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arXiv:1812.00062 · Notices of the American Mathematical Society

The Mathematics of Quantum-Enabled Applications on the D-Wave Quantum Computer

Jesse Berwald

Published Jun 1, 2019• 13 citations
arXivHTMLPDF

Abstract

Richard Feynman is credited with the initial ideas for computing with quantum mechanics, presented in a seminal talk and subsequent paper from 1982, titled "Simulating Physics with Computers" [8].Sig-
DOI
10.1090/noti1893

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There were few basic aspects of computers and computation which intrigued Richard P. Feynman, and made the subject sufficiently interesting that he would spend time teaching it. Feynman himself did the lecture on quantum computation. Charles Bennett has already prepared the way by talking about reversible computation, and Norman Margolus on the billiard ball computer, so Feynman developed quantum computation in ways which made its connection to classical reversible computers obvious. His lecture was chiefly developing the idea that an entirely reversible quantum system, without damping processes, could perform universal computation. The insight that quantum computers were really different came only later, and to others, not to Feynman. Feynman only emphasized that the physical scale and speed of computers were not limited by the classical world, since conceptually they could be built of reversible components at the atomic level.
Richard P. Feynman, a Nobel Prize winner in physics, was a physicist thought leader in the areas of quantum mechanics and quantum electrodynamics. In 1982, he published a research paper with the title “Simulating Physics with Computers”. In this paper, he asks the question if a quantum computer could be built (which he believed to be the case) or if classical computers can simulate the probabilistic behavior of a true quantum system (which he answered with a clear no). This research paper sparked interest in the scientific research community, which started to seriously explore whether or not a quantum computer can actually be built.
The history of Quantum Computing and Quantum Cryptography starts with a friendship between Charles Bennett and Stephen Wiesner, two undergraduates at Brandeis University who toyed with ideas for sending information using quantum entanglement, and John Conway's Game of Life, which stimulated interest in cellular automata at MIT in the 1970s and started a generation of computer scientists wondering if the universe might be some massive computer running a simulation of reality. In 1974 MIT professor Ed Fredkin spent his yearlong sabbatical at Caltech, where he learned quantum physics from Richard Feynman while he taught Feynman about computer science. Returning to MIT, Fredkin's ideas developed into the philosophy of digital physics, which blossomed into the 1981 Conference on Physics and Computation at MIT. Feynman's keynote at the conference described how a computer based on quantum mechanics principles could compute physics simulations much faster than today's classical compu
Quantum physics joined the mainstream in the 1920s and 1930s with the general acceptance of the theories of Max Planck, Albert Einstein, Niels Bohr (1885-1962), Erwin Schrödinger (1887-1961), Werner Heisenberg (1901-1976), Paul Dirac (1902-1984), and many other established physicists. Quantum computing is based on quantum physics, with all of its special behaviors and unusual limits. Therefore, quantum computing deals with the behaviors of atomic and subatomic particles. These behaviors are irreducibly random and the measurement of particle characteristics simultaneously, such as position and momentum, to an arbitrary precision is impossible. That is, physical phenomena of small particles do not agree often with our classical intuition. The unusual behavior results from features of quantum mechanics called superposition and interference. In the early 1980s, Richard Feynman (1918-1988) noted that there seemed to be fundamental difficulties in simulating quantum mechanical systems on digital computers, and further suggested that having computers based on the principles of quantum mechanics would overcome those difficulties. Devices that perform quantum information processing are known as quantum computers.
The last lecture course that Nobel Prize winner Richard Feynman gave to students at Caltech was not on physics but on computer science. The course in 1983 was an overview of standard and not-so-standard topics in computer science, all given in Feynman’s inimitable style. This talk will begin by giving an overview of Feynman’s long-time interest in computing - starting with his time at Los Alamos during the war through to his suggestion of simulating physics on a quantum computer at a ‘Physics of Computation Conference at MIT in 1981 and his acting as a consultant for the parallel computer company, Thinking Machines. The talk will conclude with a summary of Feynman’s long-term interest in the physical limits to computation and the exemplary way he could communicate complex ideas to all types of audience.
Hamiltonian simulation is the problem for which quantum computers were initially proposed by Richard Feynman [75], and it is a crucial problem for applications in physics: it corresponds to the simulation of the evolution of a quantum mechanical system over time. Although this book aims to be physics-free, it is useful to give at least the mathematical foundations of this problem, because Hamiltonian simulation is a central component of many quantum algorithms. We do not discuss the precise physical meaning of these concepts, and aim to provide just enough vocabulary to read the quantum computing literature without too much confusion.