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The recent high-pressure experimental discovery of superconductivity in(La,Y)H$_{10}$, (La,Ce)H$_{9}$, (La,Ce)H$_{10}$, (Y,Ce)H$_{9}$, and(La,Nd)H$_{10}$ shows that the ternary rare-earth clathrate hydride can bepromising candidate for high-temperature superconductor. In this work, wetheoretically demonstrate that the combination of actinide-metal thorium (Th)and rare-earth-metal lanthanum (La) with hydrogen can also form some ternaryhydrides with cage-like structures to be stable at 200 GPa. Using theevolutionary algorithms combined with the first-principles calculations, wehave predicted the pressure-dependent ternary phase diagram ofLa$_{x}$Th$_{y}$H$_{z}$, particularly including the case of(La$_{1-x}$Th$_{x}$)H$_{n}$ [or designated as (La,Th)H$_{n}$ for simplicity].Our calculations show that the hydrogen-rich phases such as (La,Th)H$_{9}$(only including $P\bar{6}m2$-LaThH$_{18}$) and (La,Th)H$_{10}$ (including$I4/mmm$-La$_{3}$ThH$_{40}$, $R\bar{3}m$-LaThH$_{20}$, and$I4/mmm$-LaTh$_{3}$H$_{40}$) with H$_{29}$ and H$_{32}$ cages can bethermodynamically stable below 200 GPa. However, the phase decomposition canhappen to only (La,Th)H$_{9}$ when the pressure is above 150 GPa. Moreimportantly, the electron-phonon coupling (EPC) calculations show that the(La,Th)H$_{10}$ series could the potential superconductors, of which$I4/mmm$-La$_{3}$ThH$_{40}$ at 200 GPa exhibits the large EPC constant$\lambda$ = 2.46 with a highest transition temperature ($T_\mathrm{c}$) of 210K. Since there are few previous studies on ternary hydrides composed ofactinide metals, the present work would greatly stimulate the further discoveryof this type of ternary hydrides and provide useful guidance for thehigh-pressure experimental studies on them.

(La,Th)H$_{10}$: the potential high-$T_{c}$ superconductors stabilized thermodynamically below 200 GPa