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- aggregation classification "A1".
- aggregation creator person.
- aggregation creator person.
- aggregation creator person.
- aggregation date "2012".
- aggregation format "application/pdf".
- aggregation hasFormat 5831878.bibtex.
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- aggregation isPartOf urn:issn:1542-3980.
- aggregation language "eng".
- aggregation rights "I have transferred the copyright for this publication to the publisher".
- aggregation subject "Mathematics and Statistics".
- aggregation title "Reversible computation, quantum computation and computer architectures in between".
- aggregation abstract "Thanks to the cosine-sine decomposition of unitary matrices, an arbitrary quantum circuit, acting on w qubits, can be decomposed into 2(w) - 1 elementary quantum gates, called controlled V gates. Thanks to the Birkhoff decomposition of doubly stochastic matrices, an arbitrary (classical) reversible circuit, acting on w bits, can be decomposed into 2(w) - 1 elementary gates, called controlled NOT gates. The question arises under which conditions these two synthesis methods are applicable for intermediate cases, i.e. computers based on some group, which simultaneously is a subgroup of the unitary group U(2(w)) and a supergroup of the symmetric group S(2w). It turns out that many groups either belong to a class that might have a cosine-sine-like decomposition but no Birkhoff-like decomposition and a second class that might have both decompositions. For an arbitrary group, in order to find out to which class it belongs, it suffices to evaluate a function phi(m), deduced either from its order (in case of a finite group) or from its dimension (in case of a Lie group). Here m = 2(w) is the degree of the group.".
- aggregation authorList BK1319772.
- aggregation endPage "81".
- aggregation issue "1".
- aggregation startPage "67".
- aggregation volume "18".
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