Programme
Thomas Coudreau
( LMPQ, Universite Paris Diderot )
" Robust preparation, manipulation, and read-out of topologically protected qubits
"
Quantum error correcting codes are deemed a crucial tool for the implementation of quantum algorithms. They also provide a useful framework to design error resistant physical systems. It has thus recently been shown that specific, highly symmetric, Hamiltonians operating on well chosen physical qubits can reduce exponentially the influence of decoherence on logical qubits and quantum gates. In such systems, the logical qubit is protected from any local noise by a set of non-local symmetries. We have shown that it is possible to implement logical qubits which are naturally immune to decoherence using an array of trapped ions submitted to laser light. It is usually recognized that logical qubits should verify the so-called di Vincenzo criteria. In particular, it is necessary to be able to intialize, manipulate and measure them. For a protected qubit, there is an apparent conflict between the protection and the ability to manipulate the qubit. We show here how to overcome this difficulty using time varying Hamiltonians. Using numerical simulations, we also take into account explicitly the effect of random noise during all these processes. We stress that this implementation is not limited to trapped ions because it relies only on the possibility to apply Hamiltonians that contain only single-site and binary interactions. We start by recalling the properties of the long range Hamiltonian. The protected states are complex, multi-particle entangled states which can not be prepared, manipulated nor measured easily. We describe a specific initialization scheme which can be used to prepare the system in a given state of the degenerate subspace which we denote |0
L> . We then introduce an original scheme which allows to perform an arbitrary rotation within the protected subspace spanned by the logical qubits states {|0
L> , |1
L> }. The question of measurement is thus crucial. Based on error correction techniques, we suggest a measurement strategy that can be implemented using only local measurements.