TRENDS & CONTROVERSIES A quantum leap for AI By Haym Hirsh Rutgers University [email protected] November 1994 saw the near-simultaneous publication of two papers that threw the notion of computing on its head. On November 11, 1994, a paper by Leonard Adleman appeared in Science demonstrating that a vial of DNA fragments can serve as a computer for solving instances of the Hamiltonian path problem. Less than two weeks later, Peter Shor Quantum computing and AI presented a paper in Santa Fe, New Mexico, at the 35th Annual Symposium on Foundations Subhash Kak, Louisiana State University of Computer Science, demonstrating how a quantum computer could be used to factor large Every few years, we hear of a new tech- numbers in a tractable fashion. Both these publications showed how nontraditional models nology that will revolutionize AI. After of computation had the potential to effectively solve problems previously believed to be careful reflection, we find that the advance intractable under traditional models of computation. However, the latter work, using a quan- is within the framework of the Turing tum model of computation proposed by Richard Feynmann and others in the early 1980s, machine model and equivalent, in many resonated well with AI researchers who had been coming to terms with Roger Penrose’s cases, to existing statistical techniques. But 1989 book The Emperor’s New Mind. In this book (and its sequel, Shadows of the Mind: A this time, in quantum computing, we seem Search for the Missing Science of Consciousness, which appeared in paperback form only a to be on the threshold of a real revolution— month before these papers), Penrose challenges the possibility of achieving AI via traditional a “quantum” leap—because it is a true “Turing-equivalent” computation devices, conjecturing that the roots of intelligence can be frontier beyond classical computing. But traced to macroscopic quantum effects in the brain. These two quantum strands form the will these possibilities be realized any time motivation for a small community of researchers exploring the topic of this issue’s “Trends soon? and Controversies” feature—the potential uses of quantum computing for AI. Classical computers work on classical Subhash Kak’s leadoff essay provides an excellent overview of the foundations of this area, logic and can be viewed as an embodiment explaining, for example, how a quantum computer makes it possible to manipulate an expo- of classical physics. Quantum computers, nential number of states in a search problem in a single clock step. He also discusses the philo- on the other hand, are based on the super- sophical motivations that have led people to explore the use of quantum computing in AI. positional logic of quantum mechanics, To the many with the widely held belief that tractable search is a core question in achieving which is an entirely different paradigm. AI, Tad Hogg’s essay explains how quantum computing can potentially form the basis for Conventional explanation sees conscious- tractable search on what have previously been considered intractable problems. One difficulty is ness arising as an emergent property of the that the “common” quantum computing approach of amplitude amplification can yield at most a classical computations taking place in the square-root improvement in an algorithm’s runtime. Hogg proposes mapping techniques com- circuits of the brain, but this does not ad- monly used in AI to the quantum computing world, specifically by using heuristics that embody dress the question of how thoughts and knowledge about the structure of a problem (such as the number of conjuncts satisfied by a truth feelings arise. If brains perform quantum assignment for a given satisfiability problem) within the search process. processing, this might be the secret behind Finally, Dan Ventura looks at the mutual benefits received by advances in the use of quan- consciousness. Furthermore, it might ex- tum computing for AI, for both AI researchers as well as those studying quantum computa- plain several puzzling features of animal tion. Attempting to apply quantum computing to AI problems might provide the right fodder and human intelligence and provide a new for researchers in quantum computing. Similarly, the use of quantum computing might direction to develop AI machines. In this enable new advances previously thought impossible within the AI community. Ventura also brief survey, I present the rationale for the discusses some of the difficulties that may lie ahead for those hoping to achieve AI through convergence between quantum computing quantum computing. Particularly important—as anyone who has attempted interdisciplinary and AI and discuss prospects for realizing research knows—is the (understandable) gap in motivations, background, and vocabularies the technology. of those working in these two fields. We are still quite far from having quantum computers sitting on our desktops running The weirdness of quantum Unix or Windows. However, as advances in quantum computing continue to be made, it is mechanics nice to know that researchers such as the authors in this issue’s “Trends and Controversies” Let me begin with the quantum frame- might already be coming to an understanding of how to effectively use the results of these work. It is a theory that provides a means advances. Indeed, their work might itself become responsible for these important advances of obtaining information about a system in in quantum computing as well. the microworld associated with various As a final note, this issue marks the passing of the cartoonist’s pen from Kevin Knight, attributes (component states). A quantum who has diligently served in this role for the last four years, to Sally Lee, who is responsible state is a linear superposition of its compo- for the cartoon appearing in this installment. Although we are sorry to see Kevin’s retirement nent states. Suppose the two component from this post, we are happy to have such an able successor. Thank you both Kevin and Sally. states are represented by |0> and |1>, which —Haym Hirsh could be the two spin states of an elemen- tary particle (up or down), or polarization JULY/AUGUST 1999 9 states of a photon (horizontal or nologies, such as NMR, trapped vertical), and so on. Then, the ions, quantum dots, and cavity general form of the superposi- quantum electrodynamics. Cur- tion state, |S>, will be rent problems with quantum computer technology include |S> = a |0> + b |1>. initialization, decoherence, and error correction. The weights, a and b,are The problem of initialization called probability amplitudes arises from a fundamental and are, in general, complex uncertainty in the phase of the numbers, subject to the condi- state. This uncertainty can ren- tion that |a|2 + |b|2 = 1. The mod der the techniques for strength- squares of the probability ampli- ening of the desired state use- tudes, |a|2 and |b|2, are the proba- less. Decoherence is the bilities of obtaining either of the inability to completely shield two component states upon the quantum system from observation. unpredictable interaction with The fact that the amplitudes are the environment, causing the Schrödinger’s computer. —Sally O. Lee complex numbers implies that a state function to lose its super- quantum system cannot be effec- position; decoherence times range tively simulated by the Monte Carlo method trix. The algorithm designer must first find from a fraction of a second to a few hun- using random numbers. You cannot run a the unitary matrix for the given computing dred seconds. Techniques for error correc- physical process if its probability amplitude problem and then map the matrix into a tion of quantum bits have been proposed, is negative or complex! sequential product of smaller matrix opera- but these work under very artificial and Apart from this, the counterintuitive tions that can be implemented relatively unrealistic assumptions.3 nature of quantum mechanics arises from easily. The fact that a quantum computa- the fact that, upon interaction with a mea- tion is nothing more than matrix multipli- Quantum computing at the basis of surement apparatus, the linear superposition cation of a certain kind should give comfort biological information processing quantum state reduces to one of its compo- to computer scientists—in operational The case that quantum computing is at nent states with the appropriate probability. terms, it is not weird at all! the basis of biological information process- This aspect of quantum mechanics renders A quantum computer exploits the inher- ing and, consequently, the explanation for the framework nonlinear—and irreversible ent parallelism that is provided by the the power of animal intelligence, relies on if the time variable is changed in sign. superposition of the quantum state. A quan- the following elements: For decades, philosophers of science have tum register with n binary cells is able to agonized over the many bizarre implications store 2n sequences simultaneously, in con- • Philosophical. The argument is that, at of quantum mechanics, such as that an or- trast to a classical register, which can store the deepest level of description nature, is ganism can be both dead and alive before it only 1 of the 2n sequences at a time. By its quantum-mechanical. The world of is observed (Schrödinger’s cat paradox), the ability to simultaneously process very mathematics, as a product of the human present can influence the past (Wheeler’s many problems, the quantum computer mind, sits on