Temperature change can solve the Deutsch-Jozsa problem: An exploration of thermodynamic query complexity
Year: 2025
Type: article
Abstract: We demonstrate how a single heat exchange between a probe thermal qubit and multiqubit thermal machine encoding a Boolean function can determine whether the function is balanced or constant, thus providing a thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore a restricted Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the three-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting that quantum thermodynamics could provide an unconventional route to computing beyond classical computation.
Source: Physical Review A
DOI: 10.1103/qky6-2bfs
Author: Jake Xuereb
Institution: TU Wien
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,675
OpenAlex ID: W4417210817