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We propose an experimental scheme to simulate the dynamical quantum Hall effect and the related interactioninduced topological transition with a superconducting-qubit array. We show that a one-dimensional Heisenberg model with tunable parameters can be realized in an array of superconducting qubits. The quantized plateau, which is a feature of the dynamical quantum Hall effect, will emerge in the Berry curvature of the superconducting qubits as a function of the coupling strength between nearest-neighbor qubits. We numerically calculate the Berry curvatures of two-, four-, and six-qubit arrays and find that the interaction-induced topological transition can be easily observed with the simplest two-qubit array. Furthermore, we analyze some practical conditions in typical experiments for observing this dynamical quantum Hall effect. [ABSTRACT FROM AUTHOR]

It has been recently demonstrated that a singlet-triplet spin qubit in semiconductor double quantum dots can be controlled by changing the height of the potential barrier between the two dots ("barrier control"), which has led to a considerable reduction of charge noises as compared with the traditional tilt control method. In this paper we show, through a molecular-orbital-theoretic calculation of double quantum dots influenced by a charged impurity, that the relative charge noise for a system under the barrier control not only is smaller than that for the tilt control but actually decreases as a function of an increasing exchange interaction. This is understood as a combined consequence of the greatly suppressed detuning noise when the two dots are symmetrically operated, as well as an enhancement of the interdot hopping energy of an electron when the barrier is lowered which in turn reduces the relative charge noise at large exchange interaction values. We have also studied the response of the qubit to charged impurities at different locations and found that the improvement of barrier control is least for impurities equidistant from the two dots due to the small detuning noise they cause but is otherwise significant along other directions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin-qubit system. We consider 1/f noises having spectra proportional to 1/ωα, where the exponent α indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of randomized benchmarking and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for α≳1.5, the dynamically corrected gates offer a considerable reduction in the gate error and such a reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for α≲1.5. This critical value of αc≈1.5 is larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits. [ABSTRACT FROM AUTHOR]