# There and back again: A circuit extraction tale

@article{Backens2021ThereAB, title={There and back again: A circuit extraction tale}, author={Miriam Backens and Hector Miller-Bakewell and Giovanni de Felice and Leo Lobski and John van de Wetering}, journal={Quantum}, year={2021}, volume={5}, pages={421} }

Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for one-way computations allowing measurements in three different planes of the Bloch sphere, most research so far has focused on computations containing only measurements in the XY-plane. Here, we give the first circuit-extraction algorithm to work for one-way…

## 35 Citations

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.

Quantum Theory from Principles, Quantum Software from Diagrams

- Mathematics
- 2021

This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning,…

Completeness of the ZH-calculus

- Mathematics
- 2021

There are various gate sets used for describing quantum computation. A particularly popular one consists of Clifford gates and arbitrary single-qubit phase gates. Computations in this gate set can be…

Entanglement and Quaternions: The graphical calculus ZQ

- Computer Science
- 2020

This paper introduces the graphical calculus ZQ, which uses quaternions to represent these arbitrary rotations, similar to TriQ, and the phase-free Z spider to represent entanglement,similar to ZX, and shows that this calculus is sound and complete for qubit quantum computing, while also showing that a fully spider-based representation would have been impossible.

Graphical Calculi and their Conjecture Synthesis

- Computer Science
- 2020

This work continues the exploration of graphical calculi, inside and outside of the quantum computing setting, by investigating the algebraic structures with which the authors label diagrams, and introduces two important new calculi here.

Hypergraph Simplification: Linking the Path-sum Approach to the ZH-calculus

- Mathematics, Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

This paper establishes a correspondence between the ZH-calculus and the path-sum formalism, a technique recently introduced by Amy to verify quantum circuits, and finds a bijection between certain canonical forms of Zh-diagrams and path-Sum expressions.

AKLT-States as ZX-Diagrams: Diagrammatic Reasoning for Quantum States

- Computer SciencePRX Quantum
- 2022

The results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms.

Diagrammatic Differentiation for Quantum Machine Learning

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

This work introduces diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories and extending the method to the automatic differentation of hybrid classical-quantum circuits.

Analyzing the barren plateau phenomenon in training quantum neural network with the ZX-calculus

- Computer ScienceQuantum
- 2021

The barren plateaus theorem is extended from unitary 2-design circuits to any parameterized quantum circuits under certain reasonable assumptions and is shown that, for the hardware efficient ansatz and the MPS-inspired ansatz, there exist barren Plateaus.

Relating Measurement Patterns to Circuits via Pauli Flow

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

It is shown that Pauli flow can similarly be identified efficiently and that any measurement pattern whose underlying graph admits a Pauliflow can be efficiently transformed into a gate-based circuit without using ancilla qubits.

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