Work

On the quantum computational complexity of classical linear dynamics with geometrically local interactions: Dequantization and universality

Year: 2026

Type: article

Abstract: The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in simulating classical dynamics with long-range interactions. However, many real-world classical systems, such as those arising from partial differential equations, exhibit only local interactions. The question remains whether quantum algorithms can still provide exponential speedup under this condition. In this work, we thoroughly characterize the computational complexity of simulating such geometrically local systems on quantum computers. First, we dequantize the quantum algorithm for simulating short-time (polynomial-time) dynamics of such systems. This implies that the problem of simulating this dynamics does not yield any exponential quantum advantage. Second, we show that simulating short-time dynamics is at least as hard as polynomial-time and linear-space probabilistic classical computation. Third, we show that the computational complexity of simulating long-time (exponential-time) dynamics is captured by exponential-time and polynomial-space quantum computation. This suggests a super-polynomial time advantage when restricting the computation to polynomial-space, or an exponential space advantage otherwise. This work offers new insights into the complexity of classical dynamics governed by partial differential equations, providing a pathway for achieving quantum advantage in practical problems.

Source: Quantum

DOI: 10.22331/q-2026-08-03-2182

Authors: Kazuki Sakamoto, Keisuke Fujii

Institutions: The University of Osaka, RIKEN, RIKEN Center for Quantum Computing

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: Ministry of Education, Culture, Sports, Science and Technology, Core Research for Evolutional Science and Technology, Co-creation place formation support program