Related papers: Quantum oracles for the finite element method
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
Selecting a set of basis states is a common task in quantum computing, in order to increase and/or evaluate their probabilities. This is similar to designing WHERE clauses in classical database queries. Even though one can find heuristic…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using…
The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world…
Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…
Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
Quantum computing sets the foundation for new ways of designing algorithms, thanks to the peculiar properties inherited by quantum mechanics. The exploration of this new paradigm faces new challenges concerning which field quantum speedup…
The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distributions. The studied variational quantum gate learning…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
This paper investigates the impact of noise in the quantum query model, a fundamental framework for quantum algorithms. We focus on the scenario where the oracle is subject to non-unitary (or irreversible) noise, specifically under the…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block-encoding, time-evolving, and sampling in the eigenbasis of electronic structure Hamiltonians…
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…