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Quantum Information Processes
Published in Thiruselvan Subramanian, Archana Dhyani, Adarsh Kumar, Sukhpal Singh Gill, Artificial Intelligence, Machine Learning and Blockchain in Quantum Satellite, Drone and Network, 2023
B.S. Tewari, P. Mandal, Prashant Rawat
To achieve multi-qubit gates, entanglement amongst the qubits is essential. The single-qubit quantum gates mentioned in the above section are not sufficient for performing all types of unitary operations. This indicates a necessity for universal quantum gates that can generate all unitary matrices. Many works have been reported in this direction. It is not surprising that three-qubit quantum gates were proposed by Deutsch [32], prior to the development of a two-qubit gate. This is because three-bit gates are requisite for universal reversible operations in classical computation. Deutsch identified a three-qubit quantum gate by generalizing a three-bit classical gate known as Toffoli gate. Toffoli gate is a universal gate which can perform reversible Boolean logics. A representation of the three-bit Deutsch gate is given below.
Basics, Applications, and Design of Reversible Circuits
Published in Tomasz Wojcicki, Krzysztof Iniewski, VLSI: Circuits for Emerging Applications, 2017
Reversible functions are realized by reversible circuits. A reversible circuit G is a cascade of reversible gates, where fanout and feedback are not directly allowed [1]. A reversible gate has the form g (C;T), where C = {xi1,…,xik} ⊂ X is the set of control lines and T = {xj1,…,xjl} ⊂ X with C∩T = ; is the set of target lines. C may be empty. Control lines and unconnected lines always pass through the gate unaltered. In contrast, the gate operation is applied on the target iff all control lines are assigned to 1. The most frequently used reversible gate is the Toffoli gate [2], which inverts the value of the (single) target line in this case.
Computational analysis and comparison of reversible gates for design and test of logic circuits
Published in International Journal of Electronics, 2019
H. M. Gaur, A. K. Singh, A. Mohan, D. K. Pradhan
A Toffoli gate is a three input three output () reversible gate which maps two of its inputs directly to their respective outputs. The output of last wire defines its state of operation which is governed by the logic states of first two inputs. The quantum equivalent representation is provided in Figure 1(a). If the dot product of first two inputs is , the gate inverts the last input to its output, else the same input value will be transferred. Hence, the two primary inputs are called control inputs and the last input wire is called as target input. The gate can be scaled to –I/O order gates ( gates) to form reversible gate library, known as Multiple Control Toffoli (MCT) gates. It has m control inputs and one target input T to form reversible Boolean function. The control input is directly mapped to their respective outputs and the function is given by Equation 1, where . The illustration is also provided in Figure 1(b). The smallest member of this family is the gate without any control is known as a NOT gate, whose output is inversion of the input applied to it.
Multiple-Controlled Toffoli and Multiple-Controlled Fredkin Reversible Logic Gates-Based Reversible Synchronous Counter Design
Published in IETE Journal of Research, 2023
S. K. Binu Siva Singh, K. V. Karthikeyan
Quantum gates are the building blocks of quantum circuits, and they manipulate the state of qubits. In classical computing, logic gates such as AND, OR, and NOT gates are used to manipulate the state of bits. In quantum computing, there are a few universal gates that can be utilized to construct quantum circuits. One of these is the Toffoli gate, a three-qubit gate that functions similarly to a conventional AND gate. Another three-qubit gate is the Fredkin gate, also known as the controlled-SWAP gate, which swaps the second and third qubits if the first qubit is in the state.
A Novel Heuristic Method for Linear Nearest Neighbour Realization of Reversible Circuits
Published in IETE Journal of Research, 2022
Anirban Bhattacharjee, Chandan Bandyopadhyay, Hafizur Rahaman
Reversible gates are the essential components of the reversible circuits that are arranged in a specific order to realize the desired reversible Boolean function. In the following, we discuss some of the basic reversible logic gates. NOT gate- gate with a single input/output that inverts the logic value of the input to become the corresponding output. In other words, it inverts the logic value from 1 to –0 or vice versa. It can be represented as .CNOT gate- It is a two-input/output NOT gate, which performs the inversion operation based on the logic value of its controlled input. It maps the input (x1,x2) to the corresponding output (x1, x1⊕x2).CNOT function can be described as if and only if its controlled input (x1) is set at the logic value 1, then it performs the exclusive-or operation with its other input (x2) and assigns the corresponding value to its output; otherwise, the value of x2 remains unchanged.TOFFOLI gate –It is similar to CNOT gate but with three input/output and two controlled inputs. It determines the output (x1,x2,x1×2⊕x3) from the input combination (x1,x2,x3). Like CNOT gate, it performs the exclusive-or (inversion) operation when its controlled inputs (x1,x2) are set at logic state 1; otherwise, its third input x3 remains unchanged at the output.