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.
Questions tagged [magic-states]
62 questions
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What is the Generalized Quantum Stein's Lemma and why is it important?
I'm sensing a lot of buzz about potential re-proofs of the Generalized Quantum Stein's Lemma - a generalization of the quantum counterpart to the classical Stein's Lemma, which is of some importance in statistical inference and hypothesis…
Mark Spinelli
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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 wondering if there are more recent and pedagogic…
Marco Fellous-Asiani
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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 practice we find a code that has $\mathcal{C}$ transversal…
Eric Kubischta
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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 Steane code admits transversal Clifford operations…
Marco Fellous-Asiani
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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 $\theta$-magic…
Yunzhe
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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 | =…
Marco Fellous-Asiani
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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 uniformly spread in the literature (or if I am not understanding something).
In the original paper about them, they are defined…
Marco Fellous-Asiani
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Universal gate set for the $ [[15,1,3]] $ code
The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is an implementation of the Hadamard gate $ H $.
The…
Ian Gershon Teixeira
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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 orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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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://arxiv.org/pdf/1612.07330.pdf on Fig. 3).
For…
Diego
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Magic state distillation, eigenvectors of Clifford gates, and transversal gates
I have some (possibly mistaken) ideas about magic state distillation. Please disabuse me of them?
In section III "Universal Quantum Computation with Magic States" of the original paper on magic states, Bravyi and Kitaev give a protocol using…
Ian Gershon Teixeira
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5
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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$ state can be turned into a $|CCZ\rangle$ state, so I…
Craig Gidney
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How many physical qubits does Magic state cultivation shave off from the "20 million physical qubits for RSA 2048" result?
Keeping everything in How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits the same ($10^{-3}$ physical error rate, 8 hours to complete the computation, same logical algorithm e.t.c) but with the only difference being that…
Victory Omole
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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 ancilla states. For example, a $ |T\rangle $ state…
Ian Gershon Teixeira
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Can the W state, or any non-stabilizer state for that matter, be considered a magic state?
Some examples of magic states (these can all be found here): the $ |T\rangle $ state for implementing the $ T $ gate is
$$
T | + \rangle = \frac{1}{\sqrt{2}}(|0\rangle + e^{i\pi/4}|1\rangle)
$$
A $ |\text{CS}\rangle $ state for implementing the $…
Ian Gershon Teixeira
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