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Tensor network contraction efficiently simulates quantum circuits for problems like Max-Cut using the Quantum Approximate Optimization Algorithm (QAOA). This method is superior for graphs with regularity five and below, offering significant computational savings.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Algorithm Analysis

Background:

  • Classical simulation of quantum computation is crucial due to the limited availability of large-scale quantum computers.
  • Tensor network (TN) contraction offers an efficient method for simulating quantum circuits, reducing computational cost compared to full Hilbert space simulations.

Purpose of the Study:

  • To implement and evaluate a tensor network contraction program for simulating quantum circuits on multi-core compute nodes.
  • To assess the performance of TN contraction for the Quantum Approximate Optimization Algorithm (QAOA) on Max-Cut problems with varying graph regularities.
  • To compare different tensor contraction ordering strategies.

Main Methods:

  • Implementation of a tensor network contraction program utilizing multi-core compute nodes.
  • Simulation of Quantum Approximate Optimization Algorithm (QAOA) circuits for the Max-Cut problem on 3- to 7-regular graphs, up to 100 qubits.
  • Comparison of two tensor index contraction ordering methods: tree decomposition of the line graph and a stochastic scheme.

Main Results:

  • Successfully simulated QAOA circuits for Max-Cut up to 100 qubits.
  • Demonstrated that TN contraction efficiency increases significantly as the treewidth of the quantum circuit's line graph decreases.
  • Identified that TN contraction methods are computationally superior for simulating Max-Cut/QAOA on graphs with regularity approximately five and below.

Conclusions:

  • Tensor network contraction is a powerful tool for simulating specific quantum circuits, particularly for the Max-Cut problem using QAOA.
  • The efficiency of TN contraction is highly dependent on the treewidth of the quantum circuit's line graph.
  • The stochastic contraction method is advantageous when tree decomposition is computationally expensive, and the qTorch software package is released for general quantum circuit simulation.