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ACM/IEEE Design Automation Conference (DAC)

Designing and implementing small quantum circuits and algorithms

B. C. Travaglione

Published Jun 2, 2003• 1 citation
Publisher

Abstract

It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.

DOI
10.1145/775832.776057

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It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.
It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques.This paper explores small scale quantum algorithms from two different perspectives. Firstly, it will be shown how small scale quantum algorithms can be tailored to fit current schemes for implementing a quantum computer. Secondly, I will review a simple model of computation, based on read-only-memory. This model allows the comparison of the space-efficiency of reversible error-free classical computation with reversible, error-free quantum computation. The quantum model has been shown to be more powerful than the classical model.
It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer, a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively simple quantum algorithms using current experimental techniques. The research work presented in this thesis consists of several theoretical studies exploring small scale quantum algorithms and methods of implementing them. Included in this thesis are an investigation of a small scale version of the phase estimation algorithm, methods of implementing the quantum random walk, a discussion of protecting quantum information by encoding it in an oscillator, and a look at the power of a quantum computer with a restricted number of qubits.
Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be "translated" to a series of simple steps, each of which the computer knows how to do. This task is relatively easy to do on a classical computer and we witness the benefits of this success in our everyday life. Quantum mechanics, the physical theory of the very small, promises to enable completely novel architectures of our machines, which will provide specific tasks with higher computing power. Translating and implementing algorithms on quantum computers is hard. However, we will show that solutions to this problem can be found and yield surprising applications to number theory.
A quantum computer is a device that processes information in a quantum-mechanically coherent fashion. In principle, it can exploit coherent quantum interference and entanglement to perform computations, such as factoring large numbers or searching an unsorted database, more rapidly than classical computers. Noise, decoherence, and manufacturing problems make constructing large scale quantum computers difficult. Ion traps and optical cavities offer promising experimental approaches, but no quantum algorithm has yet been implemented with those systems. On the other hand, because of their natural isolation from the environment, nuclear spins are particularly good 'quantum bits', and their use for quantum computation is possible by applying nuclear magnetic resonance (NMR) techniques in an unconventional manner. Here, we report on the experimental implementation of a quantum algorithm using NMR to solve a purely mathematical problem in fewer steps than is possible classically. Our simple quantum computer can determine the type of an unknown function using fewer function 'calls' than is possible using a classical computer.
Currently, computing paradigm is ruled by the laws of classical physics and will continue till the dimensions of transistors reaches the size of atomic particles. Quantum computing (QC) is a new technology that employs laws of quantum mechanics to address issues such as irreversibility and power dissipation that are outside the scope of conventional computing models. QC offers a powerful stage for solving complex and compound problems like searching and number factoring. A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Unitary decomposition is a popular scheme for mapping quantum algorithms to any set of elementary quantum operations. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates, which is critical for running algorithms on prevailing quantum computers. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. This paper is the first to present quantum implementations of FRSG1 and JTF1 gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM. These gates are important in a variety of practical applications like Stochastic computing and parity generation circuits. In FRSG1 the implementation count of single qubit gates decreases by 56% and the count of two qubit gates by 15% after optimization, whereas in JTF1 gate the single qubit gate count reduces by 71% and the number of two qubit gates reduces by 41%.