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# Quantum-Twirling
A Python package designed for fast implementation of [Pauli Twirling](/##What-Is-Pauli-Twirling?) in [Qiskit](https://qiskit.org/documentation/) circuits.
A Python package designed for fast implementation of [Pauli Twirling](/#What-Is-Pauli-Twirling?) in [Qiskit](https://qiskit.org/documentation/) circuits.


## Features
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Crucially, the gates are selected such that the net operation, in the absence of noise, is unchanged.
That is, the Pauli Twirling Set for a two-qubit Clifford gate is a set of four Pauli gates that when pre-pended and appended to a circuit containing the two-qubit gate, the unitary is equal to that of the single two-qubit gate alone.

### Implementation of Pauli Twirling
### Implementation of Pauli Twirling in Academic Literature
---
- [Purification of noisy entanglement and faithful teleportation via noisy channels (Bennet, et. al., 1996)](https://arxiv.org/abs/quant-ph/9511027)
- [Mixed state entanglement and quantum error correction (Bennet, et. al., 1996)](https://arxiv.org/abs/quant-ph/9604024)
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- [Constructing smaller Pauli twirling sets for arbitrary error channels (Cai and Benjamin, 2018)](https://arxiv.org/abs/1807.04973v3)


## Supported Qiskit Gates
- [CXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CXGate.html)
- [CYGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CYGate.html)
- [CZGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CZGate.html)
- [CHGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CHGate.html)
- [DCXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.DCXGate.html)
- [CSXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CSXGate.html)
- [CSdgGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CSdgGate.html)
- [ECRGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ECRGate.html)
- [SWAPGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.SwapGate.html)
- [iSWAPGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.iSwapGate.html)
## Dictionary-Supported Qiskit Gates
Native Pauli Twirling Sets are included for the following common two-qubit Clifford gates in Qiskit:
- [CXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CXGate.html) (Controlled X Gate, a.k.a. CNOT Gate)
- [CYGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CYGate.html) (Controlled Y Gate)
- [CZGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CZGate.html) (Controlled Z Gate)
- [CHGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CHGate.html) (Controlled Hadamard Gate)
- [DCXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.DCXGate.html) (Double Controlled X Gate, a.k.a., Double CNOT Gate)
- [CSXGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CSXGate.html) (Controlled Square Root of X Gate)
- [CSdgGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.CSdgGate.html) (Controlled S^dagger Gate)
- [ECRGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ECRGate.html) (Echoed Cross-Resonance Gate)
- [SWAPGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.SwapGate.html) (Swap Gate)
- [iSWAPGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.iSwapGate.html) (Imaginary Swap Gate)


## Function Documentation
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