Autonomous quantum machines and the finite sized Quasi-Ideal clock

TL;DR

This paper introduces the Quasi-Ideal clock, a finite-sized quantum device that minimally disturbs its state when implementing unitaries, enabling autonomous quantum machines with small size and energy, and approximating ideal clocks.

Contribution

It demonstrates that a finite-sized quantum clock can implement unitaries with exponentially small back-reaction and solve the problem of approximating ideal clock evolution.

Findings

Back-reaction can be exponentially suppressed in the clock's size.

Finite-sized clocks can approximate ideal continuous evolution.

Autonomous quantum machines can operate efficiently with modest resources.

Abstract

Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.