# Quantum Circuit Optimization with AlphaTensor

arXiv: https://arxiv.org/abs/2402.14396 · HTML: https://mlsanity.com/paper/2402.14396/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 82 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Learning and Planning in Complex Action Spaces](https://mlsanity.com/paper/2104.06303/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Quantum Computing: Lecture Notes](https://mlsanity.com/paper/1907.09415/) (2019)
- [Compiler Optimization for Quantum Computing Using Reinforcement Learning](https://mlsanity.com/paper/2212.04508/) (2022)
- [Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits](https://mlsanity.com/paper/2203.16707/) (2022)

## Built on by (most cited first, 30 of 36)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning](https://mlsanity.com/paper/2405.13196/) (2024)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware](https://mlsanity.com/paper/2411.00230/) (2024)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)
- [CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs](https://mlsanity.com/paper/2502.18663/) (2025)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning](https://mlsanity.com/paper/2509.21709/) (2025)
- [Optimizing Quantum Circuits via ZX Diagrams using Reinforcement Learning and Graph Neural Networks](https://mlsanity.com/paper/2504.03429/) (2025)
- [BenchRL-QAS: Benchmarking reinforcement learning algorithms for quantum architecture search](https://mlsanity.com/paper/2507.12189/) (2025)
- [TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQE](https://mlsanity.com/paper/2509.15193/) (2025)
- [AlphaCNOT: Learning CNOT Minimization with Model-Based Planning](https://mlsanity.com/paper/2604.13812/) (2026)
- [Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis](https://mlsanity.com/paper/2605.10910/) (2026)
- [CDRL: Certification-Driven Reinforcement Learning for Neutrino Flavor Model Discovery](https://mlsanity.com/paper/2608.20686/) (2026)
- [CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)](https://mlsanity.com/paper/2509.19162/) (2025)
- [Nonstabilizerness Estimation using Graph Neural Networks](https://mlsanity.com/paper/2511.23224/) (2025)
- [When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control](https://mlsanity.com/paper/2601.18973/) (2026)
- [Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce T-count](https://mlsanity.com/paper/2601.19738/) (2026)
- [Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins](https://mlsanity.com/paper/2602.10917/) (2026)
- [QFlowNet: Fast, Diverse, and Efficient Unitary Synthesis with Generative Flow Networks](https://mlsanity.com/paper/2603.03045/) (2026)
- [Automated near-term quantum algorithm discovery for molecular ground states](https://mlsanity.com/paper/2603.26359/) (2026)
- [Replay-buffer engineering for noise-aware quantum circuit optimization](https://mlsanity.com/paper/2604.21863/) (2026)
- [Aligning Quantum Operators with Large Language Models](https://mlsanity.com/paper/2606.13811/) (2026)
- [Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis](https://mlsanity.com/paper/2606.29636/) (2026)
- [When Close Enough Is Not Enough: Autoregressive Drift in Quantum Circuit Synthesis](https://mlsanity.com/paper/2607.12780/) (2026)
- [Monte Carlo Search Algorithms Discovering Monte Carlo Tree Search Exploration Terms](https://mlsanity.com/paper/2404.09304/) (2024)
- [Monte Carlo Permutation Search](https://mlsanity.com/paper/2510.06381/) (2025)
- [Reinforcement Learning for Adaptive Composition of Quantum Circuit Optimisation Passes](https://mlsanity.com/paper/2601.21629/) (2026)
- [Q-Tag: Watermarking Quantum Circuit Generative Models](https://mlsanity.com/paper/2602.23085/) (2026)

## Abstract (arXiv)

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.