Performance optimization of tensor contraction expressions for many-body methods in quantum chemistry

Area of Science:

• Computational Quantum Chemistry
• High-Performance Computing

Background:

• Accurate electronic structure models, like coupled cluster, involve complex tensor contraction expressions.
• Efficient evaluation of these expressions is crucial for computational chemistry research.

Purpose of the Study:

• To optimize the performance of tensor contraction expressions in quantum chemistry.
• To reduce the number of arithmetic operations and improve computational efficiency on modern hardware.

Main Methods:

• Utilizing algebraic properties (commutativity, associativity) for operation minimization.
• Identifying and exploiting common subexpressions within tensor contraction sets.
• Implementing data layout transformations and efficient index permutation for modern processors.

Main Results:

• Demonstrated an effective algorithm for operation minimization with common subexpression identification.
• Showcased the effectiveness of data layout transformations for reducing cache misses and utilizing vector instructions.
• Provided experimental data validating the performance improvements of an efficient index permutation library.

Conclusions:

• Combined algebraic transformations and common subexpression elimination significantly reduce computational cost.
• Data layout optimization is critical for achieving high performance on contemporary computing architectures.
• The developed library enables efficient tensor manipulation, boosting the speed of quantum chemistry calculations.