Quantum implementation of elementary arithmetic operations

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of classical and quantum computation. This paper investigates a possible approach to the problem of programming such machines: a template high level quantum language is presented which complements a generic general purpose classical language...

Quantum computing has the power to break current cryptographic systems, disrupting online banking, shopping, data storage and communications. Quantum computing also has the power to support stronger more resistant technologies. In this paper, we describe a digital cash scheme created by Dmitry Gavinsky, which utilises the capability of quantum computing. We contribute by setting out the methods for implementing this scheme. For both the creation and verification of quantum co...

This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any physical concepts or principles. It is intended as a primer for theoretical computer scientists who do not know--and perhaps do not care to know--any physics.

We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This algorithm is an application of the quantum algorithms for the hidden subgroup problems, the same as Shor factoring algorithm. Explicit quantum circuits realized by quantum gates for this quantum algorithm are provided. We also give a computer simul...

Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part of a broader research focused on providing operations of a higher abstraction level to manipulate integers codified as a superposition. These operations are designed to be composable and efficient, so quantum software developers can reuse th...

Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with only the Toffoli gate. Draper [D00] has proposed an inherently "quantum" network for addition based on the quantum Fourier transform. His approach has the advantage that it requires no carry qubits (the previous approaches required O(n) ca...

A attempt at a quantum algorithm for solving NP problems is presented. Now withdrawn because some crucial operators were not unitary.

We introduce an abstract machine architecture for classical/quantum computations---including compilation---along with a quantum instruction language called Quil for explicitly writing these computations. With this formalism, we discuss concrete implementations of the machine and non-trivial algorithms targeting them. The introduction of this machine dovetails with ongoing development of quantum computing technology, and makes possible portable descriptions of recent classical...

In this paper, two quantum networks for the addition operation are presented. One is the Modified Quantum Plain (MQP) adder, and the other is the Quantum Carry Look-Ahead (QCLA) adder. The MQP adder is obtained by modifying the Conventional Quantum Plain (CQP) adder. The QCLA adder is an extension of conventional digital Carry Look-Ahead adder. Compared with the CQP adder, two main advantages are as follows: First, the proposed MQP and QCLA adders have less number of elementa...

Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves the way for the development of hybrid algorithms directly from classical software, which is not feasible on today's hardware but might inspire future quantum programmers.