The advent of quantum computing will compromise current asymmetric cryptography. Awaiting this moment, global superpowers are routinely collecting and storing encrypted data, so as to later decrypt it once sufficiently strong quantum computers are in place. We argue that this situation gives rise to a new mode of global surveillance that we refer to as a quantum panopticon. Unlike traditional forms of panoptic surveillance, the quantum panopticon introduces a temporal axis, whereby data subjects' future pasts can be monitored from an unknown "superposition" in the quantum future. It also introduces a new level of uncertainty, in that the future watchman's very existence becomes a function of data subjects' efforts to protect themselves from being monitored in the present. Encryption may work as a momentary protection, but increases the likelihood of long-term preservation for future decryption, because encrypted data is stored longer than plaintext data. To illustrate the political and ethical aspects of these features, we draw on cryptographic as well as theoretical surveillance literature and call for urgent consideration of the wider implications of quantum computing for the global surveillance landscape.