Pauli and Clifford groups

[speller26]

The Qiskit quantum_information contains helpful classes for efficiently manipulating quantum information, most notably the Pauli and Clifford groups. The respective Pauli and Clifford classes allow users to quickly compose operators, enabling step-by-step inspection of an evolving quantum state. Furthermore, they can be converted to circuits to run on quantum devices.

The Amazon Braket SDK contains a quantum_information module consisting of a PauliString class; this module can be expanded to fully encompass the Pauli and Clifford groups.

Describe the feature you'd like

• An implementation of CliffordTableau with, at the very least, multiplication and power operators that scale linearly with qubit count, an adjoint method, and a to_circuit method for converting to a Circuit.
• Implementing multiplication and power operators and to_circuit on the existing PauliString class.