Related papers: Predicting symmetries of quantum dynamics with opt…
We give a review of the most important results on optimal tomography as mathematical wave-pattern recognition theory emerged in the 70's in connection with the problems of optimal estimation and hypothesis testing in quantum theory. In…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…
We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from $Z_{p-1}^{m}$ to…
This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system…
We experimentally demonstrate quantum data compression exploiting hidden subgroup symmetries using a photonic quantum processor. Classical databases containing generalized periodicities-symmetries that are in the worst cases inefficient for…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Symmetric extensions are essential in quantum mechanics, providing a lens to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
The Ising model is the simplest to describe many-body effects in classical statistical mechanics. Duality analysis leads to a critical point under several assumptions. The Ising model itself has $Z(2)$ symmetry. The basis of the duality…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…