Expressing the operations of quantum computing in multiparticle geometric algebra

1998/01/03 by Shyamal S. Somaroo, Shyamal Somaroo, David G. Cory +1 · 2 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Arithmetic #Cellular algebra #Clifford algebra #Computational science #Computer science #Filtered algebra #Formalism (music) #Geometric algebra #Mathematics #Molecular spectroscopy and chirality #Multivector #Notation #Operator algebra #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum computer #Quantum mechanics #Theoretical physics #Universal geometric algebra #quant-ph

paper · pdf · doi:10.1016/s0375-9601(98)00010-3

published as Phys.Lett. A240 (1998) 1-7 · RevTeX, 10 pages, no figures; Physics Letters A, in press

arxiv created 1998/01/03 · openalex publication_date 1998/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism of NMR spectroscopy, and hence its notation leads directly to implementations of these operations via NMR pulse sequences.

Citations

• Quaternions as a practical tool for the evaluation of composite rotations
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum Computation

Cited by

• Simulating physical phenomena by quantum networks
• Universal Set of Scalable Dynamically Corrected Gates for Quantum Error Correction with Always-on Qubit Couplings