Quantum Register Machine: Efficient Implementation of Quantum Recursive Programs

2024-08-19

Proceedings of the ACM on Programming Languages

AI Summary

Quantum recursive programming faces significant efficiency challenges due to the tight coupling between quantum control flow and recursive invocation. This paper introduces the first Quantum Register Machine (QRM) architecture supporting both quantum control flow and recursion, establishing an end-to-end implementation framework encompassing source compilation, partial evaluation of control flow, and execution. Key contributions include: (1) the first formal definition of the QRM model and its accompanying quantum instruction set; (2) a recursion-aware compilation methodology with dynamic stack management; (3) a novel quantum control-flow partial evaluation technique that eliminates redundant quantum computations; and (4) an automatic parallelization scheduler based on data-dependence analysis. Evaluated on canonical subroutines such as quantum multiplexers, our approach achieves exponential speedup over naive implementations while preserving program modularity and enabling formal verification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Quantum recursive programming has been recently introduced for describing sophisticated and complicated quantum algorithms in a compact and elegant way. However, implementation of quantum recursion involves intricate interplay between quantum control flow and recursive procedure calls. In this paper, we aim at resolving this fundamental challenge and develop a series of techniques to efficiently implement quantum recursive programs. Our main contributions include: 1. We propose a notion of quantum register machine, the first quantum architecture (including an instruction set) that provides instruction-level support for quantum control flow and recursive procedure calls at the same time. 2. Based on quantum register machine, we describe the first comprehensive implementation process of quantum recursive programs, including the compilation, the partial evaluation of quantum control flow, and the execution on the quantum register machine. 3. As a bonus, our efficient implementation of quantum recursive programs also offers automatic parallelisation of quantum algorithms. For implementing certain quantum algorithmic subroutine, like the widely used quantum multiplexor, we can even obtain exponential parallel speed-up (over the straightforward implementation) from this automatic parallelisation. This demonstrates that quantum recursive programming can be win-win for both modularity of programs and efficiency of their implementation.

Problem

• Implementing quantum recursive programs efficiently
• Designing quantum register machine for control flow
• Achieving automatic parallelisation in quantum algorithms

Innovation

• Quantum register machine for control flow
• Compilation and execution of quantum recursion
• Automatic parallelization with exponential speed-up