Reduce&chop: Shallow circuits for deeper problems

TL;DR

This paper introduces Reduce&Chop, a method that enables shallow quantum circuits to simulate deeper computations by chopping circuits and using variational techniques to maintain efficiency, potentially expanding quantum algorithm capabilities.

Contribution

The work proposes a novel approach combining circuit chopping with variational optimization to mimic deeper quantum computations on shallow devices.

Findings

The method can simulate certain deeper circuits effectively.

Variational circuits help manage complexity and efficiency.

Potential to expand the utility of shallow quantum computers.

Abstract

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.