Energetic cost of Hamiltonian quantum gates

TL;DR

This paper establishes a fundamental inequality linking the energetic cost of Hamiltonian quantum gates to the change in encoded Shannon information, providing insights into energy efficiency in quantum computing.

Contribution

It introduces a new bound on the energetic cost of quantum gates based on information change, extending thermodynamic principles to unitary quantum operations.

Findings

Derived an inequality relating energy cost and information change in quantum gates

Showed how to identify energetically optimal quantum gates

Discussed energy costs in quantum error correction codes

Abstract

Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how Landauer's principle applies to unitary quantum computing is less than obvious. Here, we prove an inequality bounding the change of Shannon information encoded in the logical quantum states by quantifying the energetic cost of Hamiltonian gate operations. The utility of this bound is demonstrated by outlining how it can be applied to identify energetically optimal quantum gates in theory and experiment. The analysis is concluded by discussing the energetic cost of quantum error correcting codes with non-interacting qubits, such as Shor's code.