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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).

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles.

We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t. We obtain upper bounds on the scaling of t with the number of bosons, n, for which simulation is classically efficient. We also obtain a lower bound on the scaling of t with n for which this problem reduces to a general instance of the boson sampling problem and is hence hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11].

We present new composite pulse sequences for performing arbitrary rotations in singlet-triplet qubits that are faster than existing sequences.  We consider two sequences for performing a z rotation, one that generalizes the Hadamard-x-Hadamard sequence, and another that generalizes a sequence by Guy Ramon (G. Ramon, Phys. Rev.

The nascent field of Quantum Machine Learning has been generating a substantial buzz in the last few years. The broad theme of this field is the interplay between the disciplines of quantum information processing (QIP) and of machine learning (ML). In this talk, I will review the basic trends in this new discipline.

Quantum self-testing is a tool that can allow us to test the honesty of quantum devices without needing to have access to any trusted quantum devices.  Through classical information alone (measurement settings and outcomes, for example) we can verify that quantum devices are operating according to some specification, even if we have no information on how the devices are constructed.  Self-testing can be used to test sources, measurements, and even entire quantum computations.  In this ta

Reliable qubits are difficult to engineer.  What can we do with just a few of them?  Here are some ideas: 
 
1. Memory/dimensionality test.  An n-qubit system has 2^n dimensions---a big reason for quantum computers' exponential power!  But systems with just polynomial(n) dimensions can look like they have n qubits.  We give a test for verifying that your system really has 2^n dimensions.  
 

In this talk, I will present recent work on the properties of radiation from a one-dimensional electron liquid. Because of the large mismatch between the speed of light and the Fermi velocity, radiation serves as a direct test of spectral weight of the system which is far `off-shell'. In the Luttinger liquid model, excitations of the electron liquid are described by non-interacting bosons and this spectral weight vanishes. Thus, radiation offers a direct test of behavior which is beyond the Luttinger liquid paradigm.

Quantum correlations are fundamental for quantum information protocols and for our understanding of many-body quantum physics. The detection of these correlations in these systems is challenging because it requires the estimation of an exponentially growing amount of parameters. We present methods to alleviate this problem and discuss their application to physically relevant quantum states.

The gapless surface states of three-dimensional topological insulators are a new form of matter, and there is much active research on exotic order on the surface of topological insulators due to electron-electron interactions. In this talk, we investigate electron-electron interactions on the surface of a three-dimensional topological insulator. First, we construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator.