Theory of decoherencefree faulttolerant universal quantum computation
Abstract
Universal quantum computation on decoherencefree subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherencefree (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the systembath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural faulttolerant computation) can be performed using only twobody interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one or twobody interactions must leave the code space during the ontime of the faulttolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.
 Publication:

Physical Review A
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevA.63.042307
 arXiv:
 arXiv:quantph/0004064
 Bibcode:
 2001PhRvA..63d2307K
 Keywords:

 03.67.Lx;
 03.65.Ta;
 03.65.Fd;
 89.70.+c;
 Quantum computation;
 Foundations of quantum mechanics;
 measurement theory;
 Algebraic methods;
 Information theory and communication theory;
 Quantum Physics
 EPrint:
 40 pages (body: 30, appendices: 3, figures: 5, references: 2). Fixed problem with nonprinting figures. New references added, minor typos corrected