Quantum annealing in Sherrington–Kirkpatrick spin glass in presence of time-dependent longitudinal field

Atanu Rajak, Bikas K. Chakrabarti

Research output: Contribution to journalArticlepeer-review


Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington–Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass model by tuning both transverse and longitudinal fields. We numerically solve the time-dependent Schrödinger equation of the total Hamiltonian when both the fields are made time-dependent and eventually vanish at the same time. We have computed the time-evolution of the probability of finding the system in one of two degenerate ground states of the classical spin glass. At the end of annealing, using the configuration averaged probability, we have shown a clear advantage while the longitudinal field is annealed rather than keeping it constant throughout the process of quantum annealing. We further investigate the order parameter distribution of a quantum SK spin glass in presence of a small longitudinal field and find, from our exact diagonalization results for small system sizes, evidence for quantum tunneling induced disappearance of the classical Almeida–Thouless phase boundary separating the replica symmetry broken (non-ergodic) and replica symmetric (ergodic) spin glass phase (reported already in 2022). We believe that this longitudinal field induced ergodicity in quantum SK model to be responsible for the observed enhancement of quantum annealing (reported earlier for smaller systems by us in 2014).

Original languageEnglish
JournalIndian Journal of Physics
StateAccepted/In press - 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Indian Association for the Cultivation of Science 2024.


AR is thankful to UGC, India for Start-up Research Grant No. F. 30-509/2020(BSR) and BKC is thankful to the Indian National Science Academy for their Senior Scientist Research Grant support.

FundersFunder number
Indian National Science Academy
University Grants Commission


    • Quantum annealing
    • Quantum tunneling
    • Spin glass


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