On multi--qubit decoherence
Daniel Braun · 2005
Decoherence, i.e. the decay of coherences in a quantum system due to the coupling to an environment with many uncontrolled degrees of freedom, plays a key role in the transition from quantum mechanics to classical mechanics. Decoherence is also one of the main obstacles on the road to a large scale quantum computer, and the question whether or not one will be able in principle to maintain and manipulate coherent superpositions of an exponentially large number of states of a few thousand qubits, has become of fundamental interest. Here I show that the decoherence of superpositions of many-qubit code words in a quantum memory is governed by a generalized Hamming distance (called ``decoherence metric'') between the code words, with a time dependent metric tensor that is specific for the heat bath. The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of code-words, and for an optimization of the over-all decoherence. I apply the theory to quantum memories based on neutral atoms in optical lattices and in atomic gases, interacting with black body radiation as source of decoherence. Additional atoms, which are not addressed in the memory, can become an important source of decoherence.