>1 billion transistors per square millimeter
I'm pretty sure the heart of the average multi-GB USB stick gets close to your 120Mb per mm already and there is some density penalty in making them rewriteable etc
Current tech has a limit of about 10 million transistors per millimeter IIRC. I gave it an arbitrary 100x increase.
Also, one thing I was postulating regarding these chips is that they aren't printed chips... its a pure optical chip somehow using the atoms themselves as switches without an insulator. Instead of electrical current, its bouncing photons around. How that might work is... well... pure sci-fi, its beyond real world understanding of physics. But then again, so are the Cymbaline chips.
My thinking was this. That the Cymbaline chips, based on the description of them, are some sort of optical chip. We don't know how exactly they work, maybe its silicates with some metal impurities in some "magic mix" or maybe its some form of sillicate we haven't seen. Whatever it is, it allows these chips to form a sentient life form. I assumed, again based one what has been written, that Imperial researchers had also noticed these chips were capable of processing functions faster (or perhaps just more efficiently by doing so in a way that doesn't require as many calculations... beating the limit not by brute force but through some more "elegant" solution... call it "intuitive algorhythmic calculus"; maybe they aren't binary, maybe they're just a whole new kind of chip) than previous chips. Eventually these new chips became widespread, being used not just in transponders, but computers, digital watches, cell phones, laptops, cars, planes, trains, you get the idea. Among the unique features of these chips is that they can rewrite themselves based on information. Thus when Virus comes along, its able to so widely infect things because its spreading through Cymbaline chips which by their nature are suspectible to it. They respond and rewrite themselves because it "speaks their native language" if you will.
That was my attempt to explain how Virus was possible, how it spread so quickly and so effectively. How it was able to rewrite chips through just a radio transmission. As others have noted, without some sort of explanation Virus becomes "magical" in its ability to transmute chips, because with ordinary computer chips... such just wouldn't be possible, and worse is nonsensical (maybe the best word is simply "unbelievable").
It also offers a potential, if partial, solution. Build computers using "ordinary" and less sofisticated chips. These might require bulkier computers. Perhaps multiply equivalent cost, size, weight and power requirments by...2x, 4x, 5x? Such computers couldn't be taken over by Virus, though it could still attempt to attack them, either hacking them or just damaging their programs so they stop functioning (but they can't become sentient, that was the unique property of the Cymbaline chips).
Of course I'm sure some physics student will explain how all this if patentedly impossible and this is becoming the problem with writing sci-fi (any sci-fi, its also spawned something of a counter movement towards "sci-fantasy" which often throws science out entirely and holds the entertainment value as the only important value). Its ironic and curious that some will accept things like jump drives, or ships able to get far more energy from a fusion engine than would actually be possible; but will argue over thermodynamics and ship heat signatures. We can imagine star spanning empires, then trip ourselves over the smallest of details. I think sometimes people get too caught up in the sci in sci-fi and forget that other half... the fiction. Sci-fi isn't about being a simulation of reality, it isn't even about being realistic... its about being believeable enough to allow the suspension of disbelief so that the audience can enjoy the entertainment.
Is the above "explanation" of Virus and the Cymbaline chips absolutely realistic... no, it isn't. Is it plausible, I think so. Does it provide enough explanation for the suspension of disbelief, again, I think for most it would. For much of the sci-fi audience, that's all they want.