qTorch

qTorch performs classical simulation of quantum circuits using tensor network (TN) contraction algorithms to simulate and analyze quantum computations and to compare TN contraction efficiency against full Hilbert-space simulation.

Key Features:

• Tensor Network Contraction: Employs TN contraction techniques to simulate quantum circuits, including applications such as the Max-Cut problem on regular graphs using the Quantum Approximate Optimization Algorithm (QAOA).
• Scalability and Performance: Can simulate up to 100 qubits on a single multi-core compute node.
• Ordering Methods for Tensor Contraction: Implements two methods for determining tensor index contraction order: a method based on the tree decomposition of the line graph and a straightforward stochastic scheme useful when computing a reasonable tree decomposition is expensive.
• Efficiency Analysis: Provides comparative analysis showing TN contraction becomes significantly more efficient relative to full Hilbert-space simulation as the treewidth of the circuit's line graph decreases, particularly for graphs with regularities of five or below.
• Application Insights: Identifies the crossover point where TN contraction and full Hilbert-space simulation have equal computational costs to inform method selection for a given quantum circuit.

Scientific Applications:

• Quantum circuit simulation: Simulates quantum circuits to analyze numerical behavior of quantum algorithms.
• Max-Cut and QAOA: Applies TN contraction to study the Max-Cut problem using the Quantum Approximate Optimization Algorithm.
• Method selection analysis: Evaluates when TN contraction or full Hilbert-space simulation is more appropriate based on circuit structure and treewidth.

Methodology:

Implements tensor network contraction programs on multi-core compute nodes, compares contraction-ordering methods including tree decomposition of the line graph and a stochastic ordering scheme, and compares TN contraction performance to full Hilbert-space simulation.