# Phase Gadget Synthesis for Shallow Circuits

arXiv: https://arxiv.org/abs/1906.01734 · HTML: https://mlsanity.com/paper/1906.01734/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 9 of 9)

- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Diagrammatic Differentiation for Quantum Machine Learning](https://mlsanity.com/paper/2103.07960/) (2021)
- [How to make qubits speak](https://mlsanity.com/paper/2107.06776/) (2021)
- [Optimizing Quantum Circuits via ZX Diagrams using Reinforcement Learning and Graph Neural Networks](https://mlsanity.com/paper/2504.03429/) (2025)
- [Representing and Implementing Matrices Using Algebraic ZX-calculus](https://mlsanity.com/paper/2110.06898/) (2021)
- [Deep Learning Approaches to Quantum Error Mitigation](https://mlsanity.com/paper/2601.14226/) (2026)
- [Reinforcement Learning for Adaptive Composition of Quantum Circuit Optimisation Passes](https://mlsanity.com/paper/2601.21629/) (2026)
- [Bridge of Psi's: Quantum Circuit Optimization with Schr"odinger Bridges](https://mlsanity.com/paper/2609.25947/) (2026)
- [Quantum data loading from the learned shared structure of real signals](https://mlsanity.com/paper/2610.06076/) (2026)

## Abstract (arXiv)

We give an overview of the circuit optimisation methods used by tket, a compiler system for quantum software developed by Cambridge Quantum Computing Ltd. We focus on a novel technique based around phase gadgets, a family of multi-qubit quantum operations which occur naturally in a wide range of quantum circuits of practical interest. The phase gadgets have a simple presentation in the ZX-calculus, which makes it easy to reason about them. Taking advantage of this, we present an efficient method to translate the phase gadgets back to CNOT gates and single qubit operations suitable for execution on a quantum computer with significant reductions in gate count and circuit depth. We demonstrate the effectiveness of these methods on a quantum chemistry benchmarking set based on variational circuits for ground state estimation of small molecules.