# Synthesizing Quantum-Circuit Optimizers

arXiv: https://arxiv.org/abs/2211.09691 · HTML: https://mlsanity.com/paper/2211.09691/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2022.

## Built on by (most cited first, 5 of 5)

- [Quarl: A Learning-Based Quantum Circuit Optimizer](https://mlsanity.com/paper/2307.10120/) (2023)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Neural Guided Sampling for Quantum Circuit Optimization](https://mlsanity.com/paper/2510.12430/) (2025)
- [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)

## Abstract (arXiv)

Near-term quantum computers are expected to work in an environment where each operation is noisy, with no error correction. Therefore, quantum-circuit optimizers are applied to minimize the number of noisy operations. Today, physicists are constantly experimenting with novel devices and architectures. For every new physical substrate and for every modification of a quantum computer, we need to modify or rewrite major pieces of the optimizer to run successful experiments. In this paper, we present QUESO, an efficient approach for automatically synthesizing a quantum-circuit optimizer for a given quantum device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with high-probability correctness guarantees for IBM computers that significantly outperforms leading compilers, such as IBM's Qiskit and TKET, on the majority (85%) of the circuits in a diverse benchmark suite. A number of theoretical and algorithmic insights underlie QUESO: (1) An algebraic approach for representing rewrite rules and their semantics. This facilitates reasoning about complex symbolic rewrite rules that are beyond the scope of existing techniques. (2) A fast approach for probabilistically verifying equivalence of quantum circuits by reducing the problem to a special form of polynomial identity testing. (3) A novel probabilistic data structure, called a polynomial identity filter (PIF), for efficiently synthesizing rewrite rules. (4) A beam-search-based algorithm that efficiently applies the synthesized symbolic rewrite rules to optimize quantum circuits.