- Compilation/
Pauliopt: Holistic circuit resynthesis using phase polynomials
Pauliopt: Holistic circuit resynthesis using phase polynomials
Overview
PauliOpt was introduced in [1, 2] and is a culmination of different phase polynomial based compilation methods.
It has been shown to outperform directed acyclic graph (DAG) based compilation methods in both classical and quantum resources.
Inputs
- Arbitrary circuit
Intermediate representation
- Mixed ZX phase polynomial
Outputs
- Arbitrary circuit
Context in literature
PauliOpt phase polynomial synthesis methods such as [3] are applied to a mixed ZX phase polynomial representation [4], and subsequent CNOT tails are optimized using RowCol or PermRowCol.
The paper [1] also investigates methods such as reverse traversal and simulated annealing [4], which only slightly improve the results, and Steiner-GraySynth [5], which is outperformed by ParitySynth [3] by Vandaele et al.
Example
Let us look at the example provided in [1]. A \text{CCZ} gate is described by the phase polynomial
Using phase polynomial synthesis methods like [3], we can obtain the following circuit:
The trailing CNOT circuit can be optimized by PermRowCol.
Note how the final qubits are re-allocated, in particular, the original qubits (q_1, q_2, q_3) are mapped to (q_2, q_1, q_3), which saves extra CNOT gates.
Typical usage
The provided synthesis methods for Z and mixed ZX phase polynomials are well-suited for Hamiltonian based algorithms that provide gates in the form of exponentiated Pauli words that are not necessarily optimized for the underlying hardware. In this case, phase polynomial based compilation is advantageous in both classical and quantum resources whenever circuits are sufficiently deep. For shallow circuits, they may yield worse results.
References
[1] "A Comparison of Quantum Compilers using a DAG-based or phase polynomial-based Intermediate Representation", Arianne Meijer - van de Griend, arXiv:2304.08814, 2023
[2] "PauliOpt", "PauliOpt: A Python library to simplify quantum circuits", github.com/hashberg-io/pauliopt
[3] "Phase polynomials synthesis algorithms for NISQ architectures and beyond", Vivien Vandaele, Simon Martiel, Timothée Goubault de Brugière arXiv:2104.00934, 2021
[4] "Annealing Optimisation of Mixed ZX Phase Circuits", Stefano Gogioso, Richie Yeung, arXiv:2206.11839, 2022
[5] "Architecture-Aware Synthesis of Phase Polynomials for NISQ Devices", Arianne Meijer-van de Griend, Ross Duncan, arXiv:2004.06052, 2020
Cite this page
@misc{PennyLane-Pauliopt,
title={Pauliopt: holistic CNOT routing},
howpublished={\url{https://pennylane.ai/compilation/pauliopt-holistic-circuit-resynthesis-with-phase-polynomials}},
year={2025}
}Page author(s)
Korbinian Kottmann
Quantum simulation & open source software