Related papers: Quantum circuits for partial differential equation…
We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Recently, it has been presented some algorithms and physical models which give prospects for construction of quantum computers capable to solve systems of linear equations. The common feature which is shared in these works is the use of…
The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
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…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
Simulating quantum imaginary-time evolution (QITE) is a major promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with impractically small success probabilities or coherent (quantum…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…