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Gate fidelity of self-adjoint gates constrained by conservation laws | | Tokishiro Karasawa
; Julio Gea-Banacloche
; Masanao Ozawa
; | | Date: |
18 Sep 2008 | | Abstract: | Recent investigations show that conservation laws limit the accuracy of gate
operations in quantum computing. The inevitable error under the angular
momentum conservation law has been evaluated so far for the CNOT, Hadamard, and
NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we
consider arbitrary self-adjoint gates under arbitrary conservation laws from a
geometrical point of view. A lower bound of the gate infidelity, one minus the
squared gate fidelity, is obtained to be inversely proportional to the squared
size of the controller and proportional to the squared sine of 2 times the
relative angle between the axes of rotations on the Bloch sphere generated by
the conserved quantity and the gate operation. Taking all the directions into
account, we conclude that no self-adjoint gate on a spin 1/2 qubit can be
implemented with a gate infidelity less than $(4+4N^{2})^{-1}$ by any
rotationally invariant interaction with a spin N/2 ancilla. In the case where
the above axes are orthogonal like the NOT gate, the above bound vanishes, but
by further elaborations the gate infidelity is shown to have another non
vanishing lower bound. | | Source: | arXiv, 0809.3095 | | Services: | Forum | Review | PDF | Favorites | |
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