Complexity and Robustness of Quantum Entanglement

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Quantum computing is dramatically impacting our understanding of the possibilities and limits of information processing. Computing machines taking advantage of the counter-intuitive quantum effects of Nature will be able to perform certain tasks much faster than any computer based only on classical principles, such as simulating quantum physics, searching large databases, or breaking widely used cryptographic codes. ******One of the most intriguing aspects of quantum information processing is the physical phenomenon known “quantum entanglement,” which is a type of correlation between two distant particles that cannot be explained classically. Although entanglement began as a philosophical curiosity within quantum physics, these “spooky” correlations have been recognized as an important resource for a variety of information processing tasks. For example, quantum entanglement is a crucial ingredient in protocols for classically testing random number generation --- a task not possible in the classical world.******A primary lesson learned over the past two decades is that high entanglement complexity is a general feature of quantum states. Today, the frontier challenge in quantum information theory is understanding the robustness of such complex entanglement. So far, much of our understanding of the complexity of entanglement pertains to highly idealized settings: for example, the states of an error-free quantum computer, or physical systems at extremely low temperature, are expected to defy efficient classical simulation. But what about noisy quantum computing devices, or physical systems at room temperature? Can complex entanglement persist in these settings? ******The overarching goal of this research proposal is to address this important theme about the robustness of complex entanglement. I propose a research program that pursues two main directions, exemplified by the following questions: (a) Can complex entanglement be classically certified in a noise-tolerant manner? and (b) What is the computational complexity of quantum correlations? ******Developing a deeper understanding of the robustness of entanglement has significant theoretical as well as practical motivation. On the theoretical side, studying the questions above will likely involve using concepts and techniques from cryptography, condensed matter physics, complexity theory, and more. The answers will enrich our understanding of the computational and information-theoretic aspects of quantum entanglement in a variety of settings. On the practical side, studying robustness of entanglement is a timely topic as we enter the "Noisy Intermediate-Scale Quantum" era, where companies such as Google and IBM are on the verge of constructing quantum computers with a few hundred noisy qubits. There is a a demand for rigorous methods for testing noisy quantum devices, and furthermore, demonstrating that such devices are capable of performing computations that exceed the capabilities of classical computers.**