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arXiv:1711.06418 · Physical Review A

Leakage and sweet spots in triple-quantum-dot spin qubits: A molecular-orbital study

Chengxian Zhang, Xu-Chen Yang, Xin Wang

Published Apr 16, 2018• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.042326

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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∘{120}^{\ensuremath{\circ}}120\ensuremath∘ from z\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}z\ifmmode^\elseˆ\fi 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 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].
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 ZZZ rotations are performed directly at the sweet spot, while XXX rotations are not. Here, we quantify the ability of the sweet spot to mitigate charge noise by treating XXX and ZZZ rotations on an equal footing. Specifically, we optimize XXX 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.
We investigate the influence of electrical charge noise on a resonant exchange (RX) qubit in a triple quantum dot. This RX qubit is a variation of the exchange-only spin qubit which responds to a narrow-band resonant frequency. Our noise model includes uncorrelated charge noise in each quantum dot giving rise to two independent (noisy) bias parameters $\ensuremath{\varepsilon}$ and $\mathrm{\ensuremath{\Delta}}$. We calculate the energy splitting of the two qubit states as a function of these two bias detuning parameters to find ``sweet spots,'' where the qubit is least susceptible to noise. Our investigation shows that such sweet spots exist within the low-bias regime, in which the bias detuning parameters have the same magnitude as the hopping parameters. The location of the sweet spots in the $(\ensuremath{\varepsilon},\mathrm{\ensuremath{\Delta}})$ plane depends on the hopping strength and asymmetry between the quantum dots. In the regime of weak charge noise, we identify a new favorable operating regime for the RX qubit based on these sweet spots.
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.
Abstract The implementation of high fidelity two-qubit gates is a bottleneck in the progress toward universal quantum computation in semiconductor quantum dot qubits. We study capacitive coupling between two triple quantum dot spin qubits encoded in the S = 1/2, Sz = −1/2 decoherence-free subspace—the exchange-only (EO) spin qubits. We report exact gate sequences for CPHASE and CNOT gates, and demonstrate theoretically, the existence of multiple two-qubit sweet spots (2QSS) in the parameter space of capacitively coupled EO qubits. Gate operations have the advantage of being all-electrical, but charge noise that couple to electrical parameters of the qubits cause decoherence. Assuming noise with a 1/f spectrum, two-qubit gate fidelities and times are calculated, which provide useful information on the noise threshold necessary for fault-tolerance. We study two-qubit gates at single and multiple parameter 2QSS. In particular, for two existing EO implementations—the resonant exchange (RX) and the always-on exchange-only (AEON) qubits—we compare two-qubit gate fidelities and times at positions in parameter space where the 2QSS are simultaneously single-qubit sweet spots (1QSS) for the RX and AEON. These results provide a potential route to the realization of high fidelity quantum computation.
The exchange interaction in a singlet-triplet qubit defined by two-electron states in the double-quantum-dot system (``two-electron singlet-triplet qubit'') typically varies monotonically with the exchange interaction and thus carries no sweet spot. Here we study a singlet-triplet qubit defined by four-electron states in the double-quantum-dot system (``four-electron singlet-triplet qubit''). We demonstrate, using configuration-interaction calculations, that in the four-electron singlet-triplet qubit the exchange energy as a function of detuning can be nonmonotonic, suggesting existence of sweet spots. We further show that the tuning of the sweet spot and the corresponding exchange energy by perpendicular magnetic field can be related to the variation of orbital splitting. Our results suggest that a singlet-triplet qubit with more than two electrons can have advantages in the realization of quantum computing.