Related papers: On Modifying the Variational Quantum Singular Valu…
Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the…
We study theoretically the effects of dissipation on the performances of a variational quantum algorithm used to approximately solve a combinatorial optimization problem, the Maximum Independent Set, on a platform of neutral atoms. We take…
We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter $q \in [0,\infty]$. Our algorithm is a $q$-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
We study quantum speedups in quantum machine learning (QML) by analyzing the quantum singular value transformation (QSVT) framework. QSVT, introduced by [GSLW, STOC'19, arXiv:1806.01838], unifies all major types of quantum speedup; in…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
Variational quantum algorithms are of special importance in the research on quantum computing applications because of their applicability to current Noisy Intermediate-Scale Quantum (NISQ) devices. The main building blocks of these…
One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously.…
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…