Linear growth of quantum circuit complexity
Quantifying quantum states’ complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits’ complexity increases. Consider constructing a unitary from Haar-random two-qubit quantum gates. Implementing the unitary exactly requires a circuit of some minimal number of gates - the unitary’s exact circuit complexity.
Fault Tolerance and Holography
Abstract: In this talk I will study the extension of fault tolerance techniques to holographic quantum error correcting codes in the context of the ads/cft correspondence. I will seek to argue that the threshold here corresponds to that of the confinement/de confinement phase transition here, analogously to the situation in topological quantum error correcting codes based on Tqft’s.
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https://umd.zoom.us/j/4111099146
Meeting ID: 411 109 9146
Fundamental effects of noise and error mitigation on the trainability of variational quantum algorithms
Abstract: Variational Quantum Algorithms (VQAs) are viewed as amongst the best hope for near-term quantum advantage. A natural question is whether noise places fundamental limitations on VQA performance. In the first part of this talk, we show that noise can severely limit the trainability of VQAs by exponentially flattening the optimization landscape and suppressing the magnitudes of cost gradients.
A field theoretical approach to quantum circuits
Abstract: Quantum circuits have been widely used as a platform to explore universal properties of generic quantum many-body systems. In this talk, I will present our work in which we construct a field theoretical approach to study quantum circuits. We reformulate the sigma model for time periodic Floquet systems using the replica method, and apply it to the study of spectral statistics of the evolution operator of quantum circuits.