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Journal of Al-Nahrain University-Science

A Quantum Circuit for Three Quantum Bits to Produce Quantum Entanglement States (ML- Quadripartite)

Mezher B. Saleh, Loay Edwar George

Published Dec 1, 2016• 1 citation
Publisher

Abstract

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.

DOI
10.22401/jnus.19.4.09

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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.
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 quantum information processing, spin-3/2 electron or nuclear spin states are known as two-qubit states. For SI (S = 3/2, I = 1/2) spin system, there are eight three-qubit states. In this study, first, three-qubit CNOT logic gates are obtained. Then three-qubit entangled states are obtained by using the matrix representation of Hadamard and three-qubit CNOT logic gates. By considering single 31P@C60 molecule as SI (S = 3/2, I = 1/2) spin system, three-qubit entangled states are also obtained using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates.
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.
Abstract This laboratory work presents a practical introduction to the preparation and analysis of entangled quantum states (Bell pairs) using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is designed to provide hands-on experience with multi-qubit quantum circuits and entanglement generation. In Laboratory Work No. 3, participants construct and simulate a quantum circuit that prepares an entangled two-qubit state. As a representative example of multi-qubit operations in Qiskit, the circuit generates a Bell state by applying a Hadamard (H) gate to the first qubit q[0]q[0]q[0], followed by a controlled-NOT (CNOT) gate with q[0]q[0]q[0] as the control qubit and q[1]q[1]q[1] as the target qubit. This sequence creates a maximally entangled state, demonstrating the fundamental non-classical correlations characteristic of quantum systems. The laboratory exercise includes measurement operations applied to both qubits, illustrating how entanglement manifests in correlated classical outcomes. When the measurement operator is applied to the first qubit q[0]q[0]q[0], the corresponding classical bit records a definite value, and subsequent measurement of the second qubit q[1]q[1]q[1] yields a correlated result consistent with the structure of the Bell state. The probabilistic yet correlated outcomes provide direct evidence of quantum entanglement. The guide emphasizes the conceptual understanding of entanglement, circuit implementation in Qiskit, and the hybrid quantum-classical workflow underlying quantum computation. By bridging theoretical quantum mechanics with executable quantum circuits, this laboratory work enables students and researchers to experimentally explore one of the central phenomena of quantum information science using cloud-based quantum computing resources.
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to nderstand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.