# Reversible Pebbling Game for Quantum Memory Management

## TL;DR

This paper introduces a SAT-based tool for automatic quantum memory management that optimizes the trade-off between memory resources and operational complexity, addressing hardware limitations in quantum computing.

## Contribution

It models quantum memory management as a reversible pebbling game and develops a novel algorithm to generate efficient clean-up strategies considering hardware constraints.

## Key findings

- Achieved an average 52.77% improvement over existing methods.
- Validated the approach on cryptographic programs and near-term quantum devices.
- Demonstrated flexibility in exploring resource-operation trade-offs.

## Abstract

Quantum memory management is becoming a pressing problem, especially given the recent research effort to develop new and more complex quantum algorithms. The only existing automatic method for quantum states clean-up relies on the availability of many extra resources. In this work, we propose an automatic tool for quantum memory management. We show how this problem exactly matches the reversible pebbling game. Based on that, we develop a SAT-based algorithm that returns a valid clean-up strategy, taking the limitations of the quantum hardware into account. The developed tool empowers the designer with the flexibility required to explore the trade-off between memory resources and number of operations. We present three show-cases to prove the validity of our approach. First, we apply the algorithm to straight-line programs, widely used in cryptographic applications. Second, we perform a comparison with the existing approach, showing an average improvement of 52.77%. Finally, we show the advantage of using the tool when synthesizing a quantum circuit on a constrained near-term quantum device.