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Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia)at cosmological distances giving a model-independent inference of the Hubbleconstant ($H_0$). Future observations could provide strong lensing time-delaydistances with source redshifts up to $z\,\simeq\,4$, which are much higherthan the maximum redshift of SNe Ia observed so far. In order to make full useof time-delay distances measured at higher redshifts, we use quasars as acomplementary cosmic probe to measure cosmological distances at redshiftsbeyond those of SNe Ia and provide a model-independent method to determine$H_0$. In this work, we demonstrate a model-independent, joint constraint ofSNe Ia, quasars, and time-delay distances from strong lensed quasars. We firstgenerate mock data sets of SNe Ia, quasar, and time-delay distances based on afiducial cosmological model. Then, we calibrate the quasar parameters modelindependently using Gaussian process (GP) regression with mock SNe Ia data.Finally, we determine the value of $H_0$ model-independently using GPregression from mock quasars and time-delay distances from strong lensingsystems. As a comparison, we also show the $H_0$ results obtained from mock SNeIa in combination with time-delay lensing systems whose redshifts overlap withSNe Ia. Our results show that quasars at higher redshifts show great potentialto extend the redshift coverage of SNe Ia and thus enable the full use ofstrong lens time-delay distance measurements from ongoing cosmic surveys andimprove the accuracy of the estimation of $H_0$ from $2.1\%$ to $1.3\%$ whenthe uncertainties of the time-delay distances are $5\%$ of the distance values.

A Model-independent Method to Determine $H_0$ Using Time-Delay Lensing, Quasars and Type Ia Supernovae