Few-body spin couplings and their implications for universal quantum computation

Electron spins in semiconductor quantum dots are promising candidates for the experimental realization of solid-state qubits. We analyze the dynamics of a system of three qubits arranged in a linear geometry and a system of four qubits arranged in a square geometry. Calculations are performed for several quantum dot confining potentials. In the three-qubit case, three-body effects are identified that have an important quantitative influence upon quantum computation. In the four-qubit case, the full Hamiltonian is found to include both three-body and four-body interactions that significantly influence the dynamics in physically relevant parameter regimes. We consider the implications of these results for the encoded universality paradigm applied to the four-electron qubit code; in particular, we consider what is required to circumvent the four-body effects in an encoded system (four spins per encoded qubit) by the appropriate tuning of experimental parameters.Comment: 1st version: 33 pages, 25 figures. Described at APS March Meeting in 2004 (P36.010) and 2005 (B17.00009). Most figures made uglier here to reduce file size. 2nd version: 19 pages, 9 figures. Much mathematical detail chopped away after hearing from journal referee; a few typos correcte

Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding

The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and practical interest. Understanding the invariance of a set of states under certain transformations is mutually associated with a better understanding of some fundamental aspects of quantum mechanics as well as the practical utility of invariant subsystems. For example, DFS/NSs are potentially useful for protecting quantum information in quantum cryptography and quantum computing as well as enabling universal computation. Here we discuss transformations which are compatible with a DFS/NS that is composed of d-state systems which protect against collective noise. They are compatible in the sense that they do not take the logical (encoded) states outside of the DFS/NS during the transformation. Furthermore, it is shown that the Hamiltonian evolutions derived here can be used to perform universal quantum computation on a three qudit DFS/NS. Many of the methods used in our derivations are directly applicable to a large variety of DFS/NSs. More generally, we may also state that these transformations are compatible with collective motions.Comment: 30 pages, replaced with published versio