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Register a new userOptimal control of universal quantum gates in a double quantum dot
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We theoretically investigate electron spin operations driven by applied electric fields in a semiconductor double quantum dot (DQD). Our model describes a DQD formed in semiconductor nanowire with longitudinal potential modulated by local gating. The eigenstates for two electron occupation, including spin-orbit interaction, are calculated and then used to construct a model for the charge transport cycle in the DQD taking into account the spatial dependence and spin mixing of states. The dynamics of the system is simulated aiming at implementing protocols for qubit operations, that is, controlled transitions between the singlet and triplet states. In order to obtain fast spin manipulation, the dynamics is carried out taking advantage of the anticrossings of energy levels introduced by the spin-orbit and interdot couplings. The theory of optimal quantum control is invoked to find the specific electric-field driving that performs qubit logical operations. We demonstrate that it is possible to perform within high efficiency a universal set of quantum gates ${$CNOT, H$otimes$I, I$otimes$H, T$otimes$I, and T$otimes$I$}$, where H is the Hadamard gate, T is the $pi/8$ gate, and I is the identity, even in the presence of a fast charge transport cycle and charge noise effects.
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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.
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.
By means of optimal control techniques we model and optimize the manipulation of the external quantum state (center-of-mass motion) of atoms trapped in adjustable optical potentials. We consider in detail the cases of both non interacting and interacting atoms moving between neighboring sites in a lattice of a double-well optical potentials. Such a lattice can perform interaction-mediated entanglement of atom pairs and can realize two-qubit quantum gates. The optimized control sequences for the optical potential allow transport faster and with significantly larger fidelity than is possible with processes based on adiabatic transport.
Fernando Galve emph{et al.} $[Phys. Rev. Lett. textbf{110}, 010501 (2013)]$ introduced discording power for a two-qubit unitary gate to evaluate its capability to produce quantum discord, and found that a $pi/8$ gate has maximal discording power. This work analyzes the entangling power of a two-qubit unitary gate, which reflects its ability to generate quantum entanglement in another way. Based on the renowned Cartan decomposition of two-qubit unitary gates, we show that the magic power of the $pi/8$ gate produces maximal entanglement for a general value of purities for two-qubit states.
We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.
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