Related papers: Quantum Time-Space Tradeoffs for Matrix Problems
Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…
Given a conjunctive query and a database instance, we aim to develop an index that can efficiently answer spatial queries on the results of a conjunctive query. We are interested in some commonly used spatial queries, such as range…
We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $\epsilon$; the minimal-depth method achieves a $T$-depth of…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling…
Markov chain methods are remarkably successful in computational physics, machine learning, and combinatorial optimization. The cost of such methods often reduces to the mixing time, i.e., the time required to reach the steady state of the…
Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
We propose an approach for quantifying a quantum circuit's quantumness as a means to understand the nature of quantum algorithmic speedups. Since quantum gates that do not preserve the computational basis are necessary for achieving quantum…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
In the era of Noisy Intermediate-Scale Quantum (NISQ) computers it is crucial to design quantum algorithms which do not require many qubits or deep circuits. Unfortunately, the most well-known quantum algorithms are too demanding to be run…
Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…