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Over the past decade, it has become increasingly clear that there are deep connections between high energy physics and quantum information, with entanglement serving as a bridge. The Ryu-Takayanagi conjecture is one of the seminal results which translates questions about the entanglement entropy of a CFT state to the task of calculating the lengths of minimal geodesics. These computations are especially tractable for 1+1d CFTs, where there are a variety of additional symmetries.

I will show how to use basic facts from representation theory to derive a unitary version of Cayley's theorem (it allows embedding any finite group in a continuous subgroup of the unitary group). When applied to the symmetric group, this can be used to permute quantum systems in a continuous fashion. I will illustrate how this works for a small number of systems and conclude with some interesting open questions. My talk is loosely based on arXiv:1508.00860.

Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. In one natural special case of the Local Hamiltonian problem, the same 2-local interaction, with differing weights, is applied across each pair of qubits. I will talk about some recent work classifying the computational complexity of this problem when some additional physically motivated restrictions are made to these weights.

I divide the applications of quantum communications into three

categories: quantum cryptographic functions, quantum sensor networks, and distributed quantum computation. Some of these functions are drop-in replacements for existing, classical functionality, with additional, desirable characteristics. At least one of the most exciting is an entirely new capability brought by quantum computation.

Linear optics quantum computing is a promising candidate for the implementation of scalable quantum computing. However, it remains extremely technically challenging owing to the large number of optical elements that would be required for a large-scale device, potentially requiring millions of discrete elements. I present a substantially simplified scheme based on time-bin encoding, whereby only three optical elements are required, independent of the size of the computation.

We have developed an efficient quantum control scheme that allows for arbitrary operations on a cavity mode using strongly dispersive qubit-cavity interaction and time-dependent drives [1,2]. In addition, we have discovered a new class of bosonic quantum error correcting codes, which can correct both cavity loss and dephasing errors. Our control scheme can readily be implemented using circuit QED systems, and extended for quantum error correction to protect information encoded in bosonic codes.

Just like all other quantum information processing methods, quantum annealing requires error correction in order to become scalable. I will report on our progress in developing and analyzing quantum annealing correction methods, and their implementation using the D-Wave Two processor at USC.

Quantum mechanics is a statistical theory. It cannot with certainty predict the outcome of all single events, but instead it predicts probabilities of outcomes. This probabilistic nature of quantum theory is at odds with the determinism inherent in Newtonian physics and relativity, where outcomes can be exactly predicted given sufficient knowledge of a system.