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Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation,…
Quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the…
We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and…
As quantum computers advance, the complexity of the software they can execute increases as well. To ensure this software is efficient, maintainable, reusable, and cost-effective -key qualities of any industry-grade software-mature software…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
We study the problem of finding $K$ collision pairs in a random function $f : [N] \rightarrow [N]$ by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
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…
One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these…
Quantum computers promise to perform certain computations exponentially faster than any classical device. Precise control over their physical implementation and proper shielding from unwanted interactions with the environment become more…
Quantum computation by adiabatic evolution, as described in quant-ph/0001106, will solve satisfiability problems if the running time is long enough. In certain special cases (that are classically easy) we know that the quantum algorithm…
This paper proposes a quantum-classical algorithm to evaluate and select classical artificial neural networks architectures. The proposed algorithm is based on a probabilistic quantum memory and the possibility to train artificial neural…
Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning methods have demonstrated impressive performances in…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
Operating on the principles of quantum mechanics, quantum algorithms hold the promise for solving problems that are beyond the reach of the best-available classical algorithms. An integral part of realizing such speedup is the…
Quantum machine learning is a rapidly growing field at the intersection of quantum technology and artificial intelligence. This review provides a two-fold overview of several key approaches that can offer advancements in both the…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
In this work, we developed an efficient quantum algorithm for the simulation of non-Markovian quantum dynamics, based on the Feynman path integral formulation. The algorithm scales polynomially with the number of native gates and the number…
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…