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Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…
We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon…
Current quantum annealing experiments often suffer from restrictions in connectivity in the sense that only certain qubits can be coupled to each other. The most common strategy to overcome connectivity restrictions so far is by combining…
In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…
Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized…
Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized…
Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing…