Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size
Jahan Claes, Wim van Dam
Abstract
This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the performance of depth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn></mml:math> QAOA is independent of the specific instance in the limit of infinite sized systems and we give an explicit formula for the expected performance. We also give explicit expressions for the higher moments of the expected energy, thereby proving that the expected performance of QAOA concentrates.
Topics & Concepts
Limit (mathematics)MathematicsIndependence (probability theory)QuantumApplied mathematicsQuantum algorithmOptimization problemAlgorithmMathematical optimizationOptimization algorithmSet (abstract data type)Random variableMeasure (data warehouse)Quantum systemStatistical physicsMoment (physics)Current (fluid)Class (philosophy)Quantum phase estimation algorithmDiscrete mathematicsExpected valueMoment problemQuantum Computing Algorithms and ArchitectureQuantum many-body systemsMagnetic properties of thin films