Visualizing Exotic Quantum States of Matter

Fabien Alet, Aleksandra M. Walczak, Matthew P. A. Fisher

David Austen, Wytze Brouwer, Bailey Martin

Could Bose–Einstein condensates be used as calculators? According to Yvan Castin at the Kastler Brossel Laboratory in Paris and co-workers the answer is “yes”. It seems that these exotic states of matter could be used to visualize the roots of random polynomials for the first time ( Phys. Rev. Lett. 96 040405).

Eugene Koreshin, Denis I. Sakhno, Alexander N. Poddubny +1 more

Abstract Arrays of atoms coupled to photons, propagating in a waveguide, are now actively studied due to their prospects for generation and detection of quantum light. Quantum simulators based on waveguides with long-range couplings were also predicted to manifest unusual many-body quantum states. However, quantum tomography for large arrays with N > 20 atoms remains elusive since it requires independent access to every atom. Here, we present a novel concept for analogue quantum simulations by mapping the setup of waveguide quantum electrodynamics to the classical problem of an electromagnetic wave, propagating in a wire metamaterial. By experimentally measuring the near electromagnetic field we emulate the localization arising from polariton-polariton interactions in the quantum problem. Our results demonstrate the potential of wire metamaterials to visualize quantum light-matter coupling in a table-top experiment and may be applied to emulate other exotic quantum effects, such as quantum chaos, and self-induced topological states.

Gordon Baym

Yunzhe Zheng, Dong E. Liu

Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal T gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynamical systems under the framework of stabilizer reduction. With the proposed mapping, we are able to analyze the performance of MSD protocols using techniques from dynamical systems theory, easily simulate the distillation process of input states under arbitrary noise and visualize it using flow diagram. We apply our mapping to common MSD protocols for |T⟩ state and find some interesting properties: The [[15,1,3]] code may distill states corresponding to T gate and the [[5,1,3]] code can distill the magic state corresponding to the T gate. Besides, we examine the exotic MSD protocols that may distill into other magic states proposed in [Eur. Phys. J. D 70, 55 (2016)] and identify the condition for distillable magic states. We also study new MSD protocols generated by concatenating different codes and numerically demonstrate that concatenation can generate MSD protocols with various magic states. By concatenating efficient codes with exotic codes, we can reduce the overhead of the exotic MSD protocols. We believe our proposed method will be a useful tool for simulating and visualization MSD protocols for canonical MSD protocols on |T⟩ as well as other unexplored MSD protocols for other states.