Trade-offs between classical and quantum space using spooky pebbling

TL;DR

This paper applies spooky pebble games to general circuits to analyze classical and quantum space/time trade-offs, providing theoretical bounds and a practical solver that demonstrates potential quantum space reductions.

Contribution

It extends spooky pebble game analysis to general circuits, proves PSPACE-completeness, and develops a solver that finds strategies to reduce quantum space in circuit simulation.

Findings

Quantum space can be reduced using spooky pebble strategies.

The spooky pebble game is PSPACE-complete.

The solver effectively finds optimal trade-offs within limited runtime.

Abstract

Pebble games are used to study space/time trade-offs. Recently, spooky pebble games were introduced to study classical space / quantum space / time trade-offs for simulation of classical circuits on quantum computers. In this paper, the spooky pebble game framework is applied for the first time to general circuits. Using this framework we prove an upper bound for quantum space in the spooky pebble game. We also prove that solving the spooky pebble game is PSPACE-complete. Moreover, we present a solver for the spooky pebble game based on satisfiability solvers combined with heuristic optimizers. This spooky pebble game solver was empirically evaluated by calculating optimal classical space / quantum space / time trade-offs. Within limited runtime, the solver could find a strategy reducing quantum space when classical space is taken into account, showing that the spooky pebble model is useful to reduce quantum space.