Related papers: Permutation Invariant Optimization Problems in Qua…
Motivated by the recent advancement of quantum processors, we investigate quantum approximate optimization algorithm (QAOA) to employ quasi-maximum-likelihood (ML) decoding of classical channel codes. QAOA is a hybrid quantum-classical…
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI…
In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
Permutation equivariant neural networks are often constructed using tensor powers of $\mathbb{R}^{n}$ as their layer spaces. We show that all of the weight matrices that appear in these neural networks can be obtained from Schur-Weyl…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the…
This paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a…
Automatic differentiation is an invaluable feature of machine learning and quantum machine learning software libraries. In this work it is shown how quantum automatic differentiation can be used to solve the condensed-matter problem of…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility…
In this thesis we will study matrix models with discrete gauge group $S_N$. We will put these matrix models into a generalized Schur-Weyl duality framework where dual algebras, known as partition algebras, emerge. These form generalizations…
We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…