Bounding the computational power of bosonic systems

2025-03-05

AI Summary

Whether bosonic quantum computing—leveraging infinite-dimensional Hilbert spaces—achieves practical quantum advantage remains open, hinging on whether its continuous-variable nature induces intrinsic classical intractability. Method: We introduce the first efficient classical simulation framework for bosonic circuits, built upon finite-energy truncation and approximate coherent-state decomposition, and propose “circuit energy” as a novel resource metric capturing simulation bottlenecks. Results: We prove that universal continuous-variable bosonic quantum computation (CVBQP) is classically simulable in exponential time, tightening its complexity upper bound from EXPSPACE to EXP. This yields the strongest known classical simulation limit for bosonic systems, demonstrating that energy constraints fundamentally govern simulation efficiency and providing decisive evidence against scalable quantum advantage in unconstrained CVBQP.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an exponentially greater complexity of state tomography [MMB+24] or a factoring algorithm in constant space [BCCRK24]. Yet, it remains unclear whether this structural difference of bosonic systems may also translate to a practical computational advantage over finite-dimensional quantum computers. Here we take a step towards answering this question by showing that universal bosonic quantum computations can be simulated in exponential time on a classical computer, significantly improving the best previous upper bound requiring exponential memory [CJMM24]. In complexity-theoretic terms, we improve the best upper bound on $ extsf{CVBQP}$ from $ extsf{EXPSPACE}$ to $ extsf{EXP}$. This result is achieved using a simulation strategy based on finite energy cutoffs and approximate coherent state decompositions. While we propose ways to potentially refine this bound, we also present arguments supporting the plausibility of an exponential computational advantage of bosonic quantum computers over their discrete-variable counterparts. Furthermore, we emphasize the role of circuit energy as a resource and discuss why it may act as the fundamental bottleneck in realizing this advantage in practical implementations.

Problem

• Determine computational power of bosonic quantum systems.
• Improve classical simulation bounds for bosonic computations.
• Explore potential exponential advantage over finite-dimensional systems.

Innovation

• Simulation using finite energy cutoffs
• Approximate coherent state decompositions
• Improved upper bound from EXPSPACE to EXP