# Relating Measurement Patterns to Circuits via Pauli Flow

@article{Simmons2021RelatingMP, title={Relating Measurement Patterns to Circuits via Pauli Flow}, author={Will Simmons}, journal={ArXiv}, year={2021}, volume={abs/2109.05654} }

The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit into a one-way computation, whereas the reverse is only efficient given some constraints on the structure of the measurement pattern. Causal flow and generalised flow have already been shown as sufficient, with efficient algorithms for identifying these…

## 4 Citations

### 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.

### Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

- Computer Science
- 2022

This work shows that introducing new Z -measured qu bits, connected to any subset of the existing qubits, preserves the existence of Pauli ﬂow, and gives a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin.

### Characterising Determinism in MBQCs involving Pauli Measurements

- Computer Science
- 2022

A new characterisation of determinism in measurement-based quantum computing, called Extended Pauli Flow, is introduced that is necessary and suﬃcient for robust determinism.

### Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)

- Computer Science
- 2022

In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and…

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