Related papers: Quantum Wave Atom Transforms
Digital quantum simulation offers a promising route for studying quantum dynamics, but efficient operator representations and circuit depth remain key challenges for near-term hardware. We investigate one-dimensional wave packet dynamics…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this work, we introduce packet switching as a new paradigm for quantum data transmission in both future and…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…
An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave…
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits…
In this work, we present a case study in implementing a variational quantum algorithm for solving the Poisson equation, which is a commonly encountered partial differential equation in science and engineering. We highlight the practical…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…