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Paper 1
Celestial Quantum Error Correction II: From Qudits to Celestial CFT
Alfredo Guevara, Yangrui Hu
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2412.19653
- arXiv
- 2412.19653
A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum $N\to \infty$ limit. At finite $N$ the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied $w_{1+\infty}$ hierarchy of soft currents and its realization from a sigma model in twistor space.
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