Serial triple quantum dot (STQD) systems have received extensive attention in the past decade, not only because quantum dot scaling up is an indispensable ingredient for integrations, but also due to the fact that specific charge states of STQD can be employed to achieve fast full-electrical manipulation of spin qubits. For the latter, a comprehensive understanding of the relationship between neighboring charge occupancy states of STQD is essential for three-electron exchange-only spin qubit-based quantum computations. Charge stability diagram is usually employed to map out the charge occupation states about the plunger gate voltages of STQDs and to study the degeneracy among charge occupation states. Experimentally, two- rather than three-dimensional charge stability diagram was obtained in a lot of early studies by keeping one of plunger gates unchanged to reduce complexity. The obtained two-dimensional diagram can only provide limited information and is subject to blurred boundary of charge occupation states due to the low tunneling current and the energy level broading effects. It is, therefore, challenge to searching for the working points where quantum manipulation can be performed promptly and accurately. In principle, three-dimensional charge occupation stability diagram can be efficiently constructed by numerical simulations based on constant interaction (CI) model. In this study, we calculate the electrochemical potential of STQD about three plunger gate voltages by using the CI model-based capacitance network to reproduce any desired two-dimensional charge stability diagram. The simulated diagram not only well accords with the diagrams obtained from the early experimental data of STQD, but also provides high clarity of the charge state boundaries with tunable parameters. The systematical study of two-dimensional charge stability diagram reviews the energy degeneracy triple and quadruple points of STQD charge occupation states and concludes the energy degeneracy points in three types to compare with experimental data. For each of the energy degeneracy points, we discuss both the electron and hole transport by using the electrochemical potential alignment schematics. We reveal the common and unique triple points of STQD in comparison with those of double quantum dot. The quadruple points of STQD are also addressed in the manipulation of quantum cellular automata and quantum logical gate. The comprehensive understanding of these energy degeneracy points can efficiently guide experiments to build an optimal working point of the STQD system for quantum computations and simulations.
We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with
N=3 electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.
Charge detection utilizing a highly biased quantum point contact has become the most effective probe for studying few electron quantum dot circuits. Measurements on double and triple quantum dot circuits is performed to clarify a back action role of charge sensing on the confined electrons. The quantum point contact triggers inelastic transitions, which occur quite generally. Under specific device and measurement conditions these transitions manifest themselves as bounded regimes of telegraph noise within a stability diagram. A nonequilibrium transition from artificial atomic to molecular behavior is identified. Consequences for quantum information applications are discussed.
An all electrical manipulation with singlet and triplet states of an electron pair in a quadruple quantum dot (QD) has been studied by a configuration interaction method. We have investigated two nanodevices that consist of four weakly coupled lateral QDs, in which the electron localization can be changed by tuning the external voltages: the gate voltage in the first nanodevice and the source-drain voltage in the second. The electrons that---in the initial state---singly occupy the two identical input QDs are transferred to the two asymmetric output QDs by the sufficiently high electric field. We have shown that---for the QDs with suitably chosen parameters---the localization of the electrons in the output QDs depends on the spin states of the electron pair and the final spin state can be uniquely determined by a single-shot measurement of the electric charge gathered in only one of the output QDs. This leads to a possibility of performing the controlled operations on the electron-spin qubits in the quadruple QDs. We have found that the classical exclusive OR (XOR) logic gate can be performed with the electric field-induced transitions and the output read out by the spin-to-charge conversion.
We investigate the behavior of qubits consisting of three electron spins in double and triple quantum dots subject to external electric fields. Our model includes two independent bias parameters, $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}_{M}$, which both couple to external electromagnetic fields and can be controlled by gate voltages applied to the quantum dot structures. By varying these parameters, one can switch the qubit type by shifting the energies in the single quantum dots, thus changing the electron occupancy in each dot. Starting from the asymmetric resonant exchange qubit with a (2,0,1) and (1,0,2) charge admixture, one can smoothly cross over to the resonant exchange qubit with a detuned (1,1,1) charge configuration, and to the exchange-only qubit with the same charge configuration but equal energy levels down to the hybrid qubits with (1,2,0) and (0,2,1) charge configurations. Here,
(l,m,n) describes a configuration with
l electrons in the left dot,
m electrons in the center dot, and
n electrons in the right dot. We first focus on random electromagnetic field fluctuations, i.e., ``charge noise,'' at each quantum dot resulting in dephasing of the qubit, and we provide a complete map of the resulting dephasing time as a function of the bias parameters. We pay special attention to the so-called sweet spots and double sweet spots of the system, which are least susceptible to noise. In the second part, we investigate the coupling of the qubit system to the coherent quantized electromagnetic field in a superconducting strip-line cavity, and we also provide a complete map of the coupling strength as a function of the bias parameters. We analyze the asymmetric qubit-cavity coupling via $\ensuremath{\varepsilon}$ and the symmetric coupling via ${\ensuremath{\varepsilon}}_{M}$.
Superexchange is one of the vital resources to realize long-range interaction between distant spins for large-scale quantum computing. Recent experiments have demonstrated coherent oscillations between logical states defined by remote spins whose coupling is given by the superexchange interaction mediated by central spins. Excavating the potential of superexchange requires a full understanding of the interaction in terms of control parameters, which is still lacking in literature. Here, using full configuration interaction calculations, we study a two-electron system in a linear triple-quantum-dot device in which the left and right dots are occupied by a single electron each, whose spin states are defined as qubits. The numerical nature of the full configuration interaction calculations allows access to the microscopic details of the quantum-dot confining potential and electronic wave functions, some of which are overlooked in the celebrated Hubbard model but turn out to be critical for the behavior of superexchange. Following experimental demonstrations of superexchange interactions, we focus on the detuning regime where the charge ground state yields an empty middle dot. We have found that, when the detunings at the left and right dots are leveled, the superexchange can exhibit a nonmonotonic behavior, which ranges from positive to negative values as a function of the middle-dot detuning. We further show that a larger relative detuning between the left and right dots causes the magnitude of the superexchange to increase (decrease) for an originally positive (negative) superexchange. We then proceed to show the results for a much larger left-right dot detuning. Using a Hubbard-like model, we present analytical expressions of the superexchange and have found that they conform well qualitatively with the numerical results. Our results suggest that even a simple configuration of delocalized two-electron states in a linear triple-quantum-dot device exhibits superexchange energy with nontrivial behaviors, which could have important applications in spin-based quantum computing.