Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA framework for engineering quantum likelihood functions for expectation estimation
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We develop a framework for characterizing and analyzing engineered likelihood functions (ELFs), which play an important role in the task of estimating the expectation values of quantum observables. These ELFs are obtained by choosing tunable parameters in a parametrized quantum circuit that minimize the expected posterior variance of an estimated parameter. We derive analytical expressions for the likelihood functions arising from certain classes of quantum circuits and use these expressions to pick optimal ELF tunable parameters. Finally, we show applications of ELFs in the Bayesian inference framework.
rate research
Read More
We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper Quantum nonlocality without entanglement [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the rotated domino states, resolving a long-standing open question [BDF+99].
The advent of dispersion-engineered and highly nonlinear nanophotonics is expected to open up an all-optical path towards the strong-interaction regime of quantum optics by combining high transverse field confinement with ultra-short-pulse operation. Obtaining a full understanding of photon dynamics in such broadband devices, however, poses major challenges in the modeling and simulation of multimode non-Gaussian quantum physics, highlighting the need for sophisticated reduced models that facilitate efficient numerical study while providing useful physical insight. In this manuscript, we review our recent efforts in modeling broadband optical systems at varying levels of abstraction and generality, ranging from multimode extensions of quantum input-output theory for sync-pumped oscillators to the development of numerical methods based on a field-theoretic description of nonlinear waveguides. We expect our work not only to guide ongoing theoretical and experimental efforts towards next-generation quantum devices but also to uncover essential physics of broadband quantum photonics.
The evaluation of expectation values $Trleft[rho Oright]$ for some pure state $rho$ and Hermitian operator $O$ is of central importance in a variety of quantum algorithms. Near optimal techniques developed in the past require a number of measurements $N$ approaching the Heisenberg limit $N=mathcal{O}left(1/epsilonright)$ as a function of target accuracy $epsilon$. The use of Quantum Phase Estimation requires however long circuit depths $C=mathcal{O}left(1/epsilonright)$ making their implementation difficult on near term noisy devices. The more direct strategy of Operator Averaging is usually preferred as it can be performed using $N=mathcal{O}left(1/epsilon^2right)$ measurements and no additional gates besides those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) and show that the latter strategy can require an overly large number of measurement in order to achieve a reasonably small relative target accuracy $epsilon_r$. We propose to overcome this problem using a single step of QPE and classical post-processing. This approach leads to a circuit depth $C=mathcal{O}left(epsilon^muright)$ (with $mugeq0$) and to a number of measurements $N=mathcal{O}left(1/epsilon^{2+ u}right)$ for $0< uleq1$. We provide detailed descriptions of two implementations of our strategy for $ u=1$ and $ uapprox0.5$ and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.
An adiabatic change of parameters along a closed path may interchange the (quasi-)eigenenergies and eigenspaces of a closed quantum system. Such discrepancies induced by adiabatic cycles are refereed to as the exotic quantum holonomy, which is an extension of the geometric phase. Small adiabatic cycles induce no change on eigenspaces, whereas some large adiabatic cycles interchange eigenspaces. We explain the topological formulation for the eigenspace anholonomy, where the homotopy equivalence precisely distinguishes the larger cycles from smaller ones. An application to two level systems is explained. We also examine the cycles that involve the adiabatic evolution across an exact crossing, and the diabatic evolution across an avoided crossing. The latter is a nonadiabatic example of the exotic quantum holonomy.
In this work we build a theoretical framework for the transport of information in quantum systems. This is a framework aimed at describing how out of equilibrium open quantum systems move information around their state space, using an approach inspired by transport theories. The main goal is to build new mathematical tools, together with physical intuition, to improve our understanding of non-equilibrium phenomena in quantum systems. In particular, we are aiming at unraveling the interplay between dynamical properties and information-theoretic features. The main rationale here is to have a framework that can imitate, and potentially replicate, the decades-long history of success of transport theories in modeling non-equilibrium phenomena.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
