AlphaTensor-Quantum

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📇 Table of Contents

1. 🚀 Project Overview
2. ✨ Key Features
3. 📖 Scientific Background
4. 🛠️ Installation & Setup
5. ⚙️ Quickstart & Examples
6. 📐 System Architecture
7. 🧪 Demos & Notebooks
8. 📈 Benchmark Results
9. 🧩 API & Module Reference
10. 👥 Contributing Guidelines
11. 🗂️ Roadmap
12. 📜 License
13. 🙏 Acknowledgements

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🚀 Project Overview

AlphaTensor-Quantum is a cutting-edge framework that brings together:

• Tensor Decomposition: Representing the costly non-Clifford part of a quantum circuit as a symmetric, binary 3-tensor.
• Deep Reinforcement Learning: Casting decomposition as a single-player game (TensorGame) and training an AlphaZero-style agent to find minimal-rank decompositions.
• Gadgetization: Automatically discovering and exploiting Toffoli/CS “gadgets” to bundle multiple T-gates into ancilla-based constructions, slashing the effective T-count.

The result? Automated, state-of-the-art T-count optimization that matches or surpasses all human-designed methods on key arithmetic and quantum-chemistry primitives.

Figure 1. From Circuit → Signature Tensor → Waring Decomposition → Optimized Circuit

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✨ Key Features

• 🔍 Signature-Tensor Encoding
  Transform any Clifford+T circuit into a symmetric ternary tensor capturing its phase-polynomial.

• 🕹️ TensorGame Environment

  • Single-player game: actions = binary vectors; state = residual tensor.
  • Reward = –1 per move; gadgets yield bonus rewards.

• 🤖 Symmetrized Axial Attention Network

  • Efficiently processes large (up to 72×72×72) tensors
  • 4× speedup and 3× memory reduction vs. naive attention

• 🛠️ Domain Gadget Integration

  • Toffoli gadgets (7→2 T-equivalents)
  • Controlled-S gadgets (3→2 T-equivalents)
  • Learned purely from reward shaping—no hard-coding.

• 🎲 Sample-Based MCTS

  • Monte Carlo Tree Search explores only a sampled subset of factors
  • Balances exploration vs. exploitation in huge action spaces

• 🎓 Synthetic Demonstrations & Data Augmentation

  • Millions of random decompositions, with forced gadget patterns
  • Random basis changes (Clifford transforms) & factor permutations

• 📊 Comprehensive Benchmarks

  • Arithmetic circuits (adders, GF($2^m$) multipliers)
  • Quantum chemistry oracles (e.g., FeMoco’s Prepare/Select)
  • Unary iteration & phase-gradient primitives

• 🔧 Extensible & Modular

  • Plug in new gadgets, change metrics (T-depth, weighted gates), or adapt to NISQ devices.

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📖 Scientific Background

Quantum fault-tolerance demands minimizing T-gates (magic-state distillation is two orders-of-magnitude costlier than CNOT). The T-count optimization problem is NP-hard, and prior methods rely on hand-crafted rewrite rules or limited tensor tricks.

AlphaTensor-Quantum reframes circuit optimization as:

1. Phase-polynomial Extraction

   • Any CNOT+T circuit defines $\phi(x)=\frac\pi4(\sum a_i x_i + 2\sum b_{ij}x_ix_j + 4\sum c_{ijk}x_ix_jx_k)$.
   • Mod 2 coefficients ${c_{ijk}}$ form a symmetric 3-tensor (signature tensor).

2. Waring Decomposition

   • Find a minimal set ${u^{(r)}}$ such that
     $$\mathcal{T}=\sum_r u^{(r)}\otimes u^{(r)}\otimes u^{(r)}\pmod2.$$
   • Each $u^{(r)}$ ↔ one T-gate; factors grouping → gadget proposals.

3. Reinforcement Learning

   • State: current residual tensor + action history.
   • Action: choose vector $u\in{0,1}^N$.
   • Reward: –1 per move; gadget completions yield positive bonuses.
   • Policy-Value Net + sample-based MCTS find optimal plays.

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