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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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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. ...
Xiao H's user avatar
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Difficulties Encountered in Simulating Quantum Purification Circuits for Magic State Distillation

Recently, I've been studying Kitaev's paper on magic state distillation. Referring to Nathan Babcock's presentation, I wrote a program in MATLAB to simulate the purification circuit. Instead of the ...
Xiao H's user avatar
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4 votes
1 answer
221 views

How do magic states circumvent the Eastin-Knill theorem?

I'm trying to understand magic states and how they circumvent the Eastin-Knill theorem. I understand that these magic states are used to implement non-Clifford gates but how are these magic states ...
Karim's user avatar
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1 vote
1 answer
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How is Magic State Distillation (MSD) compatible with Stabiliser Measurement?

Suppose I have the rotated surface code in which I want to inject a $T$-state. What I don't get it is: suppose we do end up with the logical state $|0_L\rangle+e^{i\pi/4}|1_L\rangle$, then we must ...
JoJo P's user avatar
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4 votes
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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 ...
Ian Gershon Teixeira's user avatar
2 votes
3 answers
76 views

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?
Michael.Andy's user avatar
4 votes
1 answer
169 views

Is it possible to implement the controlled-S gate, such that the inner gate between the CNOTs belongs to the Clifford?

It's well known how to implement a controlled-U gate when $U$ is a single qubit gate via the decomposition of $U$ into the product $U=e^{i\phi}AXBXC$ where $ABC=I$. My question is: is it possible to ...
Dudu Ponar's user avatar
2 votes
1 answer
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How can sub-logarithmic magic state distillation be possible?

In "Distillation with sublogarithmic overhead", Hastings and Haah present a magic state distillation factory with a yield parameter $\gamma \approx 0.7$. Meaning that the number of initial ...
Craig Gidney's user avatar
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3 votes
1 answer
159 views

Clifford+T synthesis with imperfect T gates

From this paper, it has been nicely shown that the number of perfect $T$ gates required to simulate arbitrary single-qubit gates grows linearly with $\log(1/\epsilon)$, where $\epsilon$ is the error ...
Yunzhe's user avatar
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1 vote
1 answer
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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 ...
David Dentelski's user avatar
1 vote
1 answer
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Post selection during hook injection

I was reading the paper about "Cleaner magic states with hook injection"1, which is really cool, and I get technically, but it is unclear in which stages do you perform the post-selection. ...
Yaniv Kurman's user avatar
3 votes
1 answer
84 views

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 ...
user196574's user avatar
7 votes
0 answers
98 views

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 ...
Yunzhe's user avatar
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6 votes
1 answer
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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 ...
Marco Fellous-Asiani's user avatar
3 votes
1 answer
130 views

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 ...
C. Kang's user avatar
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2 votes
2 answers
232 views

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 ...
Milo Moses's user avatar
8 votes
3 answers
899 views

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 ...
Eric Kubischta's user avatar
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1 answer
71 views

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 ...
C. Kang's user avatar
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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 ...
Zehong Fan's user avatar
2 votes
0 answers
115 views

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 ...
Mr. Morgan's user avatar
2 votes
0 answers
53 views

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 ...
shixian105's user avatar
5 votes
0 answers
165 views

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:...
Diego's user avatar
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2 votes
1 answer
260 views

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}{\...
Kimbly  North's user avatar
1 vote
0 answers
59 views

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 ...
sheesymcdeezy's user avatar
1 vote
1 answer
130 views

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-...
Tuomas Laakkonen's user avatar
1 vote
1 answer
80 views

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 ...
shixian105's user avatar
3 votes
1 answer
305 views

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 $T$...
Marco Fellous-Asiani's user avatar
3 votes
1 answer
352 views

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 ...
Marco Fellous-Asiani's user avatar
3 votes
1 answer
659 views

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 ...
Doriano Brogioli's user avatar
5 votes
1 answer
373 views

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 $|W_4\rangle$ ...
Craig Gidney's user avatar
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8 votes
2 answers
479 views

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 ...
Marco Fellous-Asiani's user avatar
1 vote
1 answer
114 views

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 ...
Marco Fellous-Asiani's user avatar
6 votes
1 answer
623 views

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)...
Marco Fellous-Asiani's user avatar
7 votes
2 answers
309 views

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's user avatar
7 votes
1 answer
343 views

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 ...
Marco Fellous-Asiani's user avatar