QuICS seminar

"Property testers" are algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow “far” from having that property, a tester should efficiently distinguish between these two cases. In this talk we describe recent results obtained for quantum property testing. This area naturally falls into three parts.

Individual atoms in optical cavities can provide an efficient interface between light and matter, something essential to quantum communication. Through the cavity field, quantum gates, such as the CNOT gate, can be realized between atoms trapped in the same cavity, which can be used in e.g. a quantum repeater to swap entanglement to large distances. Nonetheless, dissipation caused by cavity decay and spontaneous emission increases the experimental difficulty of realizing high quality gates in such a setup.

We explore an approach to the coherent control and manipulation of quantum degrees of freedom in disordered, interacting systems in the many-body localized phase. Our approach leverages a number of unique features of many-body localization: a lack of thermalization, a locally gapped spectrum, and slow dephasing.

Semiconductor quantum dots in silicon are promising qubits because of long spin coherence times and their potential for scalability. However, whether qubits with fidelities above the threshold for quantum error correction can be achieved remains to be seen. We show theoretically that such high fidelities can be achieved in two types of electrically controlled double quantum dot qubits.

We derive new characterizations for the matrix Φ-entropies introduced in [Electron. J. Probab., 19(20): 1–30, 2014]. The fact that these new characterizations are a direct generalization of their corresponding equivalent statements for classical Φ-entropies provides additional justification to the original definition of matrix Φ-entropies. Moreover, these extra characterizations allow us to better understand the properties of matrix Φ-entropies, which are a powerful tool for unifying the study matrix concentration inequalities.

Fermi's golden rule is widely used, and the resulting transition rates are an important part of the thermal behaviour of open quantum systems. But this rule is curious because it is valid outside the regime in which it is derived: It is derived only for short times and for off-resonant transitions but works for all times and for resonant transitions.

Quantum entanglement is usually considered very fragile, because quantum systems tend to interact with the environment, which means that even at very low temperature, multi-particle entanglement is very hard to maintain.

A common experimental strategy for testing local realism is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. Estimating the amount of violation depends on determining when photon detections are "coincident", but usual methods for making that determination can allow a local realistic system to appear to violate the inequality. In this talk I will describe a family of Bell inequalities, which are derived from the triangle inequality, and whose violation unambiguously rejects local realism.

We describe how to use the generalized numerical ranges to help study problems in quantum error correction. Recent results and open problems will be mentioned.

Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we pursue two particular questions: (1) do adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there is only one local minimum and (2) what characterizes the boundary between large- and small- gapped Hamiltonians?