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

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    • Keywords


      n-qubit quantum computer; qubits; gates; controlled gates

    • Abstract


      LetHi, 1 ≤ i ≤n be complex finite-dimensional Hilbert spaces of dimension di,1 ≤ i ≤n respectively withdi ≥ 2 for everyi. 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 productH =H1H2 ⊗... ⊗Hn can be expressed as a composition of a finite number of unitary operators living on pair productsHiHj,1 ≤i,jn. An estimate of the number of operators appearing in such a composition is obtained.

    • Author Affiliations


      K R Parthasarathy1

      1. Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi - 110 016, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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