2024/09/16 by Reuben Tate, Stephan Eidenbenz, Tate, Reuben +1 · 1 citation
Chemistry · Materials Science · Physics and Astronomy · #Electronic and Structural Properties of Oxides #FOS: Physical sciences #Quantum Physics (quant-ph) #Semiconductor Quantum Structures and Devices #Spectroscopy and Laser Applications
paper · pdf · doi:10.48550/arxiv.2410.00027
openalex publication_date 2024/09/16 · openalex created_date 2024/10/28 · openalex updated_date 2026/07/28
In order to boost the performance of the Quantum Approximate Optimization Algorithm (QAOA) to solve problems in combinatorial optimization, researchers have leveraged the solutions returned from classical algorithms in order to create a warm-started quantum initial state for QAOA that is biased towards "good" solutions. Cain et al. showed that if the classically-obtained solutions are mapped to the poles of the Bloch sphere, then vanilla QAOA with the standard mixer "gets stuck". If the classically-obtained solution is instead mapped to within some angle θ from the poles of the Bloch sphere, creating an initial product state, then QAOA with optimal variational parameters is known to converge to the optimal solution with increased circuit depth if the mixer is modified to be "aligned" with the warm-start initial state. Leveraging recent work of Benchasattabuse et al., we provide theoretical lower bounds on the circuit depth necessary for this form of warm-started QAOA to achieve a desired change Δλ in approximation ratio; in particular, we show that for small θ, the lower bound on the circuit depth roughly scales proportionally with Δλ/θ.