On the Structure of Complex Clifford Algebra

Abstract

Abstract. The structure of a complex Clifford algebra is studied by direct sum decompositions into eigenspaces of specific linear operators.Mathematics Subject Classification (2000). 11E88, 15A66, 15A75, 30G35.

Quantum computing based on complex Clifford algebras

“…The complex Clifford algebras for small m are well known; C 0 are complex numbers itself, C 1 is the algebra of bicomplex numbers and C 2 is the algebra of biquaternions. More details on complex Clifford algebras one can find in the papers [2,3,4,8].…”

Complex Clifford algebra in repeated quantum prisoner's dilemma

“…Computations become especially efficient due to the application of the Witt basis, in which the realization of spinor space within the CCA can be constructed directly. [9][10][11] We represent n-qubits as elements of the CCA 12 C 2n = G 2n ⊕ iG 2n = G 2n ⊗ C, where the G 2n is a real Clifford algebra based on signature (2n, 0). In particular, we define the elements 𝑓 𝑗 and 𝑓 † 𝑗 of the Witt basis of the C 2n with the help of orthonormal basis elements e 𝑗 ∈ G 2n as…”

The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

“…Initially, in the quantum field theory, spinors were considered mainly in the framework of the Dirac matrix theory of spinors. The modern theory of spinors is usually formulated within the framework of the Clifford algebra formalism [30][31][32][33][34][35][36][37][38][39]. Such spinors are called algebraic.…”