Questions tagged [magic-states]
For questions regarding anything related to magic states as resources for quantum computation and information. Magic (non-stabilizer) states are crucial in the state-injection model, and generate, via T-gadgets, the T-gates which are non-Clifford and make the set Clifford+T a universal gate set. On-topic includes manipulation, measurement, geometric understanding, fault-tolerance, resource, quantification, counting, simulation of these states.
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Which single-qubit mixed states work for magic state distillation?
I recently started learning about universal quantum computation using magic states, and I'm currently reading one of the early papers on the subject by Bravyi and Kitaev .
In the paper, they showed ...
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Can we distill magic states with arbitrary angle $\theta$?
There seems to be numerous work about the distillation protocol of the $T$-magic state
$$
\frac{1}{\sqrt{2}}(|0\rangle+e^{i\pi/4}|1\rangle).
$$
Similarly, I am wondering if it is possible to distill a ...
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Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)
In Litinsky's paper, there are many circuits relations, like the one below.
The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the ...
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Why do magic state consumption circuits work?
The following circuits from Litinski's Magic State Distillation paper are two ways to consume magic states. Why do these circuits work? I've heard there's a relationship with the Choi-Jamiolkowski ...
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Is the plus state a magic state for the Hadamard gate?
Is the plus state $\left|+\right>:=\frac{\left| 0\right>+\left| 1\right>}{\sqrt{2}}$ a magic state for the Hadamard gate $H$? That is, given the ability to perform (controlled) Pauli ...
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Universal Gate Set, Magic States, and costliness of the T gate
The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In ...
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Intuition behind observable rotations during magic state injection
Cleaner magic states with hook injection writes that the ZZ rotation performed amounts to a rotation of the logical $X$ observable. This is similar to High-Fidelity Magic-State Preparation with a ...
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How to perform a multi Pauli rotation with arbitary angle?
Recently, I was trying to find some methods to perform a multi Pauli rotation gate with arbitary angle. I want to use the method proposed in the paper arXiv:1808.02892v3, and the circuit is shown as ...
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Are Clifford operations not universal unless a quantum computer is efficiently classically simulatable?
I've read this paper by Bravyi and Kitaev and got confused by this paragraph.
It is well-known that these operations are not sufficient for universal quantum computation (unless a quantum computer ...
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Quantum algorithms with few T gates?
Many existing quantum algorithms require millions or billions of T gates to reach a scale that is classically hard to simulate. However, existing Clifford + T circuits seem hard even with 100 or so T ...
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Why the perfect 5-qubit code was used for magic state distillation?
I am currently trying to understand magic state distillation. So far, my understanding is that the general idea is to find a code where a non-Clifford gate is transversal (very well explained in https:...
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How to you initialize a qubit into a magic state in IBM Quantum composer
I want to build/prepare a qubit transforming from $\vert 0 \rangle$ into a magic state. How do I do that?
the particular magic state I have in mind is the following,
$$ |\varphi\rangle = \frac{1}{\...
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Non-magic non-stabilizer multi-qubit states
Does anyone know of any resources that show examples of simple multi-qubit states which are non-stabilizer states but that are still classically efficiently stimulable? Another way to phrase it is ...
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Which phase gates can be catalyzed by Clifford+Toffoli circuits with post-selection?
$\newcommand{\ket}[1]{|#1\rangle}$Let us call some state $k$-qubit state $\ket{S}$ catalyzable by some other state $\ket{S'}$ if there is a Clifford+Toffoli circuit (possibly with ancilla and/or post-...
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Scaling of magic state distillation with single & two-qubit gate error
How does the resulting error in magic state distillation scale with the fidelity of single qubit gates and two qubit gates? In most experimental systems, two-qubit gate errors are much larger than ...
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Magic state distillation with the $15$ qubit code. How are the transversal $T$ performed? Also via a (lower level) state injection?
I have a code $C1$ that admits native fault-tolerant gates for any element in the Clifford group (for instance via transversal implementation), but that then doesn't have an easy way to perform the $T$...
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Magic state distillation with the 15 qubit code. Why is the failure $O(p^2)$ if we include $|+_L\rangle$ preparation and decoding?
My goal is to understand why the magic state distillation (for instance based upon the $15$ qubit code) improves the fidelity of the magic state. I followed this lecture to try to understand it. I ...
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Universal quantum computation by Clifford gates plus magic state
In the paper Universal quantum computation with ideal Clifford gates and noisy ancillas, it is claimed that a circuit composed by Clifford gates, plus a so-called "magic state", can perform ...
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Given a $|W_8\rangle$, perform a CCCZ using stabilizer operations
I know it's possible to perform a CCZ operation using only stabilizer operations (Cliffords + Pauli measurements + classical feedback) by consuming a $|CCZ\rangle$ state, and that a $|W_4\rangle$ ...
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Magic state distillation: why is it harder to prepare the encoded $|A_{\pi/4}\rangle$ than $|0 \rangle$
My question is the following
Let's assume I am using Steane concatenated code to do error correction. I consider that the stabilizers are extracted fault-tolerantly through the Steane method. The ...
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Pros/cons of the different schemes to have complete fault-tolerant gatesets
I am interested to have references and comment about pro/cons of the various methods that are used to implement complete gateset in a fault tolerant manner.
Usually the Clifford operations have a ...
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Definition of magic $T$ and $H$ states: are there different definitions for them?
I am a bit confused by the definition of magic $T$ and $H$ states and I would like to check if their name is actually not uniformously spread in the litterature (or if I am not understanding something)...
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Why are there eight $T$ magic state and twelve $H$ magic states?
I am learning magic state distillation.
We can define the following two states:
$$ |T\rangle \langle T | = \frac{1}{2}(I+\frac{1}{\sqrt{3}}(\sigma_x+\sigma_y+\sigma_z))$$
$$ |H\rangle \langle H | = \...
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Good references to learn magic state distillation for fault tolerance
I need to learn magic state distillation procedure and their application to fault-tolerance.
One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf
I am ...
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