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

Abstract

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.

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 corrected

References in corpus (8)

• Decoherence-Free Subspaces and Subsystems
• Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots
• The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model
• Chirality in Quantum Computation with Spin Cluster Qubits
• Exchange Interaction Between Three and Four Coupled Quantum Dots: Theory and Applications to Quantum Computing
• Three and Four-Body Interactions in Spin-Based Quantum Computers
• Decoherence, Control, and Symmetry in Quantum Computers
• Oxide-Semiconductor Materials for Quantum Computation

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• A Scalable Architecture for Coherence-Preserving Qubits
• Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
• Quantum group deformation of the Kittel--Shore model
• The Spin Density Matrix I: General Theory and Exact Master Equations
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior