Simulation of bell states for the software implementation of a quantum simulator


Аuthors

Semenov A. S.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: Semenov_Alex@yahoo.com

Abstract

The aim of this study is to enhance the efficiency and precision of quantum simulators via the simulation of Bell states utilizing diverse quantum gates, initialization, and measurement algorithms. Such research will enable us to gain a more profound comprehension of quantum solutions for intricate issues while enhancing their performance.

Bell states are a set of four entangled quantum states represented by two qubits. Each qubit can be in a superposition of two states, namely 0 and 1. These states are used as building blocks for many quantum algorithms and quantum protocols, such as teleportation and dense coding. Bell states are also used to experimentally demonstrate quantum entanglement and quantum teleportation.

Theoretical modeling of Bell states requires understanding the quantum state correlations between two qubits in an entangled state. Let us highlight three approaches to simulating Bell states: algorithms based on various quantum gates, algorithms based on density matrices that describe the statistical properties of quantum systems, and algorithms based on entanglement measures that quantify the degree of entanglement between two qubits.

Understanding the effects of noise and imperfections in quantum hardware for entangled state generation in Bell state simulations requires the development of error correction and fault tolerance methods for quantum information processing. Research into multiqubit entangled states demonstrates complex quantum phenomena such as quantum teleportation networks and quantum error correction codes.

The following algorithms simulating Bell states are considered: an algorithm based on the Hadamard and CNOT gates, an algorithm using a single-qubit Pauli-X gate, an algorithm using a single-qubit S-gate, an algorithm using a T-gate, an algorithm using an X-gate,

The initial state generation algorithm prepares qubits for quantum operations and measurements. The correct choice of the initial state can influence the results of calculations and the efficiency of the algorithm. In addition, the measurement results depend on the states of the qubits after performing quantum operations. Let's take a closer look at these algorithms.

The algorithm for generating multiple random initial states of a two-qubit system is useful for testing the behavior and stability of quantum algorithms and simulators. The Kronecker product of qubit states allows the algorithm to represent the entire state of two qubits as a 4-dimensional vector, which is used to model the evolution of a quantum system over time.

When measuring the states of a two-qubit quantum system in the Bell basis, the measurement probabilities give an idea of the chances of different measurement results. These probabilities are calculated based on algorithm n-qubit measurements. By measuring the system several times and comparing the measured results with the probabilities, the quantum mechanical predictions and the accuracy of the quantum device are checked.

The proposed algorithms improve the simulation and manipulation of Bell states, making them suitable for a wide range of applications, particularly the enhancement of software implementations of quantum simulators. This study was focused on improving software quantum simulators, providing an advancement in the field. The significance of Bell states for quantum information and computing is emphasized in the paper, along with the necessity of accurate and efficient simulation and manipulation of these states.

Keywords:

quantum computing, quantum simulator, qubit, gate, quantum circuit, quantum algorithm, Bell states, state measurement

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