Quantum Computer

          Behold your computer.  Your computer represents the culmination of years of technological advancements beginning with the early ideas of Charles Babbage (1791-1871) and eventual creation of the first computer by German engineer Konrad Zuse in 1941.  Surprisingly however, the high speed modern computer sitting in front of you is fundamentally no different from its gargantuan 30 ton ancestors, which were equipped with some 18000 vacuum tubes and 500 miles of wiring!  Although computers have become more compact and considerably faster in performing their task, the task remains the same: to manipulate and interpret an encoding of binary bits into a useful computational result.  A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer.  Each classical bit is physically realized through a macroscopic physical system, such as the magnetization on a hard disk or the charge on a capacitor.  A document, for example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones.  Herein lays a key difference between your classical computer and a quantum computer.  Where a classical computer obeys the well understood laws of classical physics, a quantum computer is a device that harnesses physical phenomenon unique to quantum mechanics (especially quantum interference) to realize a fundamentally new mode of information processing.

        In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature.  This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics which differ radically from the laws of classical physics.  A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or superposition of these classical states.  In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state.  This may seem counterintuitive because everyday phenomenon is governed by classical physics, not quantum mechanics -- which takes over at the atomic level. 

The Potential and Power of Quantum Computing

         In a traditional computer, information is encoded in a series of bits, and these bits are manipulated via Boolean logic gates arranged in succession to produce an end result.  Similarly, a quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits.  In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state.  The qubits can then be measured, with this measurement serving as the final computational result.  This similarity in calculation between a classical and quantum computer affords that in theory, a classical computer can accurately simulate a quantum computer.  In other words, a classical computer would be able to do anything a quantum computer can.  So why bother with quantum computers?  Although a classical computer can theoretically simulate a quantum computer, it is incredibly inefficient, so much so that a classical computer is effectively incapable of performing many tasks that a quantum computer could perform with ease.  The simulation of a quantum computer on a classical one is a computationally hard problem because the correlations among quantum bits are qualitatively different from correlations among classical bits, as first explained by John Bell. 

          Richard Feynman was among the first to recognize the potential in quantum superposition for solving such problems much faster.  For example, a system of 500 qubits, which is impossible to simulate classically, represents a quantum superposition of as many as 2⁵⁰⁰ states.  Each state would be classically equivalent to a single list of 500 1's and 0's.  Any quantum operation on that system --a particular pulse of radio waves, for instance, whose action might be to execute a controlled-NOT operation on the 100th and 101st qubits-- would simultaneously operate on all 2⁵⁰⁰ states.  Hence with one fell swoop, one tick of the computer clock, a quantum operation could compute not just on one machine state, as serial computers do, but on 2⁵⁰⁰ machine states at once!  The reason this is an exciting result is because this answer, derived from the massive quantum parallelism achieved through superposition, is the equivalent of performing the same operation on a classical super computer with ~10¹⁵⁰ separate processors (which is of course impossible)!!  

        Early investigators in this field were naturally excited by the potential of such immense computing power, and soon after realizing its potential, the hunt was on to find something interesting for a quantum computer to do.  Peter Shor, a research and computer scientist at AT&T's Bell Laboratories in New Jersey provided such an application by devising the first quantum computer algorithm.  Shor's algorithm harnesses the power of quantum superposition to rapidly factor very large numbers (on the order ~10²⁰⁰ digits and greater) in a matter of seconds.  The premier application of a quantum computer capable of implementing this algorithm lies in the field of encryption, where one common (and best) encryption code, known as RSA, relies heavily on the difficulty of factoring very large composite numbers into their primes.  A computer which can do this easily is naturally of great interest to numerous government agencies that use RSA -- previously considered to be "uncrackable" -- and anyone interested in electronic and financial privacy. 

         Encryption, however, is only one application of a quantum computer.  In addition, Shor has put together a toolbox of mathematical operations that can only be performed on a quantum computer, many of which he used in his factorization algorithm.  Furthermore, Feynman asserted that a quantum computer could function as a kind of simulator for quantum physics, potentially opening the doors to many discoveries in the field.  Currently the power and capability of a quantum computer is primarily theoretical speculation; the advent of the first fully functional quantum computer will undoubtedly bring many new and exciting applications.  

Obstacles and Research

        The field of quantum information processing has made numerous promising advancements since its conception, including the building of two- and three-qubit quantum computers capable of some simple arithmetic and data sorting.  However, a few potentially large obstacles still remain that prevent us from "just building one," or more precisely, building a quantum computer that can rival today's modern digital computer.   Among these difficulties, error correction, decoherence, and hardware architecture are probably the most formidable.  Error correction is rather self explanatory, but what errors need correction?  The answer is primarily those errors that arise as a direct result of decoherence, or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts, or entangles, with the state of the environment.  These interactions between the environment and qubits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus errors in computation.  Before any quantum computer will be capable of solving hard problems, research must devise a way to maintain decoherence and other potential sources of error at an acceptable level.  Thanks to the theory (and now reality) of quantum error correction, first proposed in 1995 and continually developed since, small scale quantum computers have been built and the prospects of large quantum computers are looking up.  Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system.  In 1998, researches at Los Alamos National Laboratory and MIT led by Raymond Laflamme managed to spread a single bit of quantum information (qubit) across three nuclear spins in each molecule of a liquid solution of aniline or trichloroethylene molecules.  They accomplished this using the techniques of nuclear magnetic resonance (NMR).  This experiment is significant because spreading out the information actually made it harder to corrupt.  Quantum mechanics tells us that directly measuring the state of a qubit invariably destroys the superposition of states in which it exists, forcing it to become either a 0 or 1.  The technique of spreading out the information allows researchers to utilize the property of entanglement to study the interactions between states as an indirect method for analyzing the quantum information.  Rather than a direct measurement, the group compared the spins to see if any new differences arose between them without learning the information itself.  This technique gave them the ability to detect and fix errors in a qubit's phase coherence, and thus maintain a higher level of coherence in the quantum system. 

Future Outlook

( This article is written by Muhammad Moeen, Electrical Engineer from University of Engineering and technology.)