Magic of Fluctuations
From Fluctuations in Quantum Information to Magic Resources
A. Ahmadi (TU Delft - QN/Greplová Lab)
S. Groeblacher – Promotor (TU Delft - QN/Groeblacher Lab)
E. Greplová – Copromotor (TU Delft - QCD/Greplova Lab)
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Abstract
The recent progress in quantum technologies shines a bright light on the future of quantum computation. However, resource estimation for quantum computations remains a key challenge. The resource I study in this thesis is known as Magic or Non-stabilizerness and it represents the key requirement for quantum computational advantage in computation. Recent studies in quantum information suggested wide classes of quantifiers for non-stabilizerness.
In this thesis, I develop novel techniques for quantifying non-stabilizerness with the tools fromquantuminformation theory. I am specifically interested inmaking quantum resource estimation computationally as efficient as possible so that quantum resource estimation can become a routine step in both numerical and experimental exploration of quantumcomputing.
I show that by measuring the spreading of the local information in the quantumsystem, we can quantify non-stabilizerness. The measures of such information-spreading can be classified into two categories, entropic-based measures, such as mutual information, and correlator-based measures such as Out-of-Time Ordered Correlators. I investigated both classes of measures and I related them both numerically and analytically to the estimation of non-stabilizerness.
Finally, I relate non-stabilizerness quantification to classical variational methods. Classical methods designed to approximate quantum states are by construction not restricted by non-stabilizerness. The question therefore remained how well these techniques can capture quantumresources. I provide a systematic benchmark for both classical and quantum approximate methods of expressing quantum states and their tradeoff between non-stabilizerness expressivity and ground-state energy accuracy. We observed that having better energy accuracy is necessary but insufficient to have better accuracy in non-stabilizerness.
This Thesis forms a bridge between quantum information resource theory and condensed matter physics and offers a stepping stone towards further exchange between these two fields.