TNQMetro: Tensor-network based package for efficient quantum metrology computations

Abstract

TNQMetro is a numerical package written in Python for calculations of fundamental quantum bounds on measurement precision. Thanks to the usage of the tensor-network formalism it can beat the curse of dimensionality and provides an efficient framework to calculate bounds for finite size system as well as determine the asymptotic scaling of precision in systems where quantum enhancement amounts to a constant factor improvement over the Standard Quantum Limit. It is written in a user-friendly way so that the basic functions do not require any knowledge of tensor networks. Program summaryProgram Title: TNQMetroCPC Library link to program files:https://doi.org/10.17632/wmw9xrxwgf.1Developer's repository link:https://github.com/kchabuda/TNQMetroCode Ocean capsule:https://codeocean.com/capsule/7858507Licensing provisions: MITProgramming language: PythonNature of problem: Exponential growth of the Hilbert space dimension with the number of particles involved is a serious roadblock for numerical studies of the potential of quantum enhanced metrology. It leads to an exponential growth of the computational complexity of even most elementary quantum mechanical calculations, not to mention more advanced computational tasks, such as the ones required for studying the metrological potential of quantum states, e.g. computation of the quantum Fisher information (QFI).Solution method: Thanks to the use of the tensor-network formalism, where quantum states are represented as matrix product states and operators as matrix product operators, it is possible to obtain an efficient description where space complexity scales linearly with the number of elementary particles constituting the physical system. Furthermore, it is possible to efficiently optimize QFI over quantum states and operators in those representations, applying the ideas presented in [1]. This allows to study sophisticated quantum metrological models that are beyond the grasp of the standard numerical methods utilizing the full Hilbert space representation of quantum states and operations.