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**NOTE: Building is COMPUTER SCIENCE INSTRUCTIONAL CENTER, not Computer and Space Science** 

The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T-gate, an essential quantum logic gate. Subsequently, gate synthesis intersperses many T-gates with Clifford gates to realise a desired circuit. We introduce a unified framework that implements one round of distillation and multi-qubit gate synthesis in a single step.

Many tasks in quantum information rely on accurate knowledge of a system's Hamiltonian, including calibrating control, characterizing devices, and verifying quantum simulators. In this talk, we pose the problem of learning Hamiltonians as an instance of parameter estimation. We then solve this problem with Bayesian inference, and describe how rejection and particle filtering provide efficient numerical algorithms for learning Hamiltonians.

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this talk, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir.

Every quantum gate can be decomposed into a sequence of single-qubit gates and controlled-NOTs. In many implementations, single-qubit gates are relatively 'cheap' to perform compared to C-NOTs (for instance, being less susceptible to noise), and hence it is desirable to minimize the number of C-NOT gates required to implement a circuit.

We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates.

Encryption of classical data is ubiquitous in everyday life. As quantum computation and communication gains wider use, encryption of quantum data is likely to become important as well. Until recently, the theory of quantum encryption was fairly limited, consisting primarily of the quantum analogue of the one-time pad. In this talk, I will discuss how to place quantum encryption on the same foundations as classical encryption, and how to translate many of the great achievements of classical encryption theory to the quantum setting.

Interacting disordered one-dimensional fermionic systems are an ideal test ground in order to investigate the interplay between properties of the entanglement and quantum phase transitions. Although 1D systems with uncorrelated disorder are always localized, they may exhibit a quantum phase transition to a metallic phase as function of disorder strength if the disorder is correlated (e.g., the Harper model). Once attractive interactions are considered, a transition to a metallic/superconducting phase is predicted.

The study of equivalence relations on mathematical structures is a vast theory embracing combinatorics, optimization, algebra, and mathematical logic. In this context, graph isomorphism and its hierarchy of relaxations constitute a central topic, not only for its elusive complexity, but also for its mathematical richness.  We develop a framework which succeeds in capturing salient aspects of the relaxations of graph isomorphism with tools furnished by nonlocal games. This framework allows us to introduce quantum and non-signalling isomorphism.

Hamiltonian simulation is a very promising area of quantum algorithms where quantum computers can provide a dramatic speedup over classical computers. Until recently, all algorithms had poor scaling in the allowable error. New algorithms allow for complexity scaling logarithmically in the allowable error. One is based on implementing a Taylor series, and another is based on a superposition of different numbers of steps of a quantum walk.