2009/04/30 by M. H. S. Amin, Vicky Choi, V. Choi · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Algorithm #Computation #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematical optimization #Mathematics #Maxima and minima #Perturbation (astronomy) #Phase transition #Physics #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum annealing #Quantum computer #Quantum mechanics #Quantum phase transition #Quantum phases #Statistical physics #cond-mat.dis-nn #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1103/physreva.80.062326
published as Phys. Rev. A 80, 062326 (2009) · 4 pages, 3 figures, published final version
openalex publication_date 2009/12/11 · arxiv created 2009/12/15 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the connection between local minima in the problem Hamiltonian and first-order quantum phase transitions during adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely small gap that is exponentially sensitive to the Hamiltonian parameters. Using perturbation expansion, we derive an analytical formula that cannot only predict the behavior of the gap, but also provide insight on how to controllably vary the gap size by changing the parameters. We show agreement with numerical calculations for a weighted maximum independent set problem instance.