Related papers: Enhanced observable estimation through classical o…
Quantum subspace expansion (QSE) offers promising avenues to perform spectral calculations on quantum processors but comes with a large measurement overhead. Informationally complete (IC) measurements, such as classical shadows, were…
We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…
Classical shadow tomography, harnessing randomized informationally complete (IC) measurements, provides an effective avenue for predicting many properties of unknown quantum states with sample-efficient precision. Projections onto $2^n+1$…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli…
Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. Here we establish a general link…
Classical shadows (CS) have emerged as a powerful way to estimate many properties of quantum states based on random measurements and classical post-processing. In their original formulation, they come with optimal (or close to) sampling…
We consider the statistical properties of photon detection with imperfect detectors that exhibit dark counts and less than unit efficiency, in the context of tomographic reconstruction. In this context, the detectors are used to implement…
We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment…
A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more…
Consider a photon that has just emerged from a linear polarizing filter. If the photon is then subjected to an orthogonal polarization measurement-e.g., horizontal vs vertical-the photon's preparation cannot be fully expressed in the…
Possibilistic and qualitative POMDPs (pi-POMDPs) are counterparts of POMDPs used to model situations where the agent's initial belief or observation probabilities are imprecise due to lack of past experiences or insufficient data…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…