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• Organizational Meeting - Quantum Information RIT

  Speaker: Carl Miller (University of Maryland) - http://camiller.iacs.umd.edu
  

  When: Mon, August 31, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: The Quantum Information RIT is concerned with all aspects of research at the intersection between quantum information science and mathematics. Goals for talks include: studying recent research results in quantum information from a mathematical angle; finding examples (old and new) in which existing tools from mathematics can be adapted for application in quantum information; and studying quantum algorithms for mathematical problems.
  
  This seminar is associated with QuICS and the UMD math department, and participation from other departments is encouraged.
  
  Webpage: http://camiller.iacs.umd.edu/RIT/QI-RIT2020Fall.html
  
• Pictorial Proofs Using ZX-Calculus

  Speaker: Yusuf Alnawakhtha (University of Maryland) -
  

  When: Mon, September 14, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: In this talk, we will briefly explore the use of monoidal categories in quantum information. Namely we will introduce the ZX-Calculus which is a diagrammatic formalism that strives to enhance intuition by providing pictorial proofs and we will provide examples of how some proofs can be simplified using this framework. Later in the talk, we will go over a recent application of ZX-Calculus in fault tolerant quantum computing and how it was used to provide the intuition for this result.
  
  References:
  [1] Coecke, Bob. "Quantum picturalism." Contemporary physics 51.1 (2010): 59-83.
  [2] de Beaudrap, Niel, Xiaoning Bian, and Quanlong Wang. "Fast and effective techniques for T-count reduction via spider nest identities." arXiv preprint arXiv:2004.05164 (2020).
  
• Quantum randomness and the geometry of the Schatten matrix norm

  Speaker: Carl Miller (University of Maryland) - http://camiller.iacs.umd.edu
  

  When: Mon, September 21, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: One of the most successful recent applications of quantum information has been the generation of "certified" random numbers. The unique properties of quantum devices allow the generation of numbers that are provably random, offering a potential major benefit to cryptography and other fields. Constructing the right theory to prove quantum randomness can be challenging. Quantum devices and adversaries are modeled by complex vector spaces whose dimensions may be arbitrarily large, and proving security in such a setting leads to some difficult mathematical problems. This talk will be a retrospective look at one successful approach to quantum randomness that is based on the convexity of the Schatten matrix norm.
  
• Symmetries, graph properties, and quantum speedups

  Speaker: Daochen Wang (University of Maryland) - https://wdaochen.com
  

  When: Mon, October 5, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup?
  
  In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups.
  
  In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).
  
• Quantum Query Complexity of Symmetric Oracle Problems

  Speaker: Shih-Han Hung (University of Maryland) -
  

  When: Mon, October 19, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: In this talk, I will present quantum query complexity of symmetric oracle problems. In particular, we will be exploring the query complexity of quantum learning problems in which the oracles form a group G of unitary matrices, and a description of the optimal success probability of a t-query quantum algorithm in terms of group characters. More generally, in the coset identification problem, for a subgroup H of group G, the task is to determine which coset the group element belongs to. The authors provide character-theoretic formulas for the optimal success probability achieved by a t-query algorithm for this problem. It generalizes a number of well-known quantum algorithms including the Bernstein-Vazirani problem, the van Dam problem and finite field polynomial interpolation.
  
  References:
  [1] Daniel Copeland, James Pommersheim, Quantum query complexity of symmetric oracle problems, https://arxiv.org/abs/1812.09428
  [2] Orest Bucicovschi, Daniel Copeland, David A. Meyer, and James Pommersheim. Single-query quantum algorithms for symmetric problems, https://arxiv.org/abs/1503.05548
  
• Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)

  Speaker: Matthew Coudron (University of Maryland) - https://sites.google.com/site/matthewcoudron/
  

  When: Mon, November 9, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: A conjecture of Jozsa (arXiv:quant-ph/0508124) states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson conjectured that there exists an oracle O such that BQP^O != (BPP^(BQNC))^O. These conjectures are intriguing allusions to the unresolved potential of combining classical and low-depth quantum computation. In this work we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al. (arXiv:quant-ph/0209131), cannot be solved in BPP^(BQNC), nor can it be solved in the class that Jozsa describes. This proves Aaronson's oracle separation conjecture and provides a counterpoint to Jozsa's conjecture relative to the Welded Tree oracle problem. More precisely, we define two complexity classes, HQC and JC whose languages are decided by two different families of interleaved quantum-classical circuits. HQC contains BPP^(BQNC) and is therefore relevant to Aaronson's conjecture, while JC captures the model of computation that Jozsa considers. We show that the Welded Tree Problem gives an oracle separation between either of {JC, HQC} and BQP. Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater "quantum depth" leads to strictly greater computational ability in this relativized setting.
  
• Bounding the Accuracy of Distributed Quantum Sensing

  Speaker: Jessica Thompson (University of Maryland) -
  

  When: Mon, December 7, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09
  

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  Abstract: A potential application of quantum information is to distributed sensing. The goal of a sensing problem can be described as calculating a specific value by measuring signals with a collection of sensors. With a classical signal, the accuracy in which the quantity can be determined is inversely bounded by the square root of the number of sensors; this bound is called the standard quantum limit. However, the use of quantum resources, such as entanglement and squeezed light, allows one to surpass this limit. For specific protocols, the accuracy is bounded by the quantum Cramer-Rao bound, which relies on the quantum Fisher Information of the system. In this talk, we will discuss the various quantum protocols for distributed quantum sensing and the calculation of this bound, in regards to their accuracy.