Error mitigation

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A significant barrier to the usefulness of quantum computers is by far the noise generated by various operations. For example measurement noise, that is the noise generated by taking measurements of some quantum circuit.

Qiskit and Pyquil both have noise models in there simulators to generate a so-called noisy state.

I am not sure if Yao.jl does.

Error mitigation is the general set of methods and protocols to deal with such errors. Consider

$$\hat{y} = Ax, $$

where $\hat{y}$ is a noisy probability vector, $A$ is the calibration matrix and $x$ is the ideal state. The standard method, readout error mitigation is take a noisy state and left multiply by $A^{-1}$. The $Z$ basis is often chosen (i.e. qubits are represented by a $0$ or $1$ once measured).

Now error mitigation is obviously akin to sampling problems and probility in general. In small circuits, this problem is trivial. But what about even 8 qubits. The computational basis is $2^8$ and the calibration matrix is $2^8 \times 2^8$. So as the number of qubits increases, the problem becomes untenable by standard approaches.

I would like to open the issue of developing some error mitigation techniques.