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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.

ABSTRACT: Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, H_I. Here, we point to the existence of an analytical solution for such a problem for an arbitrary H_I beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of H_I, the solution also shows a considerable quantum speedup in computations.

SUBMITTER: Yan B

PROVIDER: S-EPMC9038765 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature

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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.

Yan Bin B Sinitsyn Nikolai A NA

Nature communications 20220425 1

Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, H<sub>I</sub>. Here, we point to the existence of an analytical solution for such a problem for an arbitrary H<sub>I</sub> beyond the adiabatic limit for QA. This solution provides insight ...[more]

PMID: 35468917

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Project description:Background and objectiveCancer Immunoediting (CI) describes the cellular-level interaction between tumor cells and the Immune System (IS) that takes place in the Tumor Micro-Environment (TME). CI is a highly dynamic and complex process comprising three distinct phases (Elimination, Equilibrium and Escape) wherein the IS can both protect against cancer development as well as, over time, promote the appearance of tumors with reduced immunogenicity. Herein we present an agent-based model for the simulation of CI in the TME, with the objective of promoting the understanding of this process.MethodsOur model includes agents for tumor cells and for elements of the IS. The actions of these agents are governed by probabilistic rules, and agent recruitment (including cancer growth) is modeled via logistic functions. The system is formalized as an analogue of the Ising model from statistical mechanics to facilitate its analysis. The model was implemented in the Netlogo modeling environment and simulations were performed to verify, illustrate and characterize its operation.ResultsA main result from our simulations is the generation of emergent behavior in silico that is very difficult to observe directly in vivo or even in vitro. Our model is capable of generating the three phases of CI; it requires only a couple of control parameters and is robust to these. We demonstrate how our simulated system can be characterized through the Ising-model energy function, or Hamiltonian, which captures the "energy" involved in the interaction between agents and presents it in clear and distinct patterns for the different phases of CI.ConclusionsThe presented model is very flexible and robust, captures well the behaviors of the target system and can be easily extended to incorporate more variables such as those pertaining to different anti-cancer therapies. System characterization via the Ising-model Hamiltonian is a novel and powerful tool for a better understanding of CI and the development of more effective treatments. Since data of CI at the cellular level is very hard to procure, our hope is that tools such as this may be adopted to shed light on CI and related developing theories.

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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.

Publications

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.

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