What is it about?
Quantum mechanics assumes that physical operators are Hermitian, and their time evolutions are unitary. However, exploring modifications to these postulates has been largely unexplored. In this work, we investigate a class of non-Hermitian non- diagonalizable physical operators termed 'defective.' All such defective quantum systems exhibit exceptional points (also called non-hermitian degeneracies). Quantum sensing involves estimating a parameter with very high precision using quantum systems. Several proposals in the literature suggest exploiting defective systems for quantum sensing. This study explores a circuit-based model of such defective quantum sensors to determine if 'defective' quantum systems can enhance the precision of estimation by sensing to arbitrarily large values. We demonstrate our results on a cloud-based quantum computer.
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Why is it important?
Some articles have expressed concerns regarding the use of 'defective operators' for highly accurate quantum sensing. In order to assess the performance of a quantum sensor, we rely on Quantum Fisher Information (QFI), where higher QFI corresponds to higher precision. Certain articles argue that the divergence of QFI is not a necessary condition in these defective systems or may occur only under specific conditions. In this study, we aim to address this disagreement. Quantum sensors are essentially systems sensitive to perturbations, which are the changes they are designed to detect. Mathematically, the energy of quantum sensors is disturbed by these perturbations. We use perturbation theory, a crucial theoretical tool in quantum sensing to estimate these perturbed energies and other relevant quantities. While perturbed energies are typically expanded in the Taylor series, we refer to previous work that employed correct theoretical analysis using proper series expansions (specifically Puiseux series) upon perturbations around these exceptional points of the defective systems. We then experimentally demonstrate these effects for any general defective quantum system. Implementing these unique systems in an actual quantum setting is uncommon. Here, we constructed a circuit model of one such system and tested it on a cloud-based quantum computer. Our results confirmed the divergence of Quantum Fisher Information, indicating improved performance, as also predicted theoretically by a few previous articles using correct expansions upon perturbation around these exceptional points. In summary, we can now make these distinctive quantum systems accessible to a broader group of researchers through cloud computing. We can experimentally illustrate the divergence of Quantum Fisher Information in the presence of low noise and conduct noise analysis. This accessibility can also assist us in discovering more effective ways to use quantum sensing and overcome its limitations.
Perspectives
This work is important in two-fold ways. First is the applied aspect: it shows how to implement non-hermitian systems in the quantum computer, which essentially runs on the principle of hermitian quantum mechanics. Second is the theoretical one: this work also puts off a debate on the usability of a non-hermitian system for quantum sensing and ascertains affirmatively that these systems are indeed useful. Demonstrating the main idea in a cloud-based quantum computer says it all.
Shubhrangshu Dasgupta
Indian Institute of Technology Ropar
Read the Original
This page is a summary of: Simulation of exceptional-point systems on quantum computers for quantum sensing, AVS Quantum Science, January 2024, American Vacuum Society,
DOI: 10.1116/5.0172968.
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