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Here is a circuit that can create the desired state (similar ideas were discussed in this answer), if all mentioned measurements yield $|0\rangle$ state: or in a more compact form (the circuits are constructed via quirk). The first three qubits are ancillary qubits and the rest are the qubits where $|0_L\rangle$ will be created if after the measurements all ...


4

You can obtain the Kraus operators of the combined channel by taking products of the Kraus operators of the individual channels (using the notation from the paper you linked): Amplitude damping: $E^{AD}_1 = \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-p_{AD}} \end{bmatrix}$, $E^{AD}_2 = \begin{bmatrix} 0 & \sqrt{p_{AD}} \\ 0 & 0 \end{bmatrix}$ Phase ...


2

I'm not sure what your specific question is - the IBM Q processor does not implement an error correction scheme by default, so the theorem doesn't apply. Furthermore, the statistic provided in the Wikipedia page suggests this chip would be incapable of sufficiently depressing the error rate: At a 0.1% probability of a depolarizing error, the surface code ...


2

c_if must be used on an entire ClassicalRegister. However, it is still possible to use it on a single classical bit. You would need to create a ClassicalRegister of size 1, and attach that to your circuit. This would be the register that you input into the c_if call. from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister c1 = ...


2

As I explained in my answer on a previous question of yours, the depolarizing channel is not really 'physical' - actual quantum systems don't really behave that way. So for simulations where you, for instance, investigate the performance of some code against the depolarizing channel, it doesn't really matter what the exact value of $p$ is in your simulations....


2

I think in this case you can split the experiments into multiple jobs. The idea is that you split measurement calibration circuits generated by complete_meas_cal into a number of batches, execute the first batch and use the corresponding results to initialize a measurement correction fitter with CompleteMeasFitter. Then you can use the CompleteMeasFitter....


1

One way of defining the Steane code is via its stabilizers. There's a set of operators $\{K_n\}_{n=1}^6$ which all commute, such that a state in the code space is defined by being the $+1$ eigenstate of all these operators. So, you can perform syndrome extraction simply by measuring the value of each stabilizer. This is a standard circuit, (the $\sigma_1\...


1

The first answer discusses what the pseudothreshold is and how to find it, but I will try to give a few details on the difference between thresholds and pseudothresholds, since your first question does ask for both definitions. In quantum error correction (QEC), a logical qubit is encoded in many physical qubits. Given some underlying physical error rate $p$...


1

So the general definition of pseudothreshold is when the logical qubit outperforms a physical qubit. If your error model is idling error, for example, you want to find the physical value of T1 and T2 for which the physical qubits lifetime is lower than the logical qubit's lifetime. The easiest way to calculate this would be to write a simulation of the ...


1

The other answer already uses this, but just to make the general fact more explicit: if $\mathcal E=\mathcal E_A\circ\mathcal E_B$, that is, $\mathcal E(\rho)=\mathcal E_A(\mathcal E_B(\rho))$, and the Kraus decompositions of the single channels read $$\mathcal E_A(\rho)=\sum_a A_a\rho A_a^\dagger, \qquad \mathcal E_B(\rho)=\sum_b B_b\rho B_b^\dagger,$$ then ...


1

You are analysing the case where you know a unitary has definitely been applied on the first qubit. In that case, it should not be surprising that there's no change in entanglement. You can take a couple of perspectives: single qubit unitaries do not change entanglement. To change entanglement with a unitary requires a two-qubit unitary. If you know what ...


1

I would like to add to keisuke.akira answer. The Noise Model in which only a Single Qubit Flips is correct. However we can assume a more general Noise Model which may be more realistic and still see the use of Bit Flip Code. Since Quantum Circuits are analog, hence it is rare that a qubit flips completely. It is more likely that there is a small coherent ...


1

We're trying to build a code to protect against single bit flips. That is, we are assuming the noise model. By assumption, it has the form $\sigma_x \otimes \mathbb{I} \otimes \mathbb{I}$, therefore, it only flips one of them. Of course, in general, the noise does whatever it wants, and therefore, we need to build codes that can protect against more general ...


1

Some thoughts: A theoretical perspective From a theoretical perspective, the depolarizing channel is the 'standard' (if there is such a thing) or by some means the most applicable. Because the Paulis (together with the identity operator) form a basis for $SU(2)$, if a code can correct the $X, Y$ and $Z$ flips on a certain qubit (and it it is able to ...


1

I am no longer confused about this, since now I see in this equation we are already restricting to a subspace $||S\mathcal{E}(|u\rangle\langle u|)-S\mathcal{E}(|v\rangle\langle v|)|| = |||u\rangle\langle u|-|v\rangle\langle v|||$, and the contracting map has to contract every subspace.


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