Autonomous Quantum Processing Unit: What does it take to construct a self-contained model for quantum computation?

Computation is an input-output process, where a program encoding a problem to be solved is inserted into a machine that outputs a solution. Whilst a formalism for quantum Turing machines which lifts this input-output feature into the quantum domain has been developed, this is not how quantum computation is physically conceived. Usually, such a quantum computation is enacted by the manipulation of macroscopic control interactions according to a program executed by a classical system. To understand the fundamental limits of computation, especially in relation to the resources required, it is pivotal to work with a fully self-contained description of a quantum computation where computational and thermodynamic resources are not be obscured by the classical control. To this end, we answer the question; "Can we build a physical model for quantum computation that is fully autonomous?", i.e., where the program to be executed as well as the control are both quantum. We do so by developing a framework that we dub the autonomous Quantum Processing Unit (aQPU). This machine, consisting of a timekeeping mechanism, instruction register and computational system allows an agent to input their problem and receive the solution as an output, autonomously. Using the theory of open quantum systems and results from the field of quantum clocks we are able to use the aQPU as a formalism to investigate relationships between the thermodynamics, complexity, speed and fidelity of a desired quantum computation.