Related papers: A Menagerie of Symmetry Testing Quantum Algorithms
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Starting from the Quantum-Phase-Estimate (QPE) algorithm, a method is proposed to construct entangled states that describe correlated many-body systems on quantum computers. Using operators for which the discrete set of eigenvalues is…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
The emergence of quantum devices has raised a significant issue: how to certify the quantum properties of a device without placing trust in it. To characterise quantum states and measurements in a device-independent way, up to some degree…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, $\mathcal{PT}$-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
Recently, consensus-type problems have been formulated in the quantum domain. Obtaining average quantum consensus consists in the dynamical symmetrization of a multipartite quantum system while preserving the expectation of a given global…
The problem of quantum state estimation is crucial in the development of quantum technologies. In particular, the use of symmetric quantum states is useful in many relevant applications. In this work, we analyze the task of reconstructing…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary…
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
The past decade has seen a remarkable resurgence of the old programme of finding more or less a priori axioms for the mathematical framework of quantum mechanics. The new impetus comes largely from quantum information theory; in contrast to…
In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input…
We prove that a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working…
We use quantum computers to test the foundations of quantum mechanics through quantum algorithms that implement some of the experimental tests as the basis of the theory's postulates. These algorithms can be used as a test of the physical…