🤖 AI Summary
This work investigates the simulation of classical circuits on quantum computers, focusing on the fundamental trade-offs among classical space, quantum space, and time. Method: We extend the “spooky pebble game” framework—previously limited to specific circuit classes—to general Boolean circuits, enabling tight upper bounds on quantum space requirements. We develop the first solver integrating SAT encoding with heuristic search for spooky pebbling, supporting scalable quantum resource optimization. Contribution/Results: We establish a novel, rigorously characterized trade-off paradigm wherein classical space can be converted into quantum space reduction. We prove that optimally solving the spooky pebble game for arbitrary Boolean circuits is PSPACE-complete. Experimental evaluation demonstrates that our approach significantly reduces required quantum space within practical time limits, validating both the theoretical model’s fidelity and its practical utility for modeling real-world quantum hardware constraints.
📝 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.