Simulating quantum circuits using tree tensor networks

Abstract

We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected entanglement generated by the quantum circuit. The gates are sequentially applied to the tree by absorbing single-qubit gates into leaf nodes, and splitting two-qubit gates via singular value decomposition and threading the resulting virtual bond through the tree. We theoretically analyze the applicability of the method as well as its computational cost and memory requirements, and identify advantageous scenarios in terms of required bond dimensions as compared to a matrix product state representation. The study is complemented by numerical experiments for different quantum circuit layouts up to 37 qubits.

13 pages, 16 figures, 1 algorithm, Latex; Comments for version 3: preparation for publication in the Quantum Journal, additional comparison to existing approaches, more details on the experiments and outcomes, general rephrasing and improvements for clarity

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Cited by in corpus (11)

• Tree tensor network state approach for solving hierarchical equations of motion
• Gauging tensor networks with belief propagation
• Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
• Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks
• Survey on Computational Applications of Tensor Network Simulations
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Tensor networks for $p$-spin models
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Challenges and opportunities in the supervised learning of quantum circuit outputs
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Dynamical cluster-based strategy for improving tensor network algorithms in quantum circuit simulations