### Abstract

Original language | English |
---|---|

Article number | 042172 |

Number of pages | 39 |

Journal | AIP Advances |

Volume | 1 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2 Dec 2010 |

### Fingerprint

### Keywords

- quant-ph
- cond-mat.other
- cs.CC
- cs.LO
- math-ph
- math.MP

### Cite this

*AIP Advances*,

*1*(4), [042172]. https://doi.org/10.1063/1.3672009

**Categorical Tensor Network States.** / Biamonte, Jacob D.; Clark, Stephen R.; Jaksch, Dieter.

Research output: Contribution to journal › Article

*AIP Advances*, vol. 1, no. 4, 042172. https://doi.org/10.1063/1.3672009

}

TY - JOUR

T1 - Categorical Tensor Network States

AU - Biamonte, Jacob D.

AU - Clark, Stephen R.

AU - Jaksch, Dieter

PY - 2010/12/2

Y1 - 2010/12/2

N2 - We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state S, we present a new and general method to factor S into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

AB - We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state S, we present a new and general method to factor S into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

KW - quant-ph

KW - cond-mat.other

KW - cs.CC

KW - cs.LO

KW - math-ph

KW - math.MP

UR - http://dx.doi.org/10.1063/1.3672009

U2 - 10.1063/1.3672009

DO - 10.1063/1.3672009

M3 - Article

VL - 1

JO - AIP Advances

JF - AIP Advances

SN - 2158-3226

IS - 4

M1 - 042172

ER -