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6

(1) Both filters and attenuators are used Let me just start by saying that non-attenuating filters have not been completely ruled out by people working in the design of cold quantum computers. I will use quotes from three papers, all from 2018, to support this point. Paper #1: Distinguishing coherent and thermal photon noise in a circuit QED system "...

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The 2-norm difference typically isn't particularly physical. So no, this is most likely not the right distance. What you want from a physical point of view is a distance measure which measures the maximal distance between the two channels on any possible input (possibly on a larger system), such as the diamond norm. Note that the fact that "norms are ...

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Quantum channels are foremost, linear operators. So given a basis for the Hilbert-Schmidt operator space (for example the states $\{|0\rangle\langle 0|,|0\rangle\langle 1|,|1\rangle\langle 0|,|1\rangle\langle 1|\}$ that you've chosen above), where density matrices reside, it acts linearly on the basis elements. Perhaps, the easiest way to see it is to write ...

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For any quantum error correcting code, it is possible to construct a channel which introduces errors that the code cannot correct. However, the key point is that such channels are highly adversarial and not at all representative of any physically reasonable error mechanism. An easy way to construct such adversarial noise is to build it from the logical ...

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As Adam Zalcman has stated in his answer, channels whose Kraus operators are proportional to unitary operators are called mixed-unitary channels (or, alternatively, random unitary channels). Every mixed-unitary channel is unital (meaning that it maps the identity operator to itself), so if you want a channel that is not mixed unitary, just pick any non-...

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The standard noisy approach is not to try to determine the presence of an eavesdropper as such, but to create a final key where, even if there is an eavesdropper, you can still be confident that the eavesdropper has negligible information about the key. So you aren't trying to distinguish between noise and eavesdropping, but pessimistically assuming that ...

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That might depend on your noise model. A typical noise model is independent errors on each qubit, occurring with probability $p$. In that case, as soon as there's a non-zero chance of having a single-qubit error, there's a non-zero chance of have a two-qubit error. But it could be a negligibly small probability. Part of the point of an error correcting code ...

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Here are my thoughts. I would think the final probability gives the histogram that can help calculate the average fidelity of the circuit. The machine itself does not recognize that it is implementing an identity operator, therefore whatever you get after running the circuit can be used to track the fidelity. (I hope I understand your question correctly.) ...

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I don't know the fully general answer, but have found a solution for channels acting on a single qubit. Mixed-unitary channels Quantum channels that admit a Kraus representation consisting solely of multiples of unitary operators are known as mixed-unitary channels, i.e. $\mathcal{E}$ is a mixed-unitary channel if there exists unitary operators $U_i$ and ...

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Control errors The term control error is generally used to refer to errors due to imperfections of the qubit control system. Hardware devices that control qubit evolution have a number of knobs that the control system sets to various values. In the process known as calibration we learn the settings of the knobs that correspond to each of the supported gates. ...

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The idea of erasure being projection onto $|0\rangle$ is perhaps misleading in this context (my fault for mentioning it in a comment without having looked at the full details of what this specific paper did). This paper does not project the set of qubits $y$ onto the $|0\rangle$ state. Instead, they trace out those qubits. Perhaps the best way of writing ...

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Yes, there is a nice way to represent this composition, valid for any linear map, not only unitaries. It is so useful that it has a name, link product. Let $\mathcal E:A\to B$ and $\mathcal F:B\to C$ be two linear maps, and $J(\mathcal E)$ and $J(\mathcal F)$ their Choi representations. The Choi representation of their composition \$\mathcal F \circ \mathcal ...

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How many shots were you using? and on which device? Theoretically, you only need one shot for this algorithm, but because current devices are noisy, hence the name NISQ (Noisy Intermediate-Scale Quantum), we need to do a lot more experiments here. The maximum number of shots on IBM's machine is 8192 so I would use that. It is important to note that not all ...

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Note that OpenFermion interoperates with cirq to provide many features that are not specific to quantum chemistry. You can add noise to your circuits like this noisy = ideal.with_noise(cirq.depolarize(p=0.01)) where ideal and noisy are instances of cirq.Circuit. Alternatively, you can use a simulator such as cirq.DensityMatrixSimulator which allows you to ...

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It could have something to do with cross-talk and decoherence. By introducing the messy circuits, the other qubits are on idle as long as the messy circuits are being computed. Hence decoherence effects will certainly play a role here. As the qubits in the messy register are manipulated via randomized quantum gates, these manipulation can additionally have ...

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If there is an evasdroping, an error rate is higher than some long-term average of a quantum communication channel used for a quantum key distribution. So, when the error rate is high, the key is deleted and new one is distribuited again until noise level is at acceptable level. A natural noise can be reduced with classical error correction, something like ...

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I think what you could do is measure the bits, and then possibly flip the answer based on whether a drawn random number is less than the error rate associated with the outcome, i.e the error rates of measuring 0 but really given a 1, and measuring 1 but really given a 0. However, doing this on actual HW is a bit more tricky. Namely all of the logic needs ...

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Large datasets will not necessarily reduce the performance of an quantum kernel SVM (a Support Vector Machine trained classically using a kernel function evaluated on a quantum computer). You should actually expect the opposite: Training on larger datasets will reduce the generalization error and improve classifier (test) performance provided that you are ...

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after finding this: What are examples of Kraus operators describing the process of control error? I think I understand the issue - I incorrectly assumed that the error operator is applied to the unitary and not to the state. Once I use the definition from the link above I get the correct result, here's an example: import qiskit from qiskit import ...

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I would think the noise model are based off the calibration data of the real hardware. I am not sure how often IBM updated them. Hopefully someone from the IBM team can provide more details. In term your second question/point. After designing my quantum algorithm/circuit, I would first test it on the simulator without any noise and see how it works first. ...

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The curve you are observing seems intuitive to me, since it shows how decoherence works. As you add more gates the state of the qubits tend to the ground state asymptotically . You can probably use T1 and T2 to predict the curve.

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I'm probably late to party but I found this section today. In terms to answer your question[s] I made a lot of thoughts and read enough paper for a tree. I found 2 excellent experiments (very timely) that show their practical testing problems and solutions. And most important their preparation for a reproducible quantum state. The documentations of both ...

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I am assuming you are probably trying to do error mitigation using extrapolation technique giving in this paper: https://arxiv.org/abs/1801.03897 The other answer is great and perfectly fine. I just want to add that, you could also use circuit barrier as a way to tell Qiskit not to optimize the consecutive CNOT gates. For example:

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Yes, Qiskit's transpiler will optimize the circuit and remove redundant gates automatically. For normal operation this is desired behavior. However for cases like this where you don't want to transpiler to optimize the circuit for you and you want to send the circuit to the backend in a raw form (it will still fit it to the backend based on its constraints) ...

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It is possible from looing at here: https://github.com/quantumlib/Cirq/tree/master/cirq/devices and https://cirq.readthedocs.io/en/stable/generated/cirq.NoiseModel.html Also look at these answers on how to implement noise: How to add noise to existing gates in Cirq? https://github.com/quantumlib/Cirq/issues/1704

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