Optimizing Multi-level Magic State Factories for Fault-Tolerant Quantum Architectures

2024-11-06

arXiv.org

AI Summary

Quantum error correction demands a fundamental trade-off between physical qubit count and execution time, hindering scalable fault-tolerant quantum computation. Method: We propose a modular architecture optimization framework featuring a pipelined system with hierarchical magic-state factories and a central processor, modeling magic-state supply as a networked pipeline. We introduce a concise resource estimation model dependent solely on circuit volume, protocol error factor μ, error suppression ratio Λ, and slowdown factor β. Further, we design a multi-objective heuristic optimization framework jointly modeling quantum memory, magic-state distillation, code stretching, and logical gate operations under coupled spatial, temporal, and error constraints. Results: Under Λ = 3–10 and β ≥ 0.2, our approach supports algorithms with T-counts of 10⁶–10¹⁵ and logical qubit counts of 10²–10⁴, requiring only 10⁵–10⁸ physical qubits—significantly improving resource efficiency over prior designs.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade--offs between the number of physical qubits and the fault-tolerant execution time of a quantum algorithm. We consider a concept architecture comprising a dedicated zone as a multi-level magic state factory and a core processor for efficient logical operations, forming a supply chain network for production and consumption of magic states. Using a heuristic algorithm, we solve the multi-objective optimization problem of minimizing space and time subject to a user-defined error budget for the success of the computation, taking the performance of various fault-tolerant protocols such as quantum memory, state preparation, magic state distillation, code growth, and logical operations into account. As an application, we show that physical quantum resource estimation reduces to a simple model involving a small number of key parameters, namely, the circuit volume, the error prefactors ($mu$) and error suppression rates ($Lambda$) of the fault-tolerant protocols, and an allowed slowdown factor ($eta$). We show that, in the proposed architecture, $10^5$--$10^8$ physical qubits are required for quantum algorithms with $T$-counts in the range $10^6$--$10^{15}$ and logical qubit counts in the range $10^2$--$10^4$, when run on quantum computers with quantum memory $Lambda$ in the range 3--10, for all slowdown factors $eta geq 0.2$.

Problem

• Optimize modular quantum architecture for space-time trade-offs
• Design multi-level magic state factory and core processor
• Minimize space and time under error budget constraints

Innovation

• Modular quantum architecture with space-time trade-offs
• Multi-level magic state factory and core processor
• Heuristic algorithm for multi-objective optimization