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arXiv:2605.27515

A multilevel tensor network compression technique for simulating Lindblad dynamics in superconducting circuits

Adrien Moulinas, Xavier Waintal

quant-phcond-mat.supr-conSubmitted May 26, 2026• Announced May 28, 2026• 0 citations
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Abstract

Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the computation affordable. Here, we develop a tensor network based technique to simulate the Lindblad dynamics of a few interacting bosonic modes with a focus on superconducting quantum circuits. The technique detects and takes advantage of two very common situations: (i) the density matrix being pure or not far from pure and (ii) the entanglement between different modes being moderate (typically qubit-like). However, (iii) the occupation of the modes can be arbitrarily high (making naïve truncations inefficient). To leverage these features, we use three different nested levels of tensor network compression: (i) we work with a global purification of the density matrix, (ii) we compress the connection between different modes to account for the moderate entanglement and (iii) we use a quantics representation of the Fock occupation number. We showcase the technique for the simulation of large cat qubits as well as for the ionization of transmon qubits, demonstrating orders-of-magnitude speed-up with respect to brute force approaches. In the latter example, it brings the simulation, previously reported on a large supercomputing infrastructure, to laptop level. The favorable scaling with system size should bring genuine computer assisted design of these systems within scope.

Comments
18 pages, 13 figures

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Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the computation affordable. Here, we develop a tensor network based technique to simulate the Lindblad dynamics of a few interacting bosonic modes with a focus on superconducting quantum circuits. The technique detects and takes advantage of two very common situations: (i) the density matrix being pure or not far from pure and (ii) the entanglement between different modes being moderate (typically qubit-like). However, (iii) the occupation of the modes can be arbitrarily high (making naïve truncations inefficient). To leverage these features, we use three different nested levels of tensor network compression: (i) we work with a global purification of the density matrix, (ii) we compress the connection between different modes to account for the moderate entanglement and (iii) we use a quantics representation of the Fock occupation number. We showcase the technique for the simulation of large cat qubits as well as for the ionization of transmon qubits, demonstrating orders-of-magnitude speed-up with respect to brute force approaches. In the latter example, it brings the simulation, previously reported on a large supercomputing infrastructure, to laptop level. The favorable scaling with system size should bring genuine computer assisted design of these systems within scope.
Quantum circuits, fundamental to quantum computation, represent quantum states through a sequence of unitary transformations. The exponential growth in the Hilbert space dimension with increasing circuit size presents a significant challenge to simulation and analysis. This work introduces a novel tensor network approach to formally model and manipulate quantum circuits, specifically designed to mitigate this exponential scaling issue. The core idea is to represent the circuit's state vector as a tensor network, leveraging techniques for efficient compression and expansion. We explore the application of variational tensor networks (VTNs) to approximate the dynamics of quantum circuits, offering a pathway towards more scalable simulations. The effectiveness of this method is demonstrated through theoretical analysis and conceptual design, focusing on key aspects of tensor network construction and manipulation tailored to quantum circuit representations. This approach aims to provide a more scalable representation compared to existing methods.
Abstract We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium qubit up to a desired accuracy. We employ this numerical technique to estimate the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips from first principles, finding an agreement with previously obtained experimental results. By developing an accurate single-mode theory that captures the details of the fluxonium device, we benchmark the results obtained with the tensor network for circuits spanning a Hilbert space as large as 15180. Our algorithm is directly applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting quantum technologies.
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Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical simulation of quantum circuits is vital not only for validating and benchmarking quantum hardware but also for gaining deeper insights into the behavior of quantum algorithms. A promising framework for classical simulation is provided by tensor networks. Recently, the density-matrix renormalization group (DMRG) algorithm was developed for simulating quantum circuits using matrix product states (MPS). Although MPS are efficient for representing quantum states with one-dimensional correlation structures, the fixed linear geometry restricts the expressive power of the MPS. In this work, we extend the DMRG algorithm for simulating quantum circuits to tree tensor networks (TTNs). The framework employs a variational compression scheme that optimizes the TTN to approximate the evolved quantum state. To benchmark the method, we simulate random circuits and the quantum approximate optimization algorithm (QAOA) with various two-qubit gate connectivities. For the random circuits, we devise treelike gate layouts that are suitable for TTN and show that TTN requires less memory than MPS for the simulations. For the QAOA circuits, a naive TTN construction that exploits graph structure significantly improves the simulation fidelities. Our findings show that the DMRG algorithm with TTNs provides a promising framework for simulating quantum circuits, particularly when gate connectivities exhibit clustering or a hierarchical structure.
The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.
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