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Progress of Theoretical Physics Supplement

Physical Models for Quantum Computers

Hans A. De Raedt, Kristel F. L. Michielsen, Seiji Miyashita, Keiji Saito

Published Jan 1, 2002• 4 citations
Publisher

Abstract

We discuss the impact of the physical implementation of a quantum computer on its computational efficiency, using computer simulations of physical models of quantum computer hardware. We address the computational efficiency of practical procedures to extract the results of a quantum computation from the wave function respresenting the final state of the quantum computer.

DOI
10.1143/ptps.145.233

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We discuss the impact of the physical implementation of a quantum computer on its computational efficiency, using computer simulations of physical models of quantum computer hardware. We address the computational efficiency of practical procedures to extract the results of a quantum computation from the wave function respresenting the final state of the quantum computer.
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We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum computation are unstable with respect to the physical realization of the quantum computer. We discuss the origin of these instabilities and discuss possibilities to overcome this, for practical purposes, fundamental limitation of quantum computers.
Quantum computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive nature of current QC hardware leaves practical testing limited to trivial examples. Thus, a robust simulator is needed to study complex QC issues. Most QC simulators model ideal operations, and thus cannot predict the actual time required to execute an algorithm or quantify the effects of errors in the calculation. We have developed a novel QC simulator that models physical hardware implementations. This simulator not only allows the accurate simulation of quantum algorithms on various hardware implementations, but also takes an important step towards providing a framework to determine their true performance and vulnerability to errors.
With the increasing accessibility of quantum computers to the wider population, there is a growing demand for the education and training of a group of quantum programmers. This cohort predominantly consists of individuals who have primarily focused on the development of classical computer programs throughout their professional careers. Although existing quantum computers currently possess fewer than 100 qubits, it is widely anticipated that the quantum computing hardware will experience significant advancements in terms of qubit quantity, quality, and connectivity. The objective of this review is to elucidate the fundamental principles of quantum programming, which diverge significantly from classical programming. This will be achieved through the utilization of concise algebraic expressions, allowing for an optional comprehension of the captivating underlying principles of quantum mechanics. This paper provides an overview of quantum computing algorithms and their practical implementation on physical quantum hardware. In this study, we undertake a comprehensive examination of various quantum algorithms, with the objective of providing concise and self-contained descriptions for each. In this study, we demonstrate the practical implementation of the aforementioned algorithms on IBM's quantum computer. For each algorithm, we thoroughly analyze and compare the outcomes obtained from the implementation on the quantum computer with those obtained from the simulator. This analysis focuses on identifying and discussing any disparities that arise between the results obtained from the simulator and the actual hardware runs. This article serves as an introduction to quantum algorithms for computer scientists, physicists, and engineers, offering a comprehensive guide for their practical implementation.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.