# Best Approximate Quantum Compiling Problems

arXiv: https://arxiv.org/abs/2106.05649 · HTML: https://mlsanity.com/paper/2106.05649/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2021.

## Built on by (most cited first, 8 of 8)

- [Quantum Doubly Stochastic Transformers](https://mlsanity.com/paper/2504.16275/) (2025)
- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [Quantum Compiling with Reinforcement Learning on a Superconducting Processor](https://mlsanity.com/paper/2406.12195/) (2024)
- [Quantum Theory and Application of Contextual Optimal Transport](https://mlsanity.com/paper/2402.14991/) (2024)
- [RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training](https://mlsanity.com/paper/2311.16035/) (2023)
- [Pauli Network Circuit Synthesis with Reinforcement Learning](https://mlsanity.com/paper/2503.14448/) (2025)
- [A Novel Single-Layer Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis](https://mlsanity.com/paper/2412.03083/) (2024)
- [AI methods for approximate compiling of unitaries](https://mlsanity.com/paper/2407.21225/) (2024)

## Abstract (arXiv)

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity.