相关论文: Geometric Algebra in Quantum Information Processin…
In this paper we combine methods from projective geometry, Klein's model, and Clifford algebra. We develop a Clifford algebra whose Pin group is a double cover of the group of regular projective transformations. The Clifford algebra we use…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
We revisit the Pauli-Clifford connection to introduce a real, grade-preserving algebraic framework for $n$-qubit quantum computation based on the tensor product $C\ell_{2,0}(\mathbb{R})^{\otimes n}$. In this setting, the bivector $J =…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
Conventional quantum mechanical qubits can be lifted to states as even three dimensional geometric algebra operators that act on observables. The operators may be implemented via the two types of Maxwell equation solution polarizations.…
Events in Minkowski space-time can be obtained from the intersection of two twistors with no helicity. These can be represented within the geometric (Clifford) algebra formalism, in a particular conformal space that is constructed from a…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a reversible quantum logic for the Quantum Universe As Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality. It has a…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…