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Classical simulations of quantum computations are vital for the future development of this emerging technology. To this end, decision diagrams have been proposed as a complementary technique which frequently allows to tackle the inherent…

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…

The quantum kernel method has attracted considerable attention in the field of quantum machine learning. However, exploring the applicability of quantum kernels in more realistic settings has been hindered by the number of physical qubits…

We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…

Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading…

This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…

We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…

In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…

Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…

Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…

Due to the scarcity of quantum computing resources, researchers and developers have very limited access to real quantum computers. Therefore, judicious planning and utilization of quantum computer runtime are essential to ensure smooth…

We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of…

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…

The application of program transformation and algebraic methods to the development of efficient combinatorial optimization (CO) algorithms relies on an exhaustive combinatorial generator for the problem specification, followed by the fusion…

We present a detailed analysis of the impact on modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space…

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some…

Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…

We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…