There isn't a specific date or year established for the events of Quantum Conundrum in the game's narrative. The game's story doesn't focus on a specific time period, and it doesn't provide any clear clues to when the events occur.

However, we can infer a few things:

* The technology is advanced but not futuristic: The game features advanced scientific gadgets and time-bending concepts, but they don't seem to be completely beyond our current technological capabilities.

* The game's aesthetic has a retro-futuristic feel: The visuals and overall style of Quantum Conundrum have a nostalgic feel, reminiscent of 1950s and 1960s science fiction.

Based on these observations, we can speculate that Quantum Conundrum takes place in a somewhat near future, perhaps within a few decades from the game's release date (2012). However, the lack of concrete information leaves the exact time period open to interpretation.