If you could walk a straight line between the two, it would be more than 3,000 km. Say you can average 5km per hour for 10 hours per day - not reasonable at all in this scenario, but on flat ground, maybe. It would take you more than 60 days of continuous walking. Since you're talking about hiking across the highest mountain range in the world, it wouldn't be unreasonable to give a walking time of triple that, probably even more. Add in the need for breaks, since nobody can hike that distance continuously, and you're talking about 200+ days of travel. Probably a full year.
So your question in essence is, what are all the necessary items for a year hike, if possible. Unsupported, this isn't possible. You can't carry the necessary equipment for 3 changes of seasons and the elevation changes you would encounter. You can't carry the necessary equipment to feed yourself and purify drinking water for that long. And on top of that, you'd also be carrying camping equipment, you can't sleep exposed night after night on such a trip, and you'd need good equipment even in the warmest part of the year while crossing the Himalayas.