Multi-Target Density Matrix Renormalization Group X algorithm and its application to circuit quantum electrodynamics

TL;DR

This paper introduces the MTDMRG-X algorithm, an extension of DMRG-X, to efficiently compute localized eigenstates and excited states in large 2D transmon arrays, aiding the design of superconducting quantum processors.

Contribution

The paper presents MTDMRG-X, a novel algorithm combining DMRG-X with multi-target DMRG for efficient excited state computation in complex quantum systems.

Findings

Successfully applied to analyze long-range couplings in multi-transmon systems

Enabled eigenstate localization analysis in large-scale superconducting qubit arrays

Facilitated design and optimization of quantum processors

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 (QED)-based quantum processors. However, exact diagonalization of the device Hamiltonian is challenging for system sizes beyond tens of qubits. Here, we employ a variant of the density matrix renormalization group (DMRG) algorithm, DMRG-X, to efficiently obtain localized eigenstates of a 2D transmon array without the need to first compute lower-energy states. We also introduce MTDMRG-X, a new algorithm that combines DMRG-X with multi-target 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 multi-transmon Hamiltonian including qubits and couplers, and we discuss eigenstate localization. These developments facilitate the design and parameter optimization of large-scale superconducting quantum processors.