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Generating randomness efficiently is a key capability in both classical and quantum information processing applications. For example, Haar-random quantum states serve as primitives for applications including quantum cryptography, quantum process tomography, and randomized benchmarking. How quickly can these random states be generated? And how much randomness is really necessary for any given application? In this talk, I will address these questions in Brownian quantum circuit models, which admit a large-$N$ limit that can be solved exactly.

Interactive proof systems are a classic idea in theoretical computer science, and have led to fundamental advances in complexity theory (hardness of approximation and the PCP theorem) and cryptography. Remarkably, in quantum information, interactive proof systems with multiple provers have become an important tool for studying quantum entanglement, extending the pioneering work of Bell in the 1960s. In this talk I will discuss recent progress in characterizing the power of the complexity class MIP* of such proof systems where the provers share entanglement.

Quantized optical vortices, or the twisted photons, may carry pre-set amounts of angular momentum along their direction of propagation, thus allowing for quantum transitions otherwise forbidden for conventional plane-wave light. In this talk I will address the question of the angular momentum transfer to internal degrees of freedom of quantum systems excited by the twisted photons, and discuss appropriate polarization observables.

Building future hybrid quantum networks will require
interfacing different types of quantum systems. Photonic interconnects
between such systems have rarely been investigated due to difficulties
such as spectral mismatch. In this talk, I will discuss our progress
on interfacing photons emitted from a trapped ion with neutral
rubidium atoms. Using quantum frequency conversion, we convert 493 nm

I will give an overview of the range of algorithms for simulating Hamiltonian evolution on a quantum computer.  These include Lie-Trotter-Suzuki product formulae, quantum walks, linear combinations of unitaries, Taylor series, Dyson series, quantum signal processing and qubitisation.  I will discuss the relations between these approaches, as well as how they can be applied to quantum chemistry.  The talk will also cover a new log-depth technique for antisymmetrising states to use for quantum chemistry.

I will talk about a notion of universality in spin systems by which certain spin systems can simulate all others. We provide sufficient and necessary conditions for a spin system to be universal, and show that the Ising model and many other “simple” systems are universal. This notion of universality is somewhat similar to the notion of universality in computer science (by which there exist universal Turing machines) — I will mention ongoing work in trying to make this connection precise. 

In this talk I will introduce some basic principles of semiconductor quantum dots and show how their discrete energy spectrum can be used to generate entangled photon pairs and spin photon entanglement. I will show, how a virtual level and two photon excitation can be used to excite a (single photon) forbidden transition. And if the time allows, I will show how different degrees of freedom can be used simultaneously to generate hyper-entangled photon pairs.

Quantum processors exist — several fully programmable devices with 5-16 qubits exist today, at least one of which (the IBM Quantum Experience) is publicly accessible. Running real circuits on real quantum processors is forcing us to recognize and tackle new, “exotic” errors.

We prove a general relation between adaptive and nonadaptive strategies in the quantum setting, i.e., between strategies where the adversary can or cannot adaptively base its action on some auxiliary quantum side information. Our relation holds in a very general setting, and is applicable as long as we can control the bit-size of the side information, or, more generally, its "information content".

We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).