Martina Frau

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Driven by groundbreaking experimental advances, quantum matter is entering the era of quantum error correction, where basic forms of computation can now be realized in a fault-tolerant manner. From a many-body perspective, this raises a natural question: what characterizes states that are hard to realize within the constraints of error correction? Entanglement, while essential, is not a sufficient measure of complexity. In this talk, I will explore the complexity of many-body quantum states through the lens of nonstabilizerness — also known as magic. Magic quantifies the difficulty of realizing states in most error corrected codes, and is thus of fundamental practical importance. However, very little is known about its significance to many-body phenomena.

I will begin with a brief overview of magic in spin systems, with a focus on quantities that can be used to compute it - stabilizer Renyi entropies. I will then introduce numerical methods to compute magic using tensor network simulations, and discuss applications to various many-body systems, highlighting its interplay with entanglement.
Finally, I will show how insights from magic can help us understand and control the structure of entanglement in quantum states. In particular, I will present recent results illustrating how simple operations can significantly reduce entanglement—an insight with direct implications for both classical simulation algorithms and quantum state preparation strategies.

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SISSA
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Contact: Karim Chahine