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Stabilizer simulation can efficiently simulate an important class of quantumcircuits consisting exclusively of Clifford gates. However, all existingextensions of this simulation to arbitrary quantum circuits includingnon-Clifford gates suffer from an exponential runtime.  To address this challenge, we present a novel approach for efficientstabilizer simulation on arbitrary quantum circuits, at the cost of lostprecision. Our key idea is to compress an exponential sum representation of thequantum state into a single abstract summand covering (at least) all occurringsummands. This allows us to introduce an abstract stabilizer simulator thatefficiently manipulates abstract summands by over-approximating the effect ofcircuit operations including Clifford gates, non-Clifford gates, and (internal)measurements.  We implemented our abstract simulator in a tool called Abstraqt andexperimentally demonstrate that Abstraqt can establish circuit propertiesintractable for existing techniques.

Abstraqt: Analysis of Quantum Circuits via Abstract Stabilizer Simulation