{"product_id":"synthesis-of-quantum-circuits-vs-synthesis-of-classical-reversible-circuits-von-alexis-de-vos-yvan-van-rentergem-und-stijn-de-baerdemacker","title":"Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits","description":"At first sight, quantum computing is completely different from classical computing. Nevertheless, a link is provided by reversible computation.\u003cp\u003e\u003c\/p\u003e\nWhereas an arbitrary quantum circuit, acting on ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)).\u003cp\u003e\u003c\/p\u003e\nBoth the synthesis of a reversible logic circuit and the synthesis of a quantum logic circuit take advantage of the decomposition of a matrix: the former of a permutation matrix, the latter of a unitary matrix. In both cases the decomposition is into three matrices. In both cases the decomposition is not unique.\u003cp\u003e\u003c\/p\u003e\n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031798948\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031798948","offer_id":40176193437789,"sku":"9783031798948","price":64.19,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/bcc667ed-4233-438f-a490-5d41f1ad684e.jpg?v=1775795882","url":"https:\/\/shop.autorenwelt.de\/products\/synthesis-of-quantum-circuits-vs-synthesis-of-classical-reversible-circuits-von-alexis-de-vos-yvan-van-rentergem-und-stijn-de-baerdemacker","provider":"Autorenwelt Shop","version":"1.0","type":"link"}