# Tag Info

12

T2 is so-called dephasing time. It describes how long the phase of a qubit stays intact. In your words, it is time from $|+\rangle= \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ to $|-\rangle= \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$, or conversely. Just note that both T1 and T2 are not actually "time from state x to state y" but rather decay ...

11

What you call a black box is simply isolating the quantum system that stores (or represents) your qubits from the environment. This can be done in several ways depending on your physical realization. For example, in an ion trap based quantum computer, one uses states of a single ion to represent a qubit, and isolates that from the environment by levitating ...

11

Slight correction to Martin Vesely's answer: $T_2$ is not the (decay constant) time after which an initial state $|+\rangle$ will necessarily switch to the state $|-\rangle$. If it were, then error correction would be easy. Instead, it's the (decay constant) time after which an initial state $|+\rangle$ will evolve into an equal classical probabilistic ...

10

In simpler terms your question is: if noise/decoherence keeps entering the computation, how can a big computation possibly survive? The key concept you're missing is quantum error correction, which can pump noise/decoherence back out of the system. Of particular practical interest is the surface code.

9

The naming started in NMR and it has become the difference between the following two experiments. Experiment one: Prepare the qubit in a superposition state (apply a H gate) and vary the wait time and then measure in the superposition basis (apply another H gate). The decay time of this experiment is $T_2^*$. We commonly call this a Ramsey experiment. ...

8

In short: "coherence"! It's the crucial difference between quantum and classical. $\rho=|0\rangle\langle 0|+|1\rangle\langle 1|$ is just a statistical mixture, and behaves like a classical coin - any measurement that you perform on it gives a 50:50 split between the two possible outcomes. By contrast, $|+\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$ is a very ...

