On Ubuntu (and possibly other) Linux distros, run vainfo to see which Intel QuickSync profiles are supported.
For example, these profiles are supported on an Intel Haswell chip:
libva info: VA-API version 0.39.0
libva info: va_getDriverName() returns 0
libva info: Trying to open /usr/lib/x86_64-linux-gnu/dri/i965_drv_video.so
libva info: Found init function __vaDriverInit_0_39
libva info: va_openDriver() returns 0
vainfo: VA-API version: 0.39 (libva 1.7.0)
vainfo: Driver version: Intel i965 driver for Intel(R) Haswell Desktop - 1.7.0
vainfo: Supported profile and entrypoints
VAProfileMPEG2Simple : VAEntrypointVLD
VAProfileMPEG2Simple : VAEntrypointEncSlice
VAProfileMPEG2Main : VAEntrypointVLD
VAProfileMPEG2Main : VAEntrypointEncSlice
VAProfileH264ConstrainedBaseline: VAEntrypointVLD
VAProfileH264ConstrainedBaseline: VAEntrypointEncSlice
VAProfileH264Main : VAEntrypointVLD
VAProfileH264Main : VAEntrypointEncSlice
VAProfileH264High : VAEntrypointVLD
VAProfileH264High : VAEntrypointEncSlice
VAProfileH264MultiviewHigh : VAEntrypointVLD
VAProfileH264MultiviewHigh : VAEntrypointEncSlice
VAProfileH264StereoHigh : VAEntrypointVLD
VAProfileH264StereoHigh : VAEntrypointEncSlice
VAProfileVC1Simple : VAEntrypointVLD
VAProfileVC1Main : VAEntrypointVLD
VAProfileVC1Advanced : VAEntrypointVLD
VAProfileNone : VAEntrypointVideoProc
VAProfileJPEGBaseline : VAEntrypointVLD
References: