<p dir="ltr">This thesis advances the methodologies of quantum state tomography (QST) to validate and optimize quantum processing on Noisy Intermediate-Scale Quantum (NISQ) devices, crucial for the transition to practical quantum systems. Inspired by recent advancements in the field, we propose a novel QST method based on the maximal entropy formalism, specifically addressing scenarios with incomplete measurement sets to provide a robust framework for state reconstruction. We extend this formalism to an informationally complete (IC) set of observables and introduce a variational approach for quantum state preparation, easily implementable on near-term quantum devices. Our developed maximal entropy-based QST protocol is applied to ultrafast molecular dynamics specifically for studying photoexcited ammonia molecule, enabling direct measurement and manipulation of electronic quantum coherences and exploring entanglement effects in molecular systems. Through this approach, we achieve a groundbreaking milestone by, for the first time, constructing the entanglement entropy of the electronic subsystem - an otherwise inaccessible metric. In doing so it also provides the first physical interpretation of the maximal entropy parameters in an experimental setting and highlights the potential for feedback between time-resolved quantum dynamics and quantum information science. Furthermore, building upon our advancements in state tomography, we propose a variational quantum algorithm for Hamiltonian learning that leverages the time dynamics of observables. Additionally, we reverse engineer the maximal entropy approach and demonstrate the use of entropy to refine the traditional geometric Brownian motion (GBM) method for better capturing real system complexities by addressing its log-normality restrictions, which opens new avenues for quantum sampling techniques. Through these contributions, this thesis showcases the Maximal Entropy formalism’s efficacy in QST and set the stage for future innovations and applications in cutting-edge quantum research.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/26790346 |
| Date | 23 August 2024 |
| Creators | Rishabh Gupta (19452091) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Maximal_Entropy_Formalism_for_Quantum_State_Tomography_and_Applications/26790346 |
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