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Multitarget DMRG-X algorithm and its application to circuit quantum electrodynamics

Sofía González-García1,2,*, Aaron Szasz1, Alice Pagano1, Dvir Kafri1, Guifré Vidal1, and Agustin Di Paolo1

  • *Contact author: sofiagonzalezgarcia@ucsb.edu
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Phys. Rev. Applied 25, 064070 – Published 29 June, 2026

DOI: https://doi.org/10.1103/qz9v-p4j5

Abstract

Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics- (circuit-QED) based quantum processors. However, exact diagonalization of the device Hamiltonian is challenging for system sizes beyond tens of qubits. Here, we employ a tensor network method based on a variant of the density matrix renormalization group (DMRG) algorithm, DMRG-X, to efficiently obtain localized eigenstates of a two-dimensional transmon array without the need to first compute lower-energy states. We also introduce MTDMRG-X, a new algorithm that combines DMRG-X with multitarget DMRG to efficiently compute excited states even in regimes with strong eigenstate hybridization. We showcase the use of these methods for the analysis of long-range couplings in a multitransmon Hamiltonian including qubits and couplers, and we discuss eigenstate localization. These developments facilitate the design and parameter optimization of large-scale superconducting quantum processors.

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Phys. Rev. Applied 25, 064070– Published 29 June, 2026
  • Received 25 July 2025
  • Revised 1 December 2025
  • Accepted 21 May 2026
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