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 is 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). To
benchmark the method, we simulate random and QAOA circuits with various
two-qubit gate connectivities. For the random circuits, we devise tree-like
gate layouts that are suitable for TTN and show that TTN requires less memory
than MPS for the simulations. For the QAOA circuits, a TTN construction that
exploits graph structure significantly improves the simulation fidelities. Our
findings show that TTNs provide a promising framework for simulating quantum
circuits, particularly when gate connectivities exhibit clustering or a
hierarchical structure.

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