The thermodynamics of one qubit

Abstract

Information processes are fundamentally physical. One cannot shy away from the fact that when executing an algorithm on a quantum computer, one is seeing a hamiltonian play out it front of their eyes. Maxwell, Gibbs, Szilard, Landauer [1, 2, 3, 4] and others have all shown in different ways that changes in the distribution of information in a system have thermodynamic repercussions. Since, quantum systems are arguably the richest in terms of their information structures, the resulting thermodynamics must be equally rich. This is a mysterious area, as is epitomised by the black hole information paradox, but developments in recent years [5] are starting to show paths towards understanding. In the research presented in this dissertation, a small step down where these paths lead is taken. The lofty goal of understanding the thermodynamics of quantum information processes is transformed into an examination of a specific and smaller instance, examining the thermodyanmics of the DQC1 circuit [6] via its entanglement. A problem which ultimately revolves around the quantification of multipartite entanglement. The intent of this document is for the reader to be able to understand the problem of multipartite entanglement quantification, how entanglement is closely related to thermodynamics and the research carried out by the author in this space. To do so I will begin in the first chapter by introducing the landscape of quantum mechanics after which I will zoom in on the sub-field of quantum information, introducing all the tools needed for the research carried out. After this, I delve into the research problem of quantifying the entanglement of the DQC1 circuit towards making use of Huber et al’s relationship between entanglement and thermodynamic work [7]. Describing the solution to this challenge and how this led to an understanding of the minimal thermodynamics of this algorithm. Lastly, I speak of the implications of this work, the importance of understanding the thermodynamics of quantum algorithms and improving our methods of entanglement quantification as well as future work.