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Quantum information processing aims to leverage the properties of quantum mechanics to manipulate information in ways that are not otherwise possible. This would enable, for example, quantum computers that could solve certain problems exponentially faster than a conventional supercomputer. One promising approach for building such a machine is to use gated silicon quantum dots. In the approach taken at HRL Laboratories, individual electrons are trapped in a gated potential well at the barrier of a Si/SiGe heterostructure.

Quantum theory is a theory of information, imposing new -- and often counter-intuitive -- rules on how it can be acquired, processed and shared. To understand these rules, one can draw on the framework of causal Bayesian networks, which successfully addresses questions concerning knowledge, causation and inference in the context of classical statistics. The process of adapting classical causal models to accommodate quantum theory provides a new perspective on the fundamental differences between the two.

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian.

Suppose you have access to iid samples from an unknown probability distribution $p = (p_1, …, p_d)$ on $[d]$, and you want to learn or test something about it. For example, if one wants to estimate $p$ itself, then the empirical distribution will suffice when the number of samples, $n$, is $O(d/epsilon^2)$. In general, you can ask many more specific questions about $p$---Is it close to some known distribution $q$? Does it have high entropy? etc.

In this seminar, we look at how one can use certain properties of quantum physics to bypass the fair-sampling assumption commonly used in most practical Bell experiments. Our approach is based on an alternative nonlocality framework called “semi-quantum nonlocality”, where measurement instructions are represented by quantum inputs instead of classical inputs. A key feature of this framework is that all “entangled states are nonlocal”, in the sense that for any entangled state there is always a semi-quantum Bell inequality with which violation can be achieved.

Topological quantum computation is a fault tolerant protocol for quantum computing using non-abelian topological phases of matter. Information is encoded in states of multi-quasiparticle excitations(anyons), and quantum gates are realized by braiding of anyons. The mathematical foundation of anyon systems is described by unitary modular tensor categories.

In the study of Markovian processes, one of the principal achievements is the equivalence between the Φ-Sobolev inequalities and an exponential decrease of the Φ-entropies. In this work, we develop a framework of Markov semigroups on matrix-valued functions and generalize the above equivalence to the exponential decay of matrix Φ-entropies. This result also specializes to spectral gap inequalities and modified logarithmic Sobolev inequalities in the random matrix setting.

The discovery of postquantum nonlocality, i.e. the existence of nonlocal correlations stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers.

Is it possible to create a source of provable random numbers? If the answer to this question is "yes," it would be of importance in information security, where the safety of protocols such as RSA depends on the ability to generate random encryption keys. Bell inequality violations offer a potential solution: if a device exhibits a Bell inequality violation, then its outputs must have been computed by some quantum process and are therefore random.

Cellular automata (CA) are computational structures spaciously and temporally discrete which were originally proposed by John von Neumann in the late 1940’s. They have the same computational power of Turing machines.This tool enables us to simulate a large number of different problems in distinct areas.