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.
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.
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.
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.
Quantum information processing has a wide range of uses, including the solution of complex algorithms, cryptography, dense coding, quantum computation, and quantum teleportation. Quantum entanglement, a phenomenon that is crucial to many different applications of quantum computation, is an essential resource for quantum computation, and the need for quantum circuits that generate entangled states is one of the ongoing needs for constructing quantum computers. In this study, we present a general approach to the design of quantum circuits that produce entangled states. The approach can be applied to the design of various entanglement circuits with any number of qubits (n-qubit systems), and it makes use of a set of CNOT and Hadamard gates, where the number of CNOT gates should always be (n-1) and each gate connects the two adjacent qubits. In this paper, a three-entangled teleportation scheme of a GHZ-like state (named after its inventor Greenberger-Horne-Zeilinger) through three particles as a quantum channel is presented. The probability of successful teleportation depends on the degree of entanglement of GHZ-like states. A 5-qubit quantum teleportation over a GHZ-like channel has also been used. And single-qubit gates are defined, which are Pauli gates. These gates are represented by arrays I, X, Y, and Z. The results in this paper are good and promising theoretical results in the field of quantum entanglement and quantum teleportation using the Mathematica program.
In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a random-number approach to generate maximally entangled basis vectors and their corresponding circuits, while also detailing the required number of single-qubit and CNOT gates. This approach not only provides a solid theoretical foundation but also establishes a practical technique for technological applications, bypassing the difficulty of storing large-scale encoding data.
Abstract There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and two-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses two-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov and Nam 2018 New J. Phys. 20 033018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n − 18 reported in (Maslov and Nam 2018 New J. Phys. 20 033018) to 6n − 8.
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications, information processing, and artificial intelligence. However, quantum computers face a fundamental issue since quantum bits are extremely noisy and prone to decoherence. Keeping qubits error free is one of the most important steps towards reliable quantum computing. Different stabilizer codes for quantum error correction have been proposed in past decades and several methods have been proposed to import classical error correcting codes to the quantum domain. Design of encoding and decoding circuits for the stabilizer codes have also been proposed. Optimization of these circuits in terms of the number of gates is critical for reliability of these circuits. In this paper, we propose a procedure for optimization of encoder circuits for stabilizer codes. Using the proposed method, we optimize the encoder circuit in terms of the number of 2-qubit gates used. The proposed optimized eight-qubit encoder uses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates, 33 2-qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder circuits are verified using IBM Qiskit. We also present encoder circuits for the Steane code and a 13-qubit code, that are optimized with respect to the number of gates used, leading to a reduction in number of CNOT gates by 1 and 8, respectively.