A remark on the unitary group of a tensor product of n finite-dimensional Hilbert spaces

Parthasarathy, K. R. (2003) A remark on the unitary group of a tensor product of n finite-dimensional Hilbert spaces Proceedings of the Indian Academy of Sciences Mathematical Sciences, 113 (1). pp. 3-13. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/mathsci/vol113/feb2003/Pm1984...

Related URL: http://dx.doi.org/10.1007/BF02829676

Abstract

Let H i, 1 ≤ i ≤n be complex finite-dimensional Hilbert spaces of dimension di,1 ≤ i ≤ n respectively with di ≥ 2 for every i. By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product H =H1 ⊗ H2 ⊗... ⊗ Hn can be expressed as a composition of a finite number of unitary operators living on pair products Hi ⊗ Hj,1 ≤i,j ≤ n. An estimate of the number of operators appearing in such a composition is obtained.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:n-Qubit Quantum Computer; Qubits; Gates; Controlled Gates
ID Code:36150
Deposited On:25 May 2011 13:36
Last Modified:17 May 2016 19:07

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