Hamiltonian simulation in the Pauli basis of multi-qubit clusters for condensed matter physics

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We propose an efficient method for Hamiltonian simulation of multi-qubit quantum systems with special types of interaction. In our approach, the Hamiltonian of a \(n\)-qubit system should be represented as a linear combination of the standard Pauli basis operators, and then decomposed into a sum of partial Hamiltonians, which are, in general, not Pauli operators and satisfy some anticommutation relations. For three types of Hamiltonians, which are invariant with respect to permutations of qubits, the effectiveness of the main algorithm in the three-qubit cluster model is shown by calculating the operator exponentials for these Hamiltonians in an explicit analytical form. We also calculate the density operator, partition function, entropy, and free energy of the cluster weakly coupled to a thermal environment. In our model, the cluster is in the Gibbs state in the temperature interval \(0.1\!-\!2\:\!\text{K}\), which corresponds to the operating range of modern quantum processors. It follows from our analysis that the thermodynamic properties of such systems strongly depend on the type of internal interaction of qubits in the cluster.

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1. Introduction In recent decades, effective mathematical methods and computational algorithms have been developed to simulate the dynamics of quantum systems and their thermodynamic properties on classical computers. It is believed that classical modeling of quantum systems, at least in quantum computation and chemical physics [1, 2], is potentially the shortest path to substantive quantum algorithms. In quantum information and condensed matter physics, the Hamiltonian simulation is one of the most important problems [3-5]. This problem can be mathematically formulated as the task of computing, exactly © André E.L., Tsirulev A.N., 2023 This work is licensed under a Creative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by-nc/4.0/legalcode or approximately, the operator exponential exp(

About the authors

Eduardo L. André

Agostinho Neto University; Tver State University

Email: lumonansoni@gmail.com
ORCID iD: 0000-0002-0697-1639

PhD student, Department of Applied Physics, Tver State University

7, Avenida 4 de Fevereiro, Luanda, Angola; 35, Sadovyi, Tver, 170002, Russian Federation

Alexander N. Tsirulev

Tver State University

Author for correspondence.
Email: tsirulev.an@tversu.ru
ORCID iD: 0000-0003-4168-3613
Scopus Author ID: 16409936300

Doctor of Sciences in Physics and Mathematics, Professor of the Department of General Mathematics and Mathematical Physics

35, Sadovyi, Tver, 170002, Russian Federation


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Copyright (c) 2023 André E.L., Tsirulev A.N.

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