Related papers: Quantum and Classical Algorithms for Bounded Dista…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Quantum low-density parity-check (LDPC) codes, a class of quantum error correcting codes, are considered a blueprint for scalable quantum circuits. To use these codes, one needs efficient decoding algorithms. In the classical setting, there…
Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
In a seminal work [PRL85.4972], Walgate, Short, Hardy, and Vedral prove in finite dimensions that for every pair of pure multipartite orthogonal quantum states, there exists a one-way local operations and classical communication (LOCC)…
Quantum computing offers the potential of exponential speedups for certain classical computations. Over the last decade, many quantum machine learning (QML) algorithms have been proposed as candidates for such exponential improvements.…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
We study the algorithmic complexity of the problem of deciding whether a Linear Time Invariant dynamical system with rational coefficients has bounded trajectories. Despite its ubiquitous and elementary nature in Systems and Control, it…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…
We study on-line strategies for solving problems with hybrid algorithms. There is a problem Q and w basic algorithms for solving Q. For some lambda <= w, we have a computer with lambda disjoint memory areas, each of which can be used to run…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…