QuasiTheory.ErrorMitigation¶

QuasiTheory.ErrorMitigation.ProbErrorCancel(Noise_channel)¶

Produce an HPTP map (Choi) to inverse the Noise_channel.

\[\mathcal{N}^{-1} = c_1 \mathcal{D}_1 + c_2 \mathcal{D}_2.\]

Parameters:¶

Noise_channel (matrix) – The Choi matrix of the input noise channel.

Returns:¶

c1: The coefficient of the first component.

c2: The coefficient of the second component.

J1: The choi matrix of the quantum channel \(\mathcal{D}_1\).

J2: The choi matrix of the quantum channel \(\mathcal{D}_2\).

Return type:¶

[numeric, numeric, matrix, matrix]

Note

Temme, Kristan, Sergey Bravyi, and Jay M. Gambetta. Error mitigation for short-depth quantum circuits. Physical review letters 119.18 (2017): 180509.

QuasiTheory.ErrorMitigation.ProbErrorCancelO(Noise_channel, O)¶

Produce an HPTP map (Choi) to inverse the Noise_channel with respect to observable \(O\).

\[\mathcal{N}^\dagger\circ\mathcal{D}^\dagger(O) = O,\]

Parameters:¶

• Noise_channel (matrix) – The Choi matrix of the noise channel.

• O – Observable.

Returns:¶

c1: The coefficient of the first component.

c2: The coefficient of the second component.

J1: The choi matrix of the quantum channel \(\mathcal{D}_1\).

J2: The choi matrix of the quantum channel \(\mathcal{D}_2\).

Return type:¶

[numeric, numeric, matrix, matrix]

Note

Zhao, X., Zhao, B., Xia, Z., & Wang, X. (2023). Information recoverability of noisy quantum states. Quantum, 7, 978.

QuasiTheory.ErrorMitigation.ProbErrorCancelOS(Noise_channel, O)¶

Provide a CPTP map to inverse the Noise_channel with respect to observable \(O\) with the method called observable shift.

\[\mathcal{N}^\dagger\circ\mathcal{D}^\dagger(O) = \frac{1}{f} (O + tI)\]

Parameters:¶

• Noise_channel (matrix) – The Choi matrix of the noise channel.

• O (matrix) – Observable.

Returns:¶

overhead: The sampling overhead to retrieve classical information, which equals to \(f\).

t: The shifted distance.

JD: The choi matrix of the target channel to implement.

Return type:¶

[numeric, numeric, matrix]

Note

Zhao, B., Jing, M., Zhang, L., Zhao, X., Wang, K., & Wang, X. (2023). Retrieving non-linear features from noisy quantum states. arXiv preprint arXiv:2309.11403.