6

To simplify things a bit, let's take a single qubit and a single qutrit for comparison. First, the amplitude damping channel (giving e.g. emission of a photon) for a qubit is $\mathcal E\left(\rho\right) = E_0\rho E_0^\dagger + E_1\rho E_1^\dagger$, where $$E_0 = \begin{pmatrix}1 && 0 \\ 0 &&\sqrt{1-\gamma}\end{pmatrix}, \quad E_1 = \begin{... 6 The statement in Wikipedia is very generic, and only cites this paper as a reference. Quoting from the abstract of the paper: We demonstrate that decoherence of many-spin systems can drastically differ from decoherence of single spin systems. The difference originates at the most basic level, being determined by parity of the central system, i.e., ... 5 There are multiple ways to mathematically express the state of a quantum system. One is to write it as a linear combination of basis states, as either a vector or a matrix, as you have here. This is useful in many cases, but it also seems to be confusing to newcomers, since things like \vert 0 \rangle + \vert 1 \rangle, \vert 0 \rangle \langle 0 \vert + \... 5 I agree with most of what you've written in the first paragraph, though I would say that at roughly the same time (only 1 month apart!) as the Rebentrost et al. paper you mentioned, a very similar paper was posted to arXiv by Plenio and Huelga called "Dephasing assisted transport: Quantum networks in biomolecules" and it actually got published in the same ... 5 I believe the current record is held by the Jian-Wei Pan group in China, who are able to generate entanglement via a satellite. The journal article is here, while there's plenty of media coverage that is a bit more accessible, e.g. New Scientist. This claims a distance of 1203km. 5 I have worked with NVs in nanodiamonds a little bit, and you are totally right, surface characteristics have a huge influence on how far we can push them. There are definitely multiple groups working on the chemistry/material science that are working to clean up the surfaces as much as possible. I had a colleague, Carlo Bradac who worked with our chemistry ... 5 The quantum circuit model describes a quantum computer as a closed quantum system and assumes that there is a system which executes the circuit but is completely isolated from the rest of the universe. In the real world, however, there are no known mechanisms for truly isolating a quantum system from its environment. Real quantum systems are open quantum ... 5 Decoherence is the very general term which, more or less, is anything resulting in a loss of purity during the evolution of a system. Sometimes, when people are being a bit non-specific, they might be thinking of a particular type of decoherence such as dephasing (or perhaps depolarising) when they use the term decoherence. Relaxation and dephasing are two ... 5 frequency (GHz): The frequency(energy) associated with the transition between the qubit's ground state (|0\rangle) and first excited state (|1\rangle). readout error: The probability of preparing a |0\rangle(|1\rangle) and measuring a |1\rangle(|0\rangle), ie., of having an error in your readout single qubit U2 error rate: The average error per ... 4 Why not input one half of a maximally entangled state as the input to the black box (so that half has the same dimension as the input dimension)? Then you could test your favourite measure, such as the purity, of the full output state. If the oracle corresponds to a unitary evolution, the purity is 1. The less coherent the smaller the purity. Incidentally, ... 4 Photons travel fast, and there's often the option to transfer their entanglement to solid state. Of course, the advantage of transferring entanglement to a solid state qubit is that one is able to operate with it (one- and two-qubit gates, for example) with ease and efficiency, whereas it is very hard to effect two-qubit quantum gates on photons themselves, ... 4 Suppose you have a state \rho, and a random process that changes this to a state \rho_j with probability p_j. If you know what the value of j is, your knowledge of the resulting state will be described by the corresponding \rho_j. If you have no information regarding j, your knowledge will be described by$$\sum_j ~ p_j ~ \rho_j$$This is a ... 4 You could also look at the following webpage: https://quantumcomputingreport.com/scorecards/qubit-quality/ where they provide recent (I'm not sure how often they update this scores) values for gate fidelities and decoherece times for IBM and Rigetti chips (unfortunately they don't give any results on ion traps and photonics, since these machines are not ... 4 I guess your best shot would be to look for experimental comparisons like this one on Arxiv. But I am not aware of a tracking. I do not think we can consider having a "state of the art" in this field. The goal being to make them always better of course with better connectivity for instance (a possible factor to take into account). 4 Imgine that there is a bit string \vec{k}\in\{0,1\}^n. We use this to specify sites (bit value 1) where an error has occurred, and sites (bit value 0) where no error has occurred. The number of 1s in the bit string is k. The probability of this particular error arising is then p^k(1-p)^{n-k} because there are k sites with an error and n-k sites ... 4 I cannot give you a complete answer(I am not too familiar with the IBM quantum tools) however I might be able to give you a few hints from a NMR/EPR perspective. In magnetic resonance T2 is commonly measured by generating a spin coherence, and refocusing at progressively longer times then measuring a spin echo. In quantum gate language that would be: ... 4 For any quantum error correcting code, it is possible to construct a channel which introduces errors that the code cannot correct. However, the key point is that such channels are highly adversarial and not at all representative of any physically reasonable error mechanism. An easy way to construct such adversarial noise is to build it from the logical ... 3 You will need to know how long it takes for each gate of the circuit to be performed. Then the decoherence error rate is simply$$e^{t_{gate}/t_{decoherence}}

3

Exactly, it's a little bit difficult to find related examples except matthew mentioned. The link is out of date and the update one is here: 2_relaxation_and_decoherence 2_relaxation_and_decoherence.ipynb It contains lots of figures, perhaps they are what you want.

3

Josu, You might be mis-understanding something. Your equation for the Pauli channel says that when $t\rightarrow \infty$, all operators ($X,Y,Z,I$) have an equal probability (1/4) of transforming the density matrix $\rho$. You seem to be suggesting that $t\rightarrow \infty$, the probability of the $I$ operator acting on $\rho$ whould go to 0. Keep in mind ...

3

From Chapter 15 of NII's quantum information lecture series on "Fundamentals of Noise processes" (link here): An applied DC field $H_0$ is not completely uniform in all space points. If many spin qubits are placed in such an inhomogeneous DC field, they have different Larmor frequencies. This leads to the dephasing effect if we compare the phase ...

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Your question revolves implicitly around the concept of quantum decoherence and how to protect real-world implementations of qubits from it for a long time. This is an incredibly general problem, and at the same time, the details are wildly dependent on the technology used. If you have access to it, you can check chapter 5 : "Noise and decoherence" of ...

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The length of all backend basis gates is available from backend.properties().gate_length. For example properties = backend.properties() id_gate_length_qo = properties.gate_length('id', 0)

3

On IBM Q, it is a few tens microseconds. The best value of dephasing time T2 is around 500 microseconds. Have a look here IBM Q website and navigate to "Qubits as physical system" and then to "dephasing T2" to see development of T2 in last twenty years.

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