AU J.T. 13(3): 151-157 (Jan. 2010)

Quantum Computing David Tin Win Faculty of Science and Technology, Assumption University Bangkok, Thailand E-mail:

Abstract

A description of the general principles of is followed by a discussion of different quantum concepts, advantages, applications and documentation describing the leading scientists and institutions at the forefront in exploiting the laws of quantum governing subatomic particles for building a faster and more efficient computer. Keywords: Superposition, quantum physics, subatomic particles, qubit, quantum dot, spintronic transistor, chemical computer.

switches involve structural changes. When Introduction changing states, large molecular chunks move relative to each other. However a flat molecule Electronics are shrinking. This creates (eg. naphthalocyanine) can change states challenges on the limits of the ability to craft without undergoing any structural changes. increasingly tiny features. These features Structurally identical molecules with different etched with extremely high-energy laser light conformation are called tautomers