I think this has been discussed already in the forum, current Kaspersky home products have all the necessary to work properly in x64, You may check all the folders and files x64 in installation folder:
But they don't consider to port to x64 the GUI yet...
It would take too much effort (money). Every now and then there is a security article mentioning, that there is only a handful of native 64-but security software taking advantage of PatchGuard. Back then (Vista x64), Windows Defender was the only one for years, until some incident, that forced the change.
"In the case of security solutions, unsupported kernel modifications also limit your choices, by making it extremely difficult or impossible for multiple security solutions to co-exist reliably on a system. We want to work with security providers to make common extensions available, so that any security vendors can use them, and so that security software does not itself put your security and reliability at risk from malicious kernel modifications,"