Support alternative tensor product ordering

[kevinsung]

Description

Implement the feature requested at https://github.com/Qiskit/qiskit-terra/issues/7628. Description copied below:

Qiskit uses the little endian convention for ordering the factors in a tensor product. For example, the statevector for a 3-qubit state would use the ordering Q2 ⊗ Q1 ⊗ Q0. It would be useful to add support for specifying the tensor product order. This could be used, for example, to request a state vector using the common big endian ordering.

This can be implemented by adding a qubit_order argument to all functions that implicitly rely on a choice of tensor product ordering. This argument would be a list of the qubit indices in the desired tensor product order. So for the example above, it would be [2, 1, 0] to get the state in big-endian order.

The following is a non-exhaustive list of functions that would be affected:

• Result.get_statevector
• Result.get_counts
• Operator
• SparsePauliOp
• Statevector
• many other things in the quantum_info module

Deliverables

Issue https://github.com/Qiskit/qiskit-terra/issues/7628 is resolved.

Mentors details

• Mentor 1
  • Name: Kevin Sung
  • GitHub ID: @kevinsung
  • What they do: Qiskit Researcher

Number of mentees

1

Type of mentees

• Mentee 1
  • Required:
  • Knowledge of Qiskit and Python
  • Knowledge of linear algebra
  • Nice to have:
  • Software design experience

[HuangJunye]

Closing this issue as it was not paired with any mentee. Thank you for suggesting the project idea!