# The magic of universal quantum computing with permutations

@article{Planat2017TheMO, title={The magic of universal quantum computing with permutations}, author={Michel Planat and Rukhsan-Ul-Haq}, journal={Advances in Mathematical Physics}, year={2017}, volume={2017}, pages={1-9} }

The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject). A first classification of a few types of resulting magic states in low dimensions is performed.

## 13 Citations

### Representation Matching For Remote Quantum Computing

- Computer Science
- 2020

It is shown that the representation matching protocol is capable of reducing the communication or memory cost to almost minimum in various tasks, including delegated execution of unitary gate arrays, permutation gates, and unitary conjugation, as well as the storage and retrieval ofunitary gates.

### Magic informationally complete POVMs with permutations

- MathematicsRoyal Society Open Science
- 2017

It is shown that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs, investigated in dimensions 2–12, and exhibit simple finite geometries in their projector products.

### Study on Actual Developments in the Field of Quantum Computing in Terms of Cyber Security and Physical Systems

- Computer ScienceRomanian Cyber Security Journal
- 2022

The concept of quantum computer is described, which describes the quantum algorithms, areas of use and weaknesses or strengths of quantum computing, cyber security and circuits.

### Quantum Fourier Operators and Their Application

- Computer ScienceReal Perspective of Fourier Transforms and Current Developments in Superconductivity
- 2021

This work reviews the structure of the quantum Fourier transform and its implementation, and provides a permutation structure for putting the QFT within the context of universal computation.

### Faster quantum computation with permutations and resonant couplings

- Physics, Computer ScienceLinear Algebra and its Applications
- 2020

### Quantum computing thanks to Bianchi groups

- MathematicsEPJ Web of Conferences
- 2019

It has been shown that the concept of a magic state (in universal quantum computing: uqc) and that of a minimal informationally complete positive operator valued measure: MIC-POVMs (in quantum…

### Quantum Computing, Seifert Surfaces, and Singular Fibers

- MathematicsQuantum Reports
- 2019

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete…

### Universal Quantum Computing and Three-Manifolds

- Computer ScienceSymmetry
- 2018

This paper investigates quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy.

### Qutrit and ququint magic states

- Physics
- 2020

Non-stabilizer eigenstates of Clifford operators are natural candidates for endpoints of magic state distillation routines. We provide an explicit bestiary of all inequivalent non-stabilizer Clifford…

### Topological Quantum Computing and 3-Manifolds

- PhysicsQuantum Reports
- 2021

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of…

## References

SHOWING 1-10 OF 31 REFERENCES

### Contextuality as a resource for qubit quantum computation

- Physics
- 2015

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a…

### Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

### Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)

- Physics
- 2005

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.…

### The resource theory of stabilizer quantum computation

- Physics
- 2013

A resource theory, analogous to the theory of entanglement, is developed that is relevant for fault-tolerant stabilizer computation and introduces two quantitative measures for the amount of non-stabilizer resource, including the sum of the negative entries of the discrete Wigner representation of a quantum state.

### Negative quasi-probability as a resource for quantum computation

- Physics
- 2012

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speed-up and, in particular, for fault-tolerant quantum…

### Quantum Universality from Magic States Distillation Applied to CSS Codes

- PhysicsQuantum Inf. Process.
- 2005

A sharp threshold is shown in the Hadamard “magic” direction of the Bloch sphere between those ρ allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated.

### Contextuality supplies the ‘magic’ for quantum computation

- PhysicsNature
- 2014

This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer.

### Magic-state distillation with the four-qubit code

- Computer ScienceQuantum Inf. Comput.
- 2013

A routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest and use of this routine in combination with the 15-to-1 distillation routine described by Bravyi and Kitaev allows for further improvements in overhead.

### Improved magic states distillation for quantum universality

- Physics
- 2004

Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state ρ , can we do universal quantum computation? As motivation for this question, “magic state” distillation…

### Quasi-probability representations of quantum theory with applications to quantum information science

- Physics
- 2011

This paper comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability…