The resonant exchange (RX) qubit is a promising variant of the exchange-only spin qubit in a triple quantum dot which responds to a narrow-band resonant frequency. But the advantage of a permanently applied exchange splitting for spin control generally entails an increased susceptibility to charge noise. We have investigated the influence of electrical charge noise on a resonant exchange (RX) qubit by taking into account uncorrelated noise in each quantum dot, giving rise to two independent noisy bias parameters e and ∆ [1]. Calculating the energy splitting of the two qubit states as a function of these two bias detuning parameters, we have identified sweet spots, where the qubit is least susceptible to noise. Our investigation shows that the sweet spots exist within the low-bias regime, in which the bias detuning parameters have the same magnitude as the hopping parameters between the dots. By calculating and comparing the charge dephasing rates at the various operating points of the RX qubit, we identify a new favorable operating regime for the RX qubit in the case of weak noise, based on these double sweet spots. In contrast, spin noise can be mitigated using exchange-based dynamical decoupling sequences that have been optimized using two different strategies, Uhrig dynamical decoupling (UDD) and optimized filter function dynamical decoupling (OFDD) [2]. Finally, we give a brief outlook towards the possibility of long-distance coupling between resonant exchange qubits mediated by a microwave cavity [3]. [1] M. Russ and G. Burkard, Phys. Rev. B 91, 235411 (2015). [2] N. Rohling and G. Burkard, arXiv:1510.04098. [3] M. Russ and G. Burkard, Phys. Rev. B (accepted) [arXiv:1508.07122].
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 ${\ensuremath{\varepsilon}}_{M}$.
A triple-quantum-dot system can be operated as either an exchange-only qubit or a resonant-exchange qubit. While it is generally believed that the decisive advantage of the resonant-exchange qubit is the suppression of charge noise because it is operated at a sweet spot, we show that the leakage is also an important factor. Through molecular-orbital-theoretic calculations, we show that when the system is operated in the exchange-only scheme, the leakage to states with double electron occupancy in quantum dots is severe when rotations around the axis ${120}^{\ensuremath{\circ}}$ from $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ is performed. While this leakage can be reduced by either shrinking the dots or separating them further, the exchange interactions are also suppressed at the same time, making the gate operations unfavorably slow. When the system is operated as a resonant-exchange qubit, the leakage is three to five orders of magnitude smaller. We have also calculated the optimal detuning point which minimizes the leakage for the resonant-exchange qubit, and have found that although it does not coincide with the double sweet spot for the charge noise, they are rather close. Our results suggest that the resonant-exchange qubit has another advantage, that leakage can be greatly suppressed compared to the exchange-only qubit, and operating at the double sweet spot point should be optimal both for reducing charge noise and suppressing leakage.
The energy landscape of a single electron in a triple quantum dot can be tuned such that the energy separation between ground and excited states becomes a flat function of the relevant gate voltages.These so-called sweet spots are beneficial for charge coherence since the decoherence effects caused by small fluctuations of gate voltages or surrounding charge fluctuators are minimized.We propose a new operation point for a triple quantum dot charge qubit, a so-called CQ 3 -qubit, having a third-order sweet spot.We show strong coupling of the qubit to single photons in a frequency tunable high-impedance SQUID-array resonator.In the dispersive regime, we investigate the qubit linewidth in the vicinity of the proposed operating point.In contrast to the expectation for a higher-order sweet spot, we there find a local maximum of the linewidth.We find that this is due to a non-negligible contribution of noise on the quadrupolar detuning axis not being in a sweet spot at the proposed operating point.While the original motivation to realize a low-decoherence charge qubit was not fulfilled, our analysis provides insights into charge decoherence mechanisms relevant also for other qubits.
In the semiconductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so-called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double quantum dot systems allow the implementation of exchange gates with controllable exchange splitting
J operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot,
J can be quenched to a value smaller than the intradot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit.
Optimal working points or ``sweet spots'' have arisen as an important tool for mitigating charge noise in quantum dot logical spin qubits. The exchange-only qubit provides an ideal system for studying this effect because
Z rotations are performed directly at the sweet spot, while
X rotations are not. Here, we quantify the ability of the sweet spot to mitigate charge noise by treating
X and
Z rotations on an equal footing. Specifically, we optimize
X rotations and determine an upper bound on their fidelity. We find that sweet spots offer a fidelity improvement factor of at least 20 for typical GaAs devices, and more for Si devices.