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Compiling: Add more circuit transformer patterns #3237

@balopat

Description

@balopat

Problem: PointOptimizer is one of the main workhorses for writing an optimizer, but it can be hard to use as the semantics of the mutation pattern is not easy to understand. The goal of this feature would be to better define the basic compiling and optimizing patterns to lead to the easier construction of compilation steps. This could potentially be aided by Subcircuit features, and the methods that are accessible are tied to the complexity of the mutation methods as described in Circuit construction.

Rough requirements:

  • Classify basic mutation patterns in optimizers
  • Pull out abstractions from these patterns and develop methods to create circuit transformers for these patterns
  • Migrate current optimizers to these new patterns

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