We studied the outputs that a quantum circuit consisting of four qubits can produce by using quantum gates, which operate on the states of the qubit as a state vector that can be expressed through unitary matrices. We made the change by exploiting the superposition property of the Hadamard gate, and with its presence in the quantum circuit, we used CNOT gates, which produced entangled states . The study explained the output of a quantum circuit consisting of four qubits and gave a methodology for changing this output by installing one input type for the quantum circuit (we used the input ). It showed the importance of measurement in the quantum circuit and its effect on the and the . Starting from, produce all 16 states of the four qubits, which can be expressed as the computational basis state of a vector state using only an x-gate.
We studied the outputs that a quantum circuit consisting of four qubits can produce by using quantum gates, which operate on the states of the qubit as a state vector that can be expressed through unitary matrices. We made the change by exploiting the superposition property of the Hadamard gate, and with its presence in the quantum circuit, we used CNOT gates, which produced entangled states . The study explained the output of a quantum circuit consisting of four qubits and gave a methodology for changing this output by installing one input type for the quantum circuit (we used the input ). It showed the importance of measurement in the quantum circuit and its effect on the and the . Starting from, produce all 16 states of the four qubits, which can be expressed as the computational basis state of a vector state using only an x-gate.
Study of a quantum circuit consisting of four qubits that produces an output state consisting of eight entangled states through the CNOT –gates and the three Hadamard gates. targeting the gates to |q0q1q2q3> to show the other entangled states, We used quantum gates that give the same arrangement as the circuit gates and for the same inputs, taking into account the output of a quantum circuit that contains entangled states. As a general case, we used an X-gate and a SWAP-gate, For inputs|0000> .We obtained a general change to the output state while keeping the eight states maximally entangled.
In this research, a quantum system consists of three qubits is considered; it has eight states (|000˃, |001˃, |010˃, |011˃, |100˃, |101˃, |110˃ and |111˃).Each of these states is passed through a quantum circuit made of a sequence of quantum gates.The circuit applies X-gate on the first qubit from the left, then using CNOT-gate on the first and second qubits and using the Hadamard-gate on the first qubit.Finally, Hadamard-gate is applied on the third qubit.When the state |000˃ is passed as input through the proposed quantum circuit then the output includes four entanglement states; for the other input states the output will be another non-repeatable entanglement states.So, for using all states in quantum circuit the result will be eight equations each one consists of four entanglement states; which called ML-Quadripartite.
In Section 1.3, we introduced the circuit model of (classical) computation. We restricted attention to reversible circuits since they can simulate any non-reversible circuit with modest overhead. This model can be generalized to a model of quantum circuits. In the quantum circuit model, we have logical qubits carried along ‘wires’, and quantum gates that act on the qubits. A quantum gate acting on n qubits has the input qubits carried to it by n wires, and n other wires carry the output qubits away from the gate. A quantum circuit is often illustrated schematically by a circuit diagram as shown in Figure 4.1. The wires are shown as horizontal lines, and we imagine the qubits propagating along the wires from left to right in time. The gates are shown as rectangular blocks. For convenience, we will restrict attention to unitary quantum gates (which are also reversible). Recall from Section 3.5.3 that non-unitary (non-reversible) quantum operations can be simulated by unitary (reversible) quantum gates if we allow the possibility of adding an ancilla and of discarding some output qubits. A circuit diagram describing a superoperator being implemented using a unitary operator is illustrated in Figure 4.2. In the example of Figure 4.1, the 4-qubit state |ψi⟩= |0⟩⊗ |0⟩⊗ |0⟩⊗ |0⟩ enters the circuit at the left (recall we often write this state as |ψi⟩ = |0⟩|0⟩|0⟩|0⟩ or |ψi⟩ = |0000⟩.) These qubits are processed by the gates U1, U2, U3, and U4. At the output of the circuit we have the collective (possibly entangled) 4-qubit state |ψf⟩. A measurement is then made of the resulting state. The measurement will often be a simple qubit-by-qubit measurement in the computational basis, but in some cases may be a more general measurement of the joint state. A measurement of a single qubit in the computational basis is denoted on a circuit diagram by a small triangle, as shown in Figure 4.1 (there are other symbols used in the literature, but we adopt this one). The triangle symbol will be modified for cases in which there is a need to indicate different types of measurements.R50
This paper presents a study of the influence of the quantum phase on the qubit state in circuits with Hadamard gates in series for further minimisation in software or hardware modelling. The study is carried out using the Azure Quantum computing platform to simulate quantum algorithms and run quantum applications on dedicated hardware. The study provides an overview of the qubit as a unit of quantum information, describes in detail the operation of the Hadamard gate, simulates the operation of a circuit of two Hadamard gates in series with initial inputs and , and simulates the operation of a circuit with a sequential shift on and Hadamard gate inputs and . In the course of the study, it was found how the same intermediate state of the qubit can have different outputs after the Hadamard gate, by means of phase. Also, the results of the schemes where the first Hadamard gate is replaced by a sequential shift on . The results obtained can be used to test the Hadamard gate model when creating its digital model. Key words: Hadamard gate, quantum computing, quantum gates, superposition.
Abstract Quantum gates, equivalent to logic gates, modify the state vectors. Linear algebra calls these gates linear transformations. In quantum language, they are “operators.” These gates include the NOT gate, the Pauli gates, and the Hadamard gate. The operations of the gates are represented both as abstract symbols and by matrices multiplying state vectors (expressed as column vectors). Quantum computers use a series of gates called a quantum circuit. The chapter explains how to read a quantum circuit diagram and translate it into linear algebra mathematics. The mathematical requirements on the matrices allowed to be used is delineated. Gates are reversible by applying the same gate twice, but measurements are not reversible.
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.