  State-of-the-art quantum computers can only reliably execute circuits with
limited qubit numbers and computational depth. This severely reduces the scope
of algorithms that can be run. While numerous techniques have been invented to
exploit few-qubit devices, corresponding schemes for depth-limited computations
are less explored. This work investigates to what extent we can mimic the
performance of a deeper quantum computation by repeatedly using a shallower
device. We propose a method for this purpose, inspired by Feynman simulation,
where a given circuit is chopped in two pieces. The first piece is executed and
measured early on, and the second piece is run based on the previous outcome.
This method is inefficient if applied in a straightforward manner due to the
high number of possible outcomes. To mitigate this issue, we propose a shallow
variational circuit, whose purpose is to maintain the complexity of the method
within pre-defined tolerable limits, and provide a novel optimisation method to
find such circuit. The composition of these components of the methods is called
reduce\&chop. As we discuss, this approach works for certain cases of interest.
We believe this work may stimulate new research towards exploiting the
potential of shallow quantum computers.
