Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
arXiv:2504.16718 · doi:10.1103/64hd-q4z5
Abstract
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). 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 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 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.
14 pages, 18 figures
References in corpus (57)
- Quantum Computing in the NISQ era and beyond
- Finding community structure in very large networks
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- Ising formulations of many NP problems
- Efficient classical simulation of slightly entangled quantum computations
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Strong quantum computational advantage using a superconducting quantum processor
- Unifying time evolution and optimization with matrix product states
- Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
- Time-evolution methods for matrix-product states
- Quantum optimization using variational algorithms on near-term quantum devices
- Classical simulation of quantum many-body systems with a tree tensor network
- Demonstration of the trapped-ion quantum-CCD computer architecture
- Simulating chemistry using quantum computers
- Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
- Sequential generation of entangled multi-qubit states
- Tensor product methods and entanglement optimization for ab initio quantum chemistry
- Average-case complexity versus approximate simulation of commuting quantum computations
- Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
- Unsupervised Generative Modeling Using Matrix Product States
- Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
- What limits the simulation of quantum computers?
- Hyper-optimized tensor network contraction
- Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
- Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
- The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
- Tensor Network Algorithms: a Route Map
- Learning Relevant Features of Data with Multi-scale Tensor Networks
- Efficient simulation of infinite tree tensor network states on the Bethe lattice
- Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
- Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
- Computing vibrational eigenstates with tree tensor network states (TTNS)
- A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
- The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
- Quantum Fourier Transform Has Small Entanglement
- T3NS: three-legged tree tensor network states
- Critical properties of homogeneous binary trees
- Constant-depth preparation of matrix product states with adaptive quantum circuits
- Classical algorithm for simulating experimental Gaussian boson sampling
- Automatic structural optimization of tree tensor networks
- The computational power of random quantum circuits in arbitrary geometries
- Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
- Studying dynamics in two-dimensional quantum lattices using tree tensor network states
- Adaptive-weighted tree tensor networks for disordered quantum many-body systems
- Simulating quantum circuits using tree tensor networks
- Calibrating the role of entanglement in variational quantum circuits
- A tree tensor network approach to simulating Shor's algorithm
- Tensor networks for quantum computing
- Opening the Black Box Inside Grover's Algorithm
- The Quantum House Of Cards
- Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
- Roughening dynamics of interfaces in the two-dimensional quantum Ising model
- Tensor networks and efficient descriptions of classical data
- Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
- Ab-Initio Approach to Many-Body Quantum Spin Dynamics