Related papers: Cliffordons

A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…

The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a…

Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra…

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 =…

Unitary $t$-designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers, little is known about unitary $t$-designs…

Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.

Let $G$ be a finite group, $N$ a normal subgroup of $G$, and $k$ a field of characteristic $p>0$. In this paper, we formulate the brick version of Clifford's theorem under suitable assumptions and prove it by using the theory of wide…

Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…

Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…

This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the…

Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and…

Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass…

In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…

The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of…

Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra…

A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…