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Allow for Sums of PauliStrings #1256

@sesmart

Description

@sesmart

Describe the feature you'd like

The PauliString class contains logic for creating and manipulating PauliStrings, though only exists in single instances. The proposed class is a container for PauliStrings, which allows for:

  1. Addition and subtraction of Pauli Strings, including with weights
  2. Multiplication by floats
  3. Multiplication by PauliStrings
  4. Single-item index-ability & inclusion checks
  5. Conversion to & from Sum & list of tuple[float, str]
  6. [extra] Inter and extra-class operations (i.e. commutes with another operator, self commuting, etc.)
    This may require changes to PauliString as well, depending on how coefficients are treated.

uH 2026

Please note that we're still waiting for Unitary Foundation to review and approve our issues, so these are subject to change.

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