Cesar Lema | Searcharxiv

arXiv2025

Reading Qubits with Sequential Weak Measurements: Limits of Information Extraction

Quantum information processing and computation requires high accuracy qubit configuration readout. In many practical schemes, the initial qubit configuration has to be inferred from readout that is a time-dependent weak measurement record. However, a combination of the measurement scheme and intrinsic dynamics can end up scrambling the initial state and lose information irretrievably. Here, we study the information physics of quantum trajectories based on weak measurements in order to address the optimal achievable performance in qubit configuration readout for two realistic models of single qubit readout: (i) Model I is informationally complete, but without intrinsic dynamics; (ii) Model II is informationally incomplete weak measurements with intrinsic dynamics. We first use mutual information to characterize how much intrinsic information about the initial state is encoded in the measurement record. Using a fixed discrete time-step formulation, we compute the mutual information while varying the measurement strength, duration of measurement record, and the relative strength of intrinsic dynamics in our measurement schemes. We also exploit the emergence of continuum scaling and the Stochastic Master Equation in the weak measurement limit. We develop an asymptotic expansion in the measurement efficiency parameter to calculate mutual information, which captures qualitative and quantitative features of the numerical data. The bounds on information extraction are manifested as plateaux in mutual information, our analysis obtains these bounds and also optimal duration of measurement required to saturate them. Our results should be useful both for quantum device operation and optimization and also, possibly, for improving the performance of recent machine learning approaches for qubit and multiqubit configuration readout in current Noisy Intermediate-Scale Quantum (NISQ) experiment regimes.

quant-ph↗

arXiv2020

Approximating Ground State Energies and Wave Functions of Physical Systems with Neural Networks

Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However closed form solutions to this equation are only available for a few systems and approximation methods are typically used to find solutions. In this paper we address the problem of solving the time independent Schr\"odinger equation for the ground state solution of physical systems. We propose using end-to-end deep learning approach in a variational optimization scheme for approximating the ground state energies and wave functions of these systems. A neural network realizes a universal trial wave function and is trained in an unsupervised learning framework by optimizing the expectation value of the Hamiltonian of a physical system. The proposed approach is evaluated on physical systems consisting of a particle in a box with and without a perturbation. We demonstrate that our approach obtains approximations of ground state energies and wave functions that are highly accurate, which makes it a potentially plausible candidate for solving more complex physical systems for which analytical solutions are beyond reach.

quant-ph↗