Degree vs. Approximate Degree and Quantum Implications of Huang’s Sensitivity Theorem
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function f, deg(f) = O(~deg(f)^2): The degree of f is at most quadratic in the approximate degree of f. This is optimal as witnessed by the OR function. D(f) = O(Q(f)^4): The deterministic query complexity of f is at most quartic in the quantum query complexity of f. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017). We apply these results to resolve the quantum analogue of the Aanderaa--Karp--Rosenberg conjecture.
Fundamental aspects of solving quantum problems with machine learning
Machine learning (ML) provides the potential to solve challenging quantum many-body problems in physics and chemistry. Yet, this prospect has not been fully justified. In this work, we establish rigorous results to understand the power of classical ML and the potential for quantum advantage in an important example application: predicting outcomes of quantum mechanical processes. We prove that for achieving a small average prediction error, one can always design a classical ML model whose sample complexity is comparable to the best quantum ML model (up to a small polynomial factor).
Multi-terminal Josephson effect
Dissertation Committee Chair: Vladimir Manucharyan
Committee:
Christopher Lobb
James Williams
Steven Anlage
Ichiro Takeuchi (Dean’s rep)
Abstract:
Quantum Photonics in the Frequency Domain
Quantum frequency conversion is the process by which the wavelength of a light field is converted to another wavelength while still fully maintaining its quantum state. We describe our recent research that utilizes the nonlinear optical process of four-wave mixing to perform ultralow noise quantum frequency conversion with efficiencies approaching 100%. We also show how this nonlinear process can be used to realize other novel quantum phenomena in the frequency domain including Hong-Ou-Mandel interference, near-deterministic single-photon generation, single-photon Ramsey interference, and
Supersolidity in the ultracold: when atoms behave as crystal and superfluid at the same time
Exotic and counterintuitive phases of quantum matter have been recently discovered in degenerate quantum gases of highly magnetic atoms (Erbium and Dysprosium). The very fact such atoms possess a large magnetic moment means that their interactions at the many-body level and their quantum correlations acquire a unique long-range and anisotropic character. This property opens novel avenues of investigation beyond the contact-interaction paradigm.
Synthesis and characterization of quantum defects for quantum network applications: from deep centers in diamond to shallow impurities in ZnO
Point defects in crystals are the solid state analog to trapped ions. Thus these “quantum defects” have gained popularity as qubit candidates for scalable quantum networks. In this talk, I will introduce some of the basic quantum defect properties desirable for quantum network applications and give some illustrative examples of recent successes toward scalable quantum networks, highlighting my group’s work on single NV centers in diamond and shallow donors in ZnO.
Thermodynamics of quantum information
We are on the verge of a technological revolution. Over the last couple of years the first computational devices have become commercially available that promise to exploit so-called quantum advantage. Even though the thermodynamic cost for processing classical information has been known since the 1960s, the thermodynamic description of quantum computers is still at its infancy. This is due to the fact that many notions of classical thermodynamics, such as work and heat, do not readily generalize to quantum systems in the presence of thermal and quantum noise.
Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene
We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene. The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that minimally twisted bilayer graphene realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps.
Quantum information processing with nuclear spins in diamond
Abstract: Spins associated to defects in solids are promising qubits for quantum information processing. We have developed novel control gates for an electron spin coupled to nuclear spins, and applied this scheme to realise a universally connected 10-qubit register using an NV-centre in diamond [1]. Moreover, we employed dynamical decoupling of the register to realise coherence times up to 63(2) seconds. Building upon these techniques, we have also recently demonstrated the 3D imaging of a system of 27 coupled nuclear spins with atomic scale resolution [2].