Compare Papers
Paper 1
On the Necessity of Entanglement for the Explanation of Quantum Speedup
Michael E. Cuffaro
- Year
- 2011
- Journal
- arXiv preprint
- DOI
- arXiv:1112.1347
- arXiv
- 1112.1347
In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play.
Open paperPaper 2
DQC1 as an Open Quantum System
Jake Xuereb, Steve Campbell, John Goold, André Xuereb
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.03947
- arXiv
- 2209.03947
The DQC1 complexity class, or power of one qubit model, is examined as an open quantum system. We study the dynamics of a register of qubits carrying out a DQC1 algorithm and show that, for any algorithm in the complexity class, the evolution of the logical qubit can be described as an open quantum system undergoing a dynamics which is unital. Unital quantum channels respect the Tasaki-Crooks fluctuation theorem and we demonstrate how this is captured by the thermodynamics of the logical qubit. As an application, we investigate the equilibrium and non-equilibrium thermodynamics of the DQC1 trace estimation algorithm. We show that different computational inputs, i.e. different traces being estimated, lead to different energetic exchanges across the register of qubits and that the temperature of the logical qubit impacts the magnitude of fluctuations experienced and quality of the algorithm.
Open paper