feat: add PauliStringSum class for sums of weighted PauliStrings

[tanishqbagriaresearch-hue]

Summary

Fixes #1256

This PR introduces a new PauliStringSum class that represents a linear combination (weighted sum) of PauliString objects, enabling richer algebraic operations on Pauli operators.

Changes

New File: src/braket/quantum_information/pauli_string_sum.py

• Added PauliStringSum class to represent sums of weighted PauliString objects
• Supports addition and subtraction of PauliString objects with optional scalar weights
• Supports scalar (float) multiplication via __mul__ and __rmul__
• Supports multiplication by PauliString (element-wise Pauli product) via __mul__ and __rmul__
• Supports single-item index access (__getitem__) and in checks (__contains__)
• Provides to_list() method for conversion to list of (float, str) tuples
• Provides from_list() class method for constructing from list of (float, str) tuples
• Implements commutes_with() for checking commutativity with another PauliString
• Implements is_self_commuting() to check if all terms in the sum mutually commute

Bug Fix: PauliString.__mul__

• Fixed PauliString.__mul__ to return NotImplemented for non-PauliString types, allowing Python to correctly fall back to PauliStringSum.__rmul__ when multiplying a PauliString by a PauliStringSum

Testing

• Added 46 unit tests, all passing, covering:
  • Addition and subtraction of PauliStrings
  • Scalar multiplication
  • PauliString multiplication
  • Index access and in checks
  • to_list() / from_list() round-trips
  • commutes_with() and is_self_commuting() checks
  • Edge cases and error handling

Merge Checklist

• I have read the CONTRIBUTING doc
• I used the PR title format described in CONTRIBUTING
• I have updated any necessary documentation, including READMEs and API docs (if appropriate)

Tests

• I have added tests that prove my fix is effective or that my feature works (if appropriate)
• I have checked that my tests are not configured for a specific region or account (if appropriate)

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.