Benedikt Placke

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Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error correction. Here, we introduce the concept of topological quantum spin glass (TQSG) order which marries these two notions, exhibiting both the complex energy landscapes of spin glasses, and the quantum memory and long-range entanglement characteristic of topologically ordered systems. We use techniques from (quantum) coding theory to show that TQSG order is the low-temperature phase of various quantum LDPC codes on expander graphs, including hypergraph and balanced product codes. En route, we develop a quantum generalization of Gibbs state decompositions and prove of a bottleneck theorem for quantum channels, which generalizes its well-known counterpart applying to classical Markov chains. Our techniques are also applicable to classical spin glasses, where we provide a novel proof of the shattering of the Gibbs state in a wide range of spin glass models based on classical error correcting codes.

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Oxford
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Contact: Simon Trebst