Questions tagged [state-distillation]
For questions about the process of transforming multiple copies of a state into Bell pairs using only local operations and classical communication.
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What's so bad about preparing magic states by measuring Clifford gates?
Suppose we want to perform a gate from the third level of the Clifford hierarchy for example $ T,CS, CCZ, CCX $. To implement such a gate using gate teleportation we need to take as an input certain ...
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Deriving |𝐶𝐶𝑍⟩ magic states from |𝐶𝐶𝐶𝑍⟩?
Analogous to the $|T\rangle$ and $|CCZ\rangle$ magic states, one can define a $|C^n Z\rangle$ magic state. Is there any known quantification of the amount of magic of this state, and is there a way to ...
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How are these T-distillation circuits derived?
I'm trying to wrap my head around T-distillation circuits, specifically for the 15-to-1 distillation code. My question is, how does one discover these circuits from the description of the code?
There ...
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How do two-way protocols allow to extract entanglement from states like Werner's?
As discussed in [Lo and Popescu 1999], it is always possible to distill entanglement from pure bipartite states using a one-way protocol. The gist of the idea, as I understand it, is Proposition 1 in ...
glS♦
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Two Quantum State Density Matrices with Unequal Off-Diagonal Elements but Equal Magnitudes
I recently read Kitaev's paper on magic state distillation. I want to verify whether the circuit for the [5,1,3] encoder can map a single qubit state T_0 to the logical state T_1 in the encoded space. ...
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Does the preparation of magic states need magic gates?
It is well known that universal quantum computation needs magic states. So we need to prepare magic states although it is noisy. My question is does the preparation of magic states needs magic gates?
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Magic state distillation of physical vs logical qubit
In the original paper by Bravyi and Kitaev, the distillation procedure takes 5 physical qubits, each prepared in a faulty T state. The qubits are in a product state, and error can be detected by ...
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15-to-1 distillation protocol in lattice surgery: doesn't the potential rejection of the level-1 magic states makes it last longer than $15$ timestep?
Overview of my question
I am following Litinsky's paper, and I would like to better understand how the duration of the level-2 15-to-1 distillation protocol is being estimated. Litinsky's says that it ...
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15-to-1 distillation protocol implemented with lattice surgery: don't we loose transversality by commuting Clifford toward measurements?
I am following Litinsky's paper explaining the 15-to-1 distillation protocol.
The usual "trick" done to distill, say the $|T \rangle \equiv T |+ \rangle$ magic state, is to use a code ...
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15-to-1 distillation protocol: why is the probability of error of the distilled state $35p^3$ and not $\binom{15}{3} p^3=455p^3$?
The circuit performing the $15$-to-$1$ distillation of the magic state $T|+\rangle$ is shown below (figure taken from Litinski's paper).
The first gates encode the $|+\rangle$ of the 15 qubit code. A ...
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Injecting arbitrary rotations into the surface code
I'm trying to find an exact resource count for specific QFTs.
A QFT generally needs small power-of-two rotations. These can be constructed out of Clifford+T, but I'm wondering if one can inject them ...
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Understanding entanglement distillation via stabilizer codes?
I am having some trouble understanding the distillation of EPR pairs using a stabilizer code. This idea goes back to the paper by Bennet, DiVincenzo, Smolin, and Wooters.
The idea (I think) is that $k$...
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How to prove that the distillable entanglement satisfies $E_D(|\psi_d\rangle\!\langle\psi_d|)\ge \log d$?
If I have a pure state vector:
$$
\left|\psi_d\right\rangle=\frac{1}{\sqrt{d}}\sum^{d}_{i=1}\left|ii\right\rangle
$$
then the distillable entanglement satisfies:
$$
E_{D}(\left|\psi_d\right\rangle\...
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What are good pedagogical introductions to entanglement distillation?
I have a basic understanding of what entanglement distillation entails, up to the typical subspace projection protocol described in Nielsen & Chuang, and I would like to read more on the subject. ...
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Equivalence between entanglement purification and quantum error correction
I've recently been reading the seminal paper recently (BDSW 1996), where they established the equivalence between 1-EPP (one-way classical communication) and error correction through explicit ...
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