Related papers: Quantum arithmetic operations based on quantum Fou…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…
Quantum key distribution (QKD) and quantum message encryption protocols promise a secure way to distribute information while detecting eavesdropping. However, current protocols may suffer from significantly reduced eavesdropping protection…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
In dynamic quantum circuits, classical information from mid-circuit measurements is fed forward during circuit execution. This emerging capability of quantum computers confers numerous advantages that can enable more efficient and powerful…
Quantum computing is emerging as an alternative computing technology, which is built on the principles of subatomic physics. In spite of continuing progress in developing increasingly more sophisticated hardware and software, access to…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
This chapter summarizes quantum computation, including the motivation for introducing quantum resources into computation and how quantum computation is done. Finally, this chapter articulates advantages and limitations of quantum…
The problem of infinities in quantum field theory (QRT) is a long standing problem in physics.For solving this problem, different renormalization techniques have been suggested but the problem still persists. Here we suggest another…
Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von…
In 1998, Brassard, Hoyer, Mosca, and Tapp (BHMT) gave a quantum algorithm for approximate counting. Given a list of $N$ items, $K$ of them marked, their algorithm estimates $K$ to within relative error $\varepsilon$ by making only $O\left(…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
We apply quantum integration to elementary particle-physics processes. In particular, we look at scattering processes such as ${\rm e}^+{\rm e}^- \to q \bar q$ and ${\rm e}^+{\rm e}^- \to q \bar q' {\rm W}$. The corresponding probability…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…