# Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum Circuits

arXiv: https://arxiv.org/abs/2012.07711 · HTML: https://mlsanity.com/paper/2012.07711/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2020.

## Built on by (most cited first, 6 of 6)

- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Representation of binary classification trees with binary features by quantum circuits](https://mlsanity.com/paper/2108.13207/) (2021)
- [AutoQC: Automated Synthesis of Quantum Circuits Using Neural Network](https://mlsanity.com/paper/2210.02766/) (2022)
- [Pauli Network Circuit Synthesis with Reinforcement Learning](https://mlsanity.com/paper/2503.14448/) (2025)
- [Three Birds with One Stone: Improving Performance, Convergence, and System Throughput with Nest](https://mlsanity.com/paper/2510.09578/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel quantum compiler optimization, named relaxed peephole optimization (RPO) for quantum computers. RPO leverages the single-qubit state information that can be determined statically by the compiler. We define that a qubit is in a basis state when, at a given point in time, its state is either in the X-, Y-, or Z-basis. When basis qubits are used as inputs to quantum gates, there exist opportunities for strength reduction, which replaces quantum operations with equivalent but less expensive ones. Compared to the existing peephole optimization for quantum programs, the difference is that our proposed optimization does not require an identical unitary matrix, thereby named `relaxed' peephole optimization. We also extend our approach to optimize the quantum gates when some input qubits are in known pure states. Both optimizations, namely the Quantum Basis-state Optimization (QBO) and the Quantum Pure-state Optimization (QPO), are implemented in the IBM's Qiskit transpiler. Our experimental results show that our proposed optimization pass is fast and effective. The circuits optimized with our compiler optimizations obtain up to 18.0% (11.7% on average) fewer CNOT gates and up to 8.2% (7.1% on average) lower transpilation time than that of the most aggressive optimization level in the Qiskit compiler. When running on real quantum computers, the success rates of 3-qubit quantum phase estimation algorithm improve by 2.30X due to the reduced gate counts.