Quantum Gates Between Two Spins in a Triple Dot System with an Empty Dot

We propose a scheme for implementing quantum gates and entanglement between spin qubits in the outer dots of a triple-dot system with an empty central dot. The voltage applied to the central dot can be tuned to realize the gate. Our scheme exemplifies the possibility of quantum gates outside the regime where each dot has an electron, so that spin-spin exchange interaction is not the only relevant mechanism. Analytic treatment is possible by mapping the problem to a t-J model. The fidelity of the entangling quantum gate between the spins is analyzed in the presence of decoherence stemming from a bath of nuclear spins, as well as from charge fluctuations. Our scheme provides an avenue for extending the scope of two qubit gate experiments to triple-dots, while requiring minimal control, namely that of the potential of a single dot, and may enhance the qubit separation to ease differential addressability.Comment: 7 pages, 6 figure

Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling

Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent $\nu \ge 2$ in one dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find $\nu \sim 1$. We introduce the Schmidt gap, new in this context, which scales near the transition with a exponent $\nu > 2$ compatible with the analytical bound. We attribute this to an insensitivity to certain finite size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.Comment: 8 pages, 7 figure

Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions

We put forward a strategy to encode a quantum operation into the unmodulated dynamics of a quantum network without the need of external control pulses, measurements or active feedback. Our optimization scheme, inspired by supervised machine learning, consists in engineering the pairwise couplings between the network qubits so that the target quantum operation is encoded in the natural reduced dynamics of a network section. The efficacy of the proposed scheme is demonstrated by the finding of uncontrolled four-qubit networks that implement either the Toffoli gate, the Fredkin gate, or remote logic operations. The proposed Toffoli gate is stable against imperfections, has a high-fidelity for fault tolerant quantum computation, and is fast, being based on the non-equilibrium dynamics.Comment: 8 pages, 3 figure