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Engineering of arbitrary U(N) transformations by quantum Householder reflection | | P. A. Ivanov
; E. S. Kyoseva
; N. V. Vitanov
; | | Date: |
21 Aug 2007 | | Abstract: | We propose a simple physical implementation of the quantum Householder
reflection (QHR) M(v)=I-2|v><v| in a quantum system of N degenerate states
(forming a qunit) coupled simultaneously to an ancillary (excited) state by N
resonant or nearly resonant pulsed external fields. We also introduce the
generalized QHR M(v;k)=I+(exp{ik}-1)|v><v|, which can be produced in the same
N-pod system when the fields are appropriately detuned from resonance with the
excited state. We use these two operators as building blocks in constructing
arbitrary preselected unitary transformations. We show that the most general
U(N) transformation can be factorized (and thereby produced) by either N-1
standard QHRs and an N-dimensional phase gate, or N-1 generalized QHRs and a
one-dimensional phase gate. Viewed mathematically, these QHR factorizations
provide parametrizations of the U(N) group. As an example, we propose a recipe
for constructing the quantum Fourier transform (QFT) by at most N interaction
steps. For example, QFT requires a single QHR for N=2, and only two QHRs for
N=3 and 4. | | Source: | arXiv, 0708.2811 | | Services: | Forum | Review | PDF | Favorites | |
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