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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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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2 votes
1 answer

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}{\...
1 vote
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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 ...
1 vote
0 answers

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-...
1 vote
1 answer

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 ...
3 votes
1 answer

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 $T$...
3 votes
1 answer

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 ...
2 votes
1 answer

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 ...
4 votes
1 answer

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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8 votes
2 answers

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 ...
1 vote
1 answer

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 ...
5 votes
1 answer

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)...
7 votes
2 answers

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 | = \...
6 votes
1 answer

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: I am ...