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Smaller Circuits for Arbitrary n-qubit Diagonal Computations | | Stephen S. Bullock
; Igor L. Markov
; | | Date: |
7 Mar 2003 | | Journal: | Quantum Information & Computation, vol 4, no 1, 027-047 (2004) | | Subject: | quant-ph | | Abstract: | A unitary operator U=sum u_{j,k} |k> ; 0 <= j <= 2^n-1}. These relative phases are often required in applications. Constructing quantum circuits for diagonal computations using standard techniques requires either O(n^2 2^n) controlled-not gates and one-qubit Bloch sphere rotations or else O (n 2^n) such gates and a work qubit. This work provides a recursive, constructive procedure which inputs the matrix coefficients of U and outputs such a diagram containing 2^{n+1}-3 alternating controlled-not gates and one-qubit z-axis Bloch sphere rotations. Up to a factor of two, these circuits are the smallest possible. Moreover, should the computation U be a tensor of diagonal one-qubit computations of the form R_z(alpha)=e^{-i alpha/2}|0><0|+ e^{i alpha/2} |1><1|, then a cancellation of controlled-not gates reduces our circuit to that of an n-qubit tensor. | | Source: | arXiv, quant-ph/0303039 | | Services: | Forum | Review | PDF | Favorites | |
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