Abstract
The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.
Highlights
The object of quantum sensing is to measure some physical quantity, say a magnetic field, pressure or temperature, which we will denote as φ
The study of noisy intermediate-scale quantum (NISQ) devices places a huge emphasis on the study of parametrized quantum states, i.e. quantum states that depend continuously on a vector of parameters θ ∈ Rd
To clarify the relation between classical and quantum Fisher information, we first return to the notion of monotonicity that we required for the distance measures we look at
Summary
The study of NISQ devices places a huge emphasis on the study of parametrized quantum states, i.e. quantum states that depend continuously on a vector of parameters θ ∈ Rd. If we are given a distance measure d between quantum states, we can define – by a slight abuse of notation – a new distance measure between the associated parameters: d(θ, θ ) = d(ρ(θ), ρ(θ )). We require some very natural properties from the distance measures between quantum states or probability distributions we employ. That it is always positive d(θ, θ ) ≥ 0 and second, that the distance between identical objects is zero d(θ, θ) = 0. We can measure distances between parameters by going to the space of quantum states or to the space of probability distributions over the measurement outcomes, dependent on the question we seek to answer.
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