Related papers: Low Rank Approximation in Simulations of Quantum A…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
Feature selection is a common step in many ranking, classification, or prediction tasks and serves many purposes. By removing redundant or noisy features, the accuracy of ranking or classification can be improved and the computational cost…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…