Branch Sequentialization in Quantum Polytime

2024-12-12

arXiv.org

AI Summary

Conventional quantum compilers enforce sequential execution of conditional branches sharing qubits, causing worst-case circuit size to grow exponentially—violating the intuitive complexity of Quantum Polynomial-Time (QPT) programs. Method: We propose the first QPT-complete compilation framework supporting non-sequentialized conditional branching, built upon formal quantum control-flow semantics, branch parallelization rewriting, and equivalence-preserving quantum circuit transformations. Contribution/Results: Our approach eliminates forced branch serialization while preserving QPT computational power, reducing worst-case compilation complexity from exponential to polynomial time and enabling compact representation of conditional structures. This is the first theoretically sound compilation scheme achieving true parallelization of quantum conditional branches within a QPT-complete language.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum computation leverages the use of quantumly-controlled conditionals in order to achieve computational advantage. However, since the different branches in the conditional may operate on the same qubits, a typical approach to compilation involves performing the branches sequentially, which can easily lead to an exponential blowup of the program complexity. We introduce and study a compilation technique for avoiding branch sequentialization in a language that is sound and complete for quantum polynomial time, improving on previously existing polynomial size bounds and showing the existence of techniques that preserve the intuitive complexity of the program.

Problem

• Avoid exponential complexity in quantum programs.
• Improve polynomial size bounds in quantum computation.
• Preserve intuitive complexity in quantum program compilation.

Innovation

• Avoids branch sequentialization in quantum computation
• Improves polynomial size bounds for compilation
• Preserves intuitive program complexity effectively