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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. ...
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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 ...
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 ...
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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 ...
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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 ...
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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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### 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 ...
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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 ...
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### 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 ...
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1 vote
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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 ...
1 vote
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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. ...
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 ...
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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 ...
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 ...
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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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