My apologies, I should have checked the math, I didn't look too carefully and in frustration posted that number. I was also directing this at the 'physical' reconstruction, where only 1.2 x 10^10 bits are required. Clearly this wouldn't be billions but it's still thousands.

10^42 is the Bekenstein bound, you cannot possibly require more data as that represents the quantum state of the system.

A billion would be ~10.37 exabytes, or ~300 petabytes with lossless compression (ideally).