LIMDD: A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States

• DOI: 10.22331/q-2023-09-11-1108
• Publication Date: 2023-09-11T15:12:21Z
• Authors: Lieuwe Vinkhuijzen; Tim Coopmans; David Elkouss; Vedran Dunjko; Alfons Laarman
• Keywords: Quantum circuit

Efficient methods for the representation and simulation of quantum states operations are crucial optimization circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable capturing relevant aspects systems, but their limits not well understood. In this work, we investigate bridge gap between existing DD-based structures stabilizer formalism, an important tool simulating circuits in tractable regime. We first show that although DDs were suggested succinctly states, they actually require exponential space certain states. To remedy this, introduce more powerful decision diagram variant, called Local Invertible Map-DD (LIMDD). prove set represented by poly-sized LIMDDs strictly contains union other variants. Finally, there exist which can efficiently simulate, while output cannot be two state-of-the-art paradigms: decomposition techniques Clifford + <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> Matrix-Product States. By uniting successful approaches, thus pave way fundamentally solutions analysis computing.