Related papers: Sparsity-dependent Complexity Lower Bound of Quant…
Causal discovery from observational data underpins applications in finance, climate modeling, and machine learning. Constraint-based causal discovery reduces structure learning to a sequence of conditional independence (CI) tests, where…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
A new approximate Quantum State Preparation (QSP) method is introduced, called the Walsh Series Loader (WSL). The WSL approximates quantum states defined by real-valued functions of single real variables with a depth independent of the…
We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity…
We consider the quantum query complexity of local search as a function of graph geometry. Given a graph $G = (V,E)$ with $n$ vertices and black box access to a function $f : V \to \mathbb{R}$, the goal is find a vertex $v$ that is a local…
The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for…
We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of…
Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…
We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using Schatten $\alpha$-norms, firstly exploiting geometric features of the quantum state space,…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
The Lasserre Hierarchy is a set of semidefinite programs which yield increasingly tight bounds on optimal solutions to many NP-hard optimization problems. The hierarchy is parameterized by levels, with a higher level corresponding to a more…
This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…
In view of the KS-tensor complementarity problem, the sparse solution of this problem is studied. Due to the nonconvexity and noncontinuity of the l_0-norm, it is a NP hard problem to find the sparse solution of the KS-tensor…