A Temperature Change can Solve the Deutsch-Jozsa Problem : An Exploration of Thermodynamic Query Complexity

TL;DR

This paper introduces a thermodynamic approach to solving the Deutsch-Jozsa problem using heat exchange with quantum thermal machines, demonstrating potential for efficient quantum query complexity solutions.

Contribution

It presents a novel thermodynamic model of quantum query complexity and shows how thermal interactions can determine Boolean function properties with constant sample complexity.

Findings

Thermal qubits can distinguish balanced from constant functions with a single heat exchange.

A linear thermal oracle enables solving the Bernstein-Vazirani problem efficiently.

Experimental proof-of-concept demonstrated for a 3-bit problem.

Abstract

We demonstrate how a single heat exchange between a probe thermal qubit and multi-qubit thermal machine encoding a Boolean function, can determine whether the function is balanced or constant, thus providing a novel 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 3-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.