# Quantum Computing with Octonions

@article{Freedman2019QuantumCW, title={Quantum Computing with Octonions}, author={Michael H. Freedman and Modjtaba Shokrian-Zini and Zhenghan Wang}, journal={Peking Mathematical Journal}, year={2019} }

There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an entanglement pattern. We abstract the common principle behind both approaches and find the notion of a graph or even continuous family of equiangular projections. This notion is the leading character in the paper. The largest continuous family, in a sense made…

## 6 Citations

### Symmetry Protected Quantum Computation

- PhysicsQuantum
- 2021

This model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet or triplet state is considered and is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit X and Z gates.

### A generic approach to the quantum mechanical transition probability

- MathematicsProceedings of the Royal Society A
- 2022

In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these…

### Quantum Probability’s Algebraic Origin

- PhysicsEntropy
- 2020

The transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

### Quantum Probability's Algebraic Origin

- PhysicsEntropy
- 2020

The transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

### M-theory cosmology, octonions, error correcting codes

- Computer Science
- 2020

These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of r = 12 α / N e 2 $$ r=12\alpha /{N}_e^2 $$ in the range 10 − 2 ≳ r ≳ 10 − 3 , to be explored by future cosmological observations.

### One underlying mechanism for two piezoelectric effects in the octonion spaces

- PhysicsThe European Physical Journal Plus
- 2022

The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major…

## References

SHOWING 1-10 OF 14 REFERENCES

### QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY

- Mathematics
- 2011

This is a one-to-one translation of a German-written Ph.D. thesis from 1999. Quantum designs are sets of orthogonal projection matrices in finite(b)-dimensional Hilbert spaces. A fundamental…

### A one-way quantum computer.

- Physics, Computer SciencePhysical review letters
- 2001

A scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, which are thus one-way quantum computers and the measurements form the program.

### Adiabatic quantum computation is equivalent to standard quantum computation

- Physics, Computer Science45th Annual IEEE Symposium on Foundations of Computer Science
- 2004

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.

### Measurement-only topological quantum computation.

- PhysicsPhysical review letters
- 2008

By using an anyonic analog of quantum state teleportation, it is shown how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.

### Quantum computations: algorithms and error correction

- Computer Science
- 1997

This book discusses classical models of computations, quantum formalism, symplecto-classical cases, and error correction in the computation process: general principles.

### Quantum Cognition: The possibility of processing with nuclear spins in the brain

- Biology, Physics
- 2015

### Quasi-Topological Phases of Matter and Topological Protection

- Physics
- 2013

We discuss systems which have some, but not all of the hallmarks of topological phases. These systems' topological character is not fully captured by a local order parameter, but they are also not…