  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.
