# 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.

24 questions
Filter by
Sorted by
Tagged with
52 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 ...
68 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 ...
201 views

### 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 ...
96 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 ...
133 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 ...
625 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 ...
46 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 ...
40 views

### 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 ...
100 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 ...
33 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 ...
107 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:...