Quantum implementation of elementary arithmetic operations

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, re...

In order to realize a Quantum CPU some schemes for executing fundamental mathematical tasks are needed. In this paper we present some quantum circuits which, using elementary arithmetic operations, allow an approximated calculation of continuous functions. Furthermore, we give an explicit example of our procedure applied to the exponential function.

In this work, we provide an overview of circuits for quantum computing. We introduce gates used in quantum computation and then present resource cost measurements used to evaluate circuits made from these gates. We then illustrate how the gates shown are then combined into quantum circuits for basic arithmetic functions. Architectures for addition, subtraction, multiplication, and division are shown. We demonstrate how to calculate the resource costs of quantum circuits. We c...

Quantum computer requires quantum arithmetic. The sophisticated design of a reversible arithmetic logic unit (reversible ALU) for quantum arithmetic has been investigated in this letter. We provide explicit construction of reversible ALU effecting basic arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the classical arithmetic and logic operation in a reversible integrated system. This letter provides actual evidence to...

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite differen...

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor's quantum factorising algorithm. We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorised.

In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable a...

The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor product Hilbert space H^{arith} of number states and operators for the basic arithmetic operations is described. Unitary maps onto a physical parameter based tensor product space H^{phy} are defined and the relations between these two spaces and...

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This work is limited to k-ary representations of length L and to the axioms for arithmetic modulo k^{L}. A model of the axioms is de...

This is an introductory review on the basic principles of quantum computation. Various important quantum logic gates and algorithms based on them are introduced. Quantum teleportation and decoherence are discussed briefly. Some problems, without solutions, are included.