In the talk, I will provide an overview of the color code. First, I will establish a connection between the color code and a well-studied model - the toric code. Then, I will explain how one can implement a universal gate set with the subsystem and the stabilizer color codes in three dimensions using techniques of code switching and gauge fixing. Next, I will discuss the problem of decoding the color code. Finally, I will explain how one can find the optimal error correction threshold by analyzing phase transitions in certain statistical-mechanical models.
The talk is based on http://arxiv.org/abs/1410.0069, http://arxiv.org/abs/1503.02065 and recent works with M. Beverland, F. Brandao, N. Delfosse, J. Preskill and K. Svore.
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On Wednesday Dec 14, 4pm in the Time room, we have
Speaker: Chris Jackson
Title: Non-holonomic tomography and detecting state-preparation and measurement correlated errors
Abstract: Quantum tomography is an important tool for characterizing the parameters of unknown states, measurements, and gates. Standard quantum tomography is the practice of estimating these parameters with known measurements, states, or both, respectively. In recent years, it has become important to address the issue of working with systems where the ``devices'' used to prepare states and make measurements
both have significant errors. Of particular concern to me is whether such state-preparation and measurement errors are correlated with each other. In this talk, I will share a solution to assessing such correlations with an object called a partial determinant. Further, I will show how this technique suggests a perspective for such correlated quantum states and observables (over the space of device settings) is analogous to the non-holonomic perspectives of thermodynamic heat and work (over the macroscopic state space.)