# Tensor Network Rewriting Strategies for Satisfiability and Counting

@inproceedings{Beaudrap2020TensorNR, title={Tensor Network Rewriting Strategies for Satisfiability and Counting}, author={J. Niel de Beaudrap and Aleks Kissinger and Konstantinos Meichanetzidis}, booktitle={QPL}, year={2020} }

We provide a graphical treatment of SAT and \#SAT on equal footing. Instances of \#SAT can be represented as tensor networks in a standard way. These tensor networks are interpreted by diagrams of the ZH-calculus: a system to reason about tensors over $\mathbb{C}$ in terms of diagrams built from simple generators, in which computation may be carried out by \emph{transformations of diagrams alone}. In general, nodes of ZH diagrams take parameters over $\mathbb{C}$ which determine the tensor…

## 8 Citations

### Classifying Complexity with the ZX-Calculus: Jones Polynomials and Potts Partition Functions

- Computer ScienceArXiv
- 2021

This work presents simplifying rewrites for the case of qutrits, which are of independent interest in the field of quantum circuit optimisation and further champions the ZX-calculus as a suitable and unifying language for studying the complexity of classical and quantum problems.

### Simplification Strategies for the Qutrit ZX-Calculus

- Computer Science
- 2021

The main contribution of this work is the derivation of efﬁcient rewrite strategies for the stabiliser fragment of the qutrit ZX-calculus, which constitutes a first non-trivial step towards the simplification ofqutrit quantum circuits.

### Well-tempered ZX and ZH calculi

- Mathematics
- 2020

The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones…

### Circuit Extraction for ZX-diagrams can be #P-hard

- Computer Science, MathematicsICALP
- 2022

This paper proves that any oracle that takes as input a ZX-diagram description of a unitary and produces samples of the output of the associated quantum computation enables eﬃcient probabilistic solutions to NP-complete problems.

### Tropical Tensor Network for Ground States of Spin Glasses.

- PhysicsPhysical review letters
- 2021

The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes the computational power of graphical processing units (GPUs).

### The ZX& calculus: A complete graphical calculus for classical circuits using spiders

- MathematicsElectronic Proceedings in Theoretical Computer Science
- 2021

It is shown that in the case of TOF, freely adding a counit, constructing the category of quantum channels, and computing the discrete Cartesian completion are all equivalent to partial functions between powers of the two element set.

### An Algebraic Axiomatisation of ZX-calculus

- MathematicsElectronic Proceedings in Theoretical Computer Science
- 2021

In this paper we give an algebraic complete axiomatisation of ZX-calculus in the sense that there are only ring operations involved for phases, without any need of trigonometry functions such as sin…

### ZX-calculus for the working quantum computer scientist

- Computer Science
- 2020

This review discusses Clifford computation and graphically prove the Gottesman-Knill theorem, a recently introduced extension of the ZX-calculus that allows for convenient reasoning about Toffoli gates, and the recent completeness theorems that show that, in principle, all reasoning about quantum computation can be done using Zx-diagrams.

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