Details
| Original language | English |
|---|---|
| Pages (from-to) | 112104, 21 |
| Journal | J. Math. Phys. |
| Volume | 49 |
| Issue number | 11 |
| Publication status | Published - 2008 |
Abstract
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In: J. Math. Phys., Vol. 49, No. 11, 2008, p. 112104, 21.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the structure of Clifford quantum cellular automata
AU - Schlingemann, Dirk-M.
AU - Vogts, Holger
AU - Werner, Reinhard F.
N1 - Funding information: H.V. is supported by the DFG Forschergruppe 635. 1
PY - 2008
Y1 - 2008
N2 - We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. In the one-dimensional (1D) case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton time step, thereby characterizing this class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions.
AB - We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. In the one-dimensional (1D) case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton time step, thereby characterizing this class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions.
U2 - 10.1063/1.3005565
DO - 10.1063/1.3005565
M3 - Article
VL - 49
SP - 112104, 21
JO - J. Math. Phys.
JF - J. Math. Phys.
SN - 1089-7658
IS - 11
ER -