相关论文: VENUS: A Geometrical Representation for Quantum St…

The qutrit comes next in complexity after qubit as a resource for quantum information processing. The qubit density matrix can be easily visualized using Bloch sphere representation of its states. In contrast, this simplicity is in general…

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…

We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using…

In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the…

Quantum computing (QC) has experienced rapid growth in recent years with the advent of robust programming environments, readily accessible software simulators and cloud-based QC hardware platforms, and growing interest in learning how to…

With the rapid development of Quantum Machine Learning, quantum neural networks (QNN) have experienced great advancement in the past few years, harnessing the advantages of quantum computing to significantly speed up classical machine…

Recent advances in neural rendering, particularly 3D Gaussian Splatting (3DGS), have enabled real-time rendering of complex scenes. However, standard 3DGS relies on spherical harmonics, which often struggle to accurately capture…

Quantum computing has attracted considerable public attention due to its exponential speedup over classical computing. Despite its advantages, today's quantum computers intrinsically suffer from noise and are error-prone. To guarantee the…

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system,…

We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…

Visual methods are of great utility in understanding and interpreting quantum mechanics at all levels of understanding. The Bloch sphere, for example, is an invaluable and widely used tool for visualising quantum dynamics of a two level…

Quantum computing is an emerging field that utilizes the unique principles of quantum mechanics to offer significant advantages in algorithm execution over classical approaches. This potential is particularly promising in the domain of…

Artificial intelligence provides an unprecedented perspective for studying phases of matter in condensed-matter systems. Image segmentation is a basic technique of computer vision that belongs to a branch of artificial intelligence. In this…

We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…

Bloch-vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of…

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…

Driven by potential exponential speedups in business, security, and scientific scenarios, interest in quantum computing is surging. This interest feeds the development of quantum computing hardware, but several challenges arise in…

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…

Existing graphical user interfaces for circuit simulators often show small visual summaries of the reduced state of each qubit, showing the probability, phase, purity, and/or Bloch sphere coordinates associated with each qubit. These…

The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…