We consider a system of two purely capacitively coupled singlet-triplet qubits and numerically simulate the energy structure of four electrons in two double quantum dots with a large potential barrier between them. We calculate the interqubit coupling strength using an extended Hund-Mulliken approach which includes excited orbitals in addition to the lowest-energy orbital for each quantum dot. We show the coupling strength as a function of the qubit separation as well as plotting it against the detunings of the two double quantum dots and show that the general qualitative features of our results can be captured by a potential-independent toy model of the system.
We consider a system of two purely capacitively coupled singlet-triplet qubits and numerically simulate the energy structure of four electrons in two double quantum dots with a large potential barrier between them. We calculate the interqubit coupling strength using an extended Hund-Mulliken approach which includes excited orbitals in addition to the lowest-energy orbital for each quantum dot. We show the coupling strength as a function of the qubit separation as well as plotting it against the detunings of the two double quantum dots and show that the general qualitative features of our results can be captured by a potential-independent toy model of the system.
We present a theoretical study of a four-electron four-quantum-dot system based on molecular-orbital methods, which hosts a pair of singlet-triplet spin qubits. We took into account the admixture of electron wave functions in all dots, and we found that this mixing of wave functions has consequences to the energy spectrum, exchange interaction, and gate crosstalk of the system. Specifically, we found that when the two singlet-triplet qubits are close enough, some of the states are no longer dominated by the computational basis states, and the exchange interaction cannot simply be understood as the energy difference between the singlet and triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters, we characterized the effective exchange interaction of the system, and we found good agreement with results calculated by taking energy differences where applicable. We studied the two commonly conceived schemes coupling two qubits, namely the exchange and capacitive coupling, and we found that when the interqubit distance is at certain intermediate values, the two kinds of coupling are comparable in strength, complicating the analyses of the evolution of the two qubits. We also investigated the gate crosstalk in the system due to the quantum-mechanical mixing of electron states, and we found that while this effect is typically very weak, it should not be ignored if the spacing between the qubits is similar to or less than the distance between the double dots that constitute the qubit.
We investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the ``double charge resonant'' regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well separated from the partially polarized (0211 and 1102) states. A rapid controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing $\ensuremath{\pi}$ pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise---charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction---and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate.
In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling strength are discussed using an accurate microscopic model and exact diagonalization of it. We find that trapezoidal quantum dot formations allow strong coupling with low charge distribution differences between the singlet and triplet states. The analysis of geometry on the capacitative coupling is also extended to the many-qubit case and the creation of cluster states.
We consider qubit coupling resulting from the capacitive coupling between two double quantum dot (DQD) singlet-triplet qubits. Calculations of the coupling when the two DQDs are detuned symmetrically or asymmetrically are performed using a full configuration interaction (CI). The full CI reveals behavior that is not observed by more commonly used approximations such as Heitler London or Hund Mulliken, particularly related to the operation of both DQDs in the (0,2) charge sector. We find that there are multiple points in detuning space where a two-qubit entangling gate can be realized, and that tradeoffs between coupling magnitude and sensitivity to fluctuations in detuning make a case for operating the gate in the (0,2) regime not commonly considered.
The search for a sweet spot, the locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron (``two-electron singlet-triplet qubit''), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots (``four-electron singlet-triplet qubit''). We theoretically demonstrate, using configuration interaction calculations, that sweet spots appear in this coupled qubit system. We further demonstrate that, under realistic charge noise and hyperfine noise, a two-qubit operation at the proposed sweet spot could offer gate fidelities ($\ensuremath{\sim}99%$) that are higher than the conventional two-electron singlet-triplet qubit system ($\ensuremath{\sim}90%$). Our results should facilitate realization of high-fidelity two-qubit gates in singlet-triplet qubit systems.
We theoretically consider the effects of having unintentional charged impurities in laterally coupled two-dimensional double (GaAs) quantum-dot systems, where each dot contains one or two electrons and a single charged impurity. Using molecular orbital and configuration interaction methods, we calculate the effect of the impurity on the two-electron energy spectrum of each individual dot as well as on the spectrum of the coupled-double-dot two-electron system. We find that the singlet-triplet exchange splitting between the two lowest-energy states, both for the individual dots and the coupled-dot system, depends sensitively on the location of the impurity and its coupling strength (i.e. the effective charge). A strong electron-impurity coupling breaks down the equality of the two doubly occupied singlets in the left and the right dots, leading to a mixing between different spin singlets. As a result, the maximally entangled qubit states are no longer fully obtained in the zero-magnetic-field case. Moreover, a repulsive impurity results in a triplet-singlet transition as the impurity effective charge increases or the impurity position changes. We comment on the impurity effect in spin qubit operations in the double-dot system based on our numerical results.