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--- abstract: 'Identifying and ameliorating dominant sources of decoherence are important steps in understanding and improving quantum systems. Here we show that the free induction decay time ($T_{2}^{*}$) and the Rabi decay rate ($\Gamma_{\mathrm{Rabi}}$) of the quantum dot hybrid qubit can be increased by more than an order of magnitude by appropriate tuning of the qubit parameters and operating points. By operating in the spin-like regime of this qubit, and choosing parameters that increase the qubit’s resilience to charge noise (which we show is presently the limiting noise source for this qubit), we achieve a Ramsey decay time $T_{2}^{*}$ of and a Rabi decay time $1/\Gamma_{\mathrm{Rabi}}$ exceeding $1~\mathrm{\mu s}$. We find that the slowest $\Gamma_{\mathrm{Rabi}}$ is limited by fluctuations in the Rabi frequency induced by charge noise and not by fluctuations in the qubit energy itself.' author: - Brandur Thorgrimsson - Dohun Kim - 'Yuan-Chi Yang' - 'L. W. Smith' - 'C. B. Simmons' - 'Daniel R. Ward' - 'Ryan H. Foote' - 'J. Corrigan' - 'D. E. Savage' - 'M. G. Lagally' - Mark Friesen - 'S. N. Coppersmith' - 'M. A. Eriksson' title: ' **Extending the coherence of a quantum dot hybrid qubit**' --- [^1] Introduction {#introduction .unnumbered} ============ There has been much progress in the development of qubits in semiconductor quantum dots [@Loss:1998p120], making use of one [@Koppens:2006p766; @Simmons:2011p156804; @Pla:2012p489; @Veldhorst:2014p981; @Kawakami:2014p666; @Yoneda:2014p267601; @Veldhorst:2015p410; @Scarlino:2015p106802; @House2016:p044016; @Takeda:2016p1600694], two [@Levy:2002p1446; @Petta:2005p2180; @Foletti:2009p903; @Petersson:2010p246804; @Maune:2012p344; @Wang:2013p046801; @Shi:2013p075416; @Wu:2014p11938; @HarveyCollard:2015preprint], and three quantum dots [@DiVincenzo:2000p1642; @Laird:2010p1985; @Gaudreau:2011p54; @Medford:2013p654; @Eng:2015p1500214; @Russ:2015p235411] to host qubits. Charge noise is often the leading source of decoherence in semiconductor qubits [@Dial:2013p146804], and an advantage of using two or more quantum dots to host a single qubit is the ability to work at sweet spots, a technique pioneered in superconducting qubits [@Vion:2002p886], that make the qubit more resistant to charge noise . In this work we focus on one such qubit, the quantum dot hybrid qubit (QDHQ) [@Shi:2012p140503; @Koh:2013p19695; @Kim:2014p70; @Ferraro:2014p1155; @Mehl:2015preprint; @DeMichielis:2015p065304; @Cao:2016p086801; @Wong:2016p035409; @Chen:2017p035408], which is formed from three electrons in a double quantum dot, and can be viewed as a hybrid of a spin qubit and a charge qubit. Fast, full electrical control of the QDHQ was recently implemented experimentally using ac gating [@Kim:2015p15004], demonstrating a free induction decay (FID) time of 11 ns through operation in the spin-like operating region (see Fig. 1). While QDHQ gating times are fast, substantial further improvements in QDHQ coherence times are required to achieve the high-fidelity gating necessary for fault-tolerant operation [@Fowler:2012p032324]. True sweet spots, which are used to increase resistance to noise and thus increase coherence, are defined by a zero derivative of the qubit energy with respect to a parameter subject to noise. Sweet spots are usually found at specific points of zero extent in parameter space, so that non-infinitesimal noise amplitude temporarily moves a qubit off the sweet spot. The spin-like regime of the QDHQ has no true sweet spot; however, it has a large and extended region of small $dE_Q/d\varepsilon$, where $E_Q$