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International Journal of Quantum Information

Quantum representation of the earth based on the bloch sphere

Chan Li, Zhu Cao, Dayong Lu, Yuewei Xu, Zhenlei Wang

Published Aug 11, 2025• 0 citations
Publisher

Abstract

Implementing a digital Earth requires processing an enormous amount of data. Compared with classical algorithms, quantum algorithms can take exponential or quadratic acceleration and are more suitable for processing big data. However, existing quantum models require massive resources to process data on the Earth due to their low compatibility with spheres. So, we propose a quantum representation of the Earth based on the Bloch sphere (QREB), which is tailor-made for the Earth. Based on this model, the scale transformation and specific rotation transformation only need to change one variable. And the time complexity of the quantum point of interest extraction algorithm based on this model is the square root of the classical algorithm. Moreover, in the example of extracting thin black lines on the basketball, the accuracy is improved from 50% to 87.5%. The QREB model can reduce the resources required to process spherical data and accelerate the realization of a digital Earth.

DOI
10.1142/s0219749925500224

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Implementing a digital Earth requires processing an enormous amount of data. Compared with classical algorithms, quantum algorithms can take exponential or quadratic acceleration and are more suitable for processing big data. However, existing quantum models require massive resources to process data on the Earth due to their low compatibility with spheres. So, we propose a quantum representation of the Earth based on the Bloch sphere (QREB), which is tailor-made for the Earth. Based on this model, the scale transformation and specific rotation transformation only need to change one variable. And the time complexity of the quantum point of interest extraction algorithm based on this model is the square root of the classical algorithm. Moreover, in the example of extracting thin black lines on the basketball, the accuracy is improved from 50% to 87.5%. The QREB model can reduce the resources required to process spherical data and accelerate the realization of a digital Earth.
In this paper we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed. The Bloch's sphere is used for visualization of results of numerical simulation. On the one hand, creation of such a quantum-like (QL) representation and its numerical approval is an important step in clarification of extremely complicated interrelation between classical and quantum randomness. On the other hand, it opens new possibilities for application the mathematical formalism of QM in other domains of science.
In this paper, we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed, cf. [1] and [2] on recent numerical simulation for quantum correlations. The Bloch's sphere is used for the visualization of results of numerical simulation. On the one hand, creation of such a quantum-like (QL) representation and its numerical approval is an important step in clarification of extremely complicated interrelation between classical and quantum randomness. On the other hand, it opens new possibilities for applying the mathematical formalism of QM in other domains of science.
To enhance the performance of the intelligent optimization algorithm, a new model of performing search on the Bloch sphere is proposed. Then, by integrating the model into the artificial fish swarm optimization, we present a quantum-inspired artificial fish swarm optimization algorithm. In proposed method, the fishes are encoded with the qubits described on the Bloch sphere. The vector product theory is adopted to establish the axis of rotation, and the Pauli matrices are used to construct the rotation matrices. The four fish behaviors, such as moving, tracking, capturing, aggregating, are achieved by rotating the current qubit about the rotation axis to the target qubit on the Bloch sphere. The Bloch coordinates of qubit can be obtained by measuring with the Pauli matrices, and the optimization solutions can be presented through the solution space transformation. The highlight advantages of this method are the ability to simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method obviously outperforms the classical one in convergence speed and achieves better levels for some benchmark functions.
Quantum computing leverages fundamental principles of quantum mechanics to perform computations far exceeding classical architectures. At the core of single-qubit quantum state manipulation is the Bloch sphere, a geometric representation mapping the state space of two-level quantum systems onto a three-dimensional unit sphere. This paper presents a comprehensive theoretical framework of qubits, starting from single-qubit geometric state vectors and expanding to rigorous multi-qubit mathematical formulations. Furthermore, it analyzes single-qubit quantum gates as unitary rotations on the Bloch sphere, evaluates multi-qubit system scaling, and explicitly proves state normalization conditions using Born's rule across multi-dimensional Hilbert spaces.
The Ordinary Kriging (OK) algorithm is an important method used in geostatistics applications for data interpolation usually based on field measurements of a variable of interest.The OK algorithm is used to estimate the value of a variable based on the variance of previous measurements.The OK algorithm has applications in areas such as environmental science, hydrogeology, mining, weather prediction and remote sensing.However, the OK algorithm is many times not suitable for large volumes of data due to its computational cost.In this work we present a study of a parallel implementation of the OK algorithm that takes advantage of heterogeneous computing environments through the usage of the Open Computing Language (OpenCL) framework.We use the OK algorithm to estimate a Digital Terrain Model (DTM) from a point cloud of a mangrove forest obtained via a terrestrial laser 3D scanning device.A downsampling procedure is applied to the raw data in order to extract the points that belong to the ground and then the OK algorithm is applied to obtain the DTM.The objective of our implementation is to effectively use all the computational resources available to accelerate the OK procedure.We show that our implementation can scale across multiple CPUs and GPUs devices and it is able to handle volumes of data that are typically produced by real world field measurements.The interpolation is a crucial step to make predictions of a variable at unknown locations, it is important to use the maximum amount of measurements possible in order to increase the performance of the prediction algorithm.Reducing the time to generate the interpolation model is, therefore, extremely important.We also compare the run times of a reference sequential implementation with our parallel one to show that the usage of parallel programming techniques can accelerate the fundamental steps of many important scientific researches.
Quantum algorithms which are performed on quantum computers are hardly developed, because the principle of quantum computers are totally different from classical computers. We would like to discuss the way of visualization to assist understanding quantum algorithms. As the first step, we have developed visualization system of the Bloch sphere, which is the popular way to show the status of one quantum bit. In the system, we can see the Bloch sphere as 3DCG and interact with it. Next, we discuss the problems of visualizing multiple quantum bits and quantum algorithms.