Related papers: A novel quantum circuit for the quantum Fourier tr…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient…
We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
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…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
The physical limitations of quantum hardware often require nearest-neighbor qubit structures, in which two-qubit gates are required to construct nearest-neighbor quantum circuits. However, two-qubit gates are considered a major cost of…
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…
Recently, the development of quantum chips has made great progress-- the number of qubits is increasing and the fidelity is getting higher. However, qubits of these chips are not always fully connected, which sets additional barriers for…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…
In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
The \textit{Temporal Fusion Transformer} (TFT), proposed by Lim \textit{et al.}, published in \textit{International Journal of Forecasting} (2021), is a state-of-the-art attention-based deep neural network architecture specifically designed…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…