منابع مشابه
The Category CNOT
We exhibit a complete set of identities for CNOT, the symmetric monoidal category generated by the controlled-not gate, the swap gate, and the computational ancillæ. We prove that CNOT is a discrete inverse category. Moreover, we prove that CNOT is equivalent to the category of partial isomorphisms of finitely-generated non-empty commutative torsors of characteristic 2. Equivalently this is the...
متن کاملAsymptotic bounds of depth for the reversible circuit consisting of NOT, CNOT and 2-CNOT gates
The paper discusses the asymptotic depth of a reversible circuit consisting of NOT, CNOT and 2-CNOT gates. Reversible circuit depth function $D(n, q)$ for a circuit implementing a transformation $f\colon \mathbb Z_2^n \to \mathbb Z_2^n$ is introduced as a function of $n$ and the number of additional inputs $q$. It is proved that for the case of implementing a permutation from $A(\mathbb Z_2^n)$...
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The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates. Though this decomposition has been known for at least 10 years, we provide here the first demonstration of its CNOT-optimality. ...
متن کاملOn the CNOT-cost of the TOFFOLI gate
Three-input TOFFOLI gates are heavily used when performing classical logic operations on quantum data, e.g., in reversible arithmetic circuits. However, in physical implementations TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates. Though this decomposition has been known for at least 10 years, we provide here the first demonstration of its CNOT-optimality. We first p...
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In this paper first we define the morphism between geometric spaces in two different types. We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories, for instance $uu$ is topological. The relation between hypergroups and geometric spaces is studied. By constructing the category $qh$ of $H_{v}$-groups we answer the question...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2018
ISSN: 2075-2180
DOI: 10.4204/eptcs.266.18