Related papers: Synthesizing Quantum Circuits for Simple Periodic …
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both…
We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
We derive many-body single- and multi-reference wave functions for quantum Monte Carlo of periodic systems with an anti-symmetric portion that explicitly integrates over the Brillouin zone of one-particle Bloch states. The wave functions…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…
We present an economical dynamical control scheme to perform quantum computation on a one dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the…
Synthesis of quaternary quantum circuits involves basic quaternary gates and logic operations in the quaternary quantum domain. In this paper, we propose new projection operations and quaternary logic gates for synthesizing quaternary logic…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
Quantum computing algorithms using the quantum Fourier transform require repeated use of a phase shift gate. In the case of qubits using optical photons for operation, this gate can be implemented using single-photon beams focused close to…
Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results…
In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study…
The generation of pseudo-random numbers is one of the interesting problems in Monte Carlo simulations, mostly because the common computer generators produce periodic numbers. We used simple pseudo-random numbers generated with the simplest…
We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
A simple method called symbolic representation for piecewise linear functions on the real line is introduced and used to compute the numbers of periodic points of all periods for some such functions. Since, for every positive integer m, the…