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.

Artificial quantum-dot helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

“…3,4,5 Along with fundamental interest in the properties of such systems, and as a test ground for highly correlated electrons, a major motivation for these growing endeavors has been the promising outlook and potential of quantum dots concerning the implementation of solid-state quantum computing and quantum information devices. 6,7,8,9,10 To this effect highly precise control of the space and spin degrees of freedom of a small number N of confined electrons (down to an empty 11,12,13 QD) needs to be achieved, and experimentally this was demonstrated recently for two electrons in a lateral double quantum dot molecule (see Ref. 2, and references therein).…”

Quadrupolar Exchange-Only Spin Qubit

“…For this implementation it is essential to be able to tune the qubit near resonance to fulfill Ω = ±(ω res − ω D ) while simultaneously matching ω D = ω q , therefore, requiring a large and controllable qubit splitting. Alternative two-qubit coupling schemes include exchange-based interaction [60,61] and capacitative coupling [41,65]. Discussion In summary, we have proposed a quadrupolar exchange (QUEX) spin qubit that uses the spin of four electrons in a TQD and gives rise to a large controllable qubit splitting.…”

Linear combination of harmonic orbitals and configuration interaction method for the voltage control of exchange interaction in gated lateral quantum dot networks

“…This dependence was studied, e.g., by Scarola and Das Sarma, 21 who used the Hubbard, variational, and exact diagonalization approaches to demonstrate that the three-spin model is valid only for a limited range of triple-dot parameters. Mizel and Lidar [14][15][16] arrived at similar conclusions using the Heitler-London and Hund-Mülliken schemes to calculate the energy levels of three coupled dots with one electron per dot. In both cases, the many-body effects were responsible for the appearance of higher-order terms in the effective spin Hamiltonian.…”