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Title:
Computational Phases of Quantum Matter
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Abstract:
The fields of quantum computation and topological phases of matter have been evolving alongside each other for over two decades, such that they are now deeply intertwined. In this talk, I will discuss this intertwinement in the context of measurement-based quantum computation (MBQC) and symmetry-protected topological (SPT) phases. I will first review how certain fixed-points of SPT phases in 1D can be used as resources for MBQC, meaning that projective measurements of SPT-ordered ground states can induce unitary evolution of an encoded logical qubit. Remarkably, this property persists throughout the entire phase of matter, leading us to label 1D SPT phases as "computational phases of matter". Next, I will show how the search for a computationally universal phase of matter---one in which measurements on any ground state within the phase can induce universal quantum computation---led us to discover an entirely new type of quantum order in 2D, namely subsystem SPT order. Then, I will discuss recent work where we applied from these studies to devise a scheme of universal MBQC that operates in a one-dimensional architecture, thereby refuting the common belief that two spatial dimensions are necessary, with immediate implications for platforms such as trapped ions. Overall, developments exemplify the symbiotic relationship between quantum computation and topological phases of matter, and I will end my talk with a short discussion of other aspects of this relationship.
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