2000/01/27 by Alexander Yu. Vlasov, Vlasov, Alexander Yu.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0001100
12 pages LaTeXe, (v2: eq.12 corrected, v3: minor changes)
openalex publication_date 2000/01/27 · arxiv created 2000/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The canonical anticommutation relations (CAR) for fermion systems can be represented by finite-dimensional matrix algebra, but it is impossible for canonical commutation relations (CCR) for bosons. After description of more simple case with representation of CAR and (bounded) quantum computational networks via Clifford algebras in the paper are discussed CCR. For representation of the algebra it is not enough to use quantum networks with fixed number of qubits and it is more convenient to consider Turing machine with essential operation of appending new cells for description of infinite tape in finite terms --- it has straightforward generalization for quantum case, but for CCR it is necessary to work with symmetrized version of the quantum Turing machine. The system is called here quantum abacus due to understanding analogy with the ancient counting devices (abacus).