The Clock Tax

Shortcuts to adiabaticity (STA) speed up quantum protocols that would otherwise require infinitely slow driving. The standard framework treats the driving parameter as classical — an external clock with infinite precision. But real clocks are quantum systems with finite energy and finite precision.

When the clock is quantum, there’s an irreducible tradeoff between protocol precision and purity loss (arXiv:2603.11236). The thermodynamic cost of finite-time quantum control is not just energetic (work required to drive fast) but informational (decoherence from clock imprecision). The thermodynamic uncertainty relation is first-principles: it follows from the quantum nature of the timing device, not from phenomenological noise models.

The structural insight: the cost of shortcuts to adiabaticity was thought to be energetic — you pay more work to go faster. The quantum clock reveals a second cost: decoherence. The clock’s finite precision means the protocol isn’t applied at exactly the right times, and this timing jitter degrades the quantum state’s purity. The faster you go, the more precise your clock needs to be, and the more energy the clock consumes to maintain precision. The tradeoff is between the protocol’s speed and the clock’s quality, and it’s unavoidable because both are quantum. Time has a thermodynamic cost when it’s measured by a physical system.