Holding a Qubit: The Retention Price of Quantum Memory

Classical retention costs almost nothing: a bit in DRAM costs 1.57e-8 J per bit-hour in self-refresh, a bit in flash at most 5.70e-14 J per bit-hour as an amortised rewrite bound, and a bit on tape on a shelf costs nothing. This paper prices the quantum analogue: holding one logical qubit, with no computation performed on it, below a cumulative failure probability of 1% for one hour, one day, and one year. Because bare qubits survive only microseconds (superconducting) to minutes (trapped ion), retention requires continuous surface-code error correction at a 100% refresh duty cycle, with code distance growing as the interval lengthens. Holding one logical qubit takes 15,741 W, 17,569 W, and 20,784 W continuously on the superconducting platform (physical error rate 1e-3, 1 microsecond cycles, distances 27/31/37, 10 kW fixed cryostat plant included) and 2,721 W, 3,057 W, and 3,681 W on the trapped-ion platform (1 ms cycles, distances 19/23/29). The energy per logical-qubit-hour exceeds the classical DRAM bit-hour by a factor of 6.23e14 to 4.76e15, the flash bit-hour by about 1e21, and is unbounded against tape on a shelf at zero holding cost. Quantum memory with present architectures is not a storage medium but a continuous power commitment. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF and markdown, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).