Proposal for a geometric algebra software package
ACM SIGSAM Bulletin
Clifford algebras with numeric and symbolic computations
Clifford algebras with numeric and symbolic computations
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Clifford Algebraic Calculus for Geometric Reasoning with Application to Computer Vision
Selected Papers from the International Workshop on Automated Deduction in Geometry
Computational Synthetic Geometry with Clifford Algebra
Selected Papers from the International Workshop on Automated Deduction in Geometry
Some Applications of Clifford Algebra to Geometries
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Clifford Term Rewriting for Geometric Reasoning in 3D
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
IEEE Transactions on Information Theory
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A qubit is a two-state quantum system, in which one bit of binary information can be stored and recovered. A qubit differs from an ordinary bit in that it can exist in a complex linear combination of its two basis states, where combinations differing by a factor are identified. This projective line, in turn, can be regarded as an entity within a Clifford or geometric algebra, which endows it with both an algebraic structure and an interpretation as a Euclidean unit 2-sphere. Testing a qubit to see if it is in a basis state generally yields a random result, and attempts to explain this in terms of random variables parametrized by the points of the spheres of the individual qubits lead to contradictions. Geometric reasoning forces one to the conclusion that the parameter space is a tensor product of projective lines, and it is shown how this structure is contained in the tensor product of their geometric algebras.