system is equal to double independent three-photon Fredkin gate in one DoF, which has advantages over consuming a less quantum resource, accelerating calculation speed, and inhibiting photon-dissipation noise. Meanwhile, the fidelity of our hyper-Fredkin gate, in principle, approach unit even for the non-identical QD-cavity systems, as the imperfections involved in practical input–output processes of three photons can be converted into heralded errors by clicking the detectors rather than infidelity. Furthermore, the flexibility of the gate can be directly extended to construct some types of hybrid hyper-Fredkin gates with the same high fidelity and efficiency, accessibly performed under existing experimental techniques, as well as used large-scale quantum information processing.

Deterministic Hyperparallel Control Gates with Weak Kerr Effects

AbstractBy harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.

Refined Fredkin gate assisted by cross-Kerr nonlinearity

Resource-efficient quantum information processing is equal to the minimal cost of the quantum resources required by quantum logic gates to a certain extent. In this paper, we propose a refined scheme for setting up a polarized Fredkin gate assisted by weak cross-Kerr nonlinearity, X-homodyne detectors, and some linear optical elements. The realization of the Fredkin gate is definite and has a highly successful probability of being close to the unit, which is feasible with the current technology. Moreover, in contrast to the Fredkin gates that have been proposed, the scheme has the advantages of requiring less quantum resource without auxiliary photons, comparatively simplified circuits, lower requirements on the interaction strength, and robustness against photon loss, thus it can be used for scalable quantum computation.

Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions

We propose a laser-free method for creation of a phonon two-mode squeezed state and a beam-splitter transformation, using time-varying electric fields and non-linear couplings between the normal modes in a linear ion crystal. Such non-linear Coulomb-mediated interactions between the collective vibrational modes arise under specific trap-frequency conditions in an ion trap. We study the quantum metrological capability for parameter estimation of the two quantum states and show that a Heisenberg limit of precision can be achieved when the initial state with n phonons evolves under the action of the beam-splitter transformation. Furthermore, we show that the phonon non-linearity and the spin-dependent force can be used for creation of a three-qubit Fredkin gate.

Numerical Modeling of a Fredkin gate using photonic-crystal-based nonlinear effects around the 1550 nm telecommunication wavelength

Numerical Modeling of a Fredkin gate using photonic-crystal-based nonlinear effects around the 1550 nm telecommunication wavelength

Design and simulation of an all-optical Fredkin gate based on silicon slab-waveguide in a 2-D photonic crystal

Design and simulation of an all-optical Fredkin gate based on silicon slab-waveguide in a 2-D photonic crystal

The Fredkin gate in reversible and quantum environments

Reversible Computing circuits are characterized by low power consumption and their proximity to circuits for quantum computing. The Fredkin gate was one of the earliest proposed controlled reversible circuits, which however, was soon superseded by the Toffoli gate, the NOT, and CNOT gates, which constituting a flexible functionally complete set could also realize the Fredkin gate as a building block. In quantum computing circuits, the Fredkin gate (under the name controlled SWAP) plays an important role regarding the superposition of states. The present paper studies extensions of the Fredkin gate in terms of mixed polarity in the reversible domain and an application in quantum computing.

Generation of Perfectly Entangled Two and Three Qubits States by Classical Random Interaction

AbstractThis study examines the possibility of finding perfect entanglers for a Hamiltonian which corresponds to several quantum information platforms of interest at the present time. However, in this study, a superconducting circuit is used that stands out from other quantum‐computing devices, especially because transmon qubits can be coupled via capacitors or microwave cavities, which enables to combine high coherence, fast gates, and high flexibility in its design parameters. There are currently two factors limiting the performance of superconducting processors: timing mismatch and the limitation of entangling gates to two qubits. In this work, a two‐qubit SWAP and a three‐qubit Fredkin gate is presented, additionally, a perfect adiabatic entanglement generation between two and three programmable superconducting qubits is also demonstrated. Furthermore, the impact of random dephasing, emission, and absorption noises on the quantum gates and entanglement is also demonstrated in this study. It is demonstrated by numerical simulation that CSWAP gate and W‐state generation can be achieved perfectly in one step with high reliability under weak coupling conditions. Hence, this scheme could contribute to quantum teleportation, quantum communication, and some other areas of quantum information processing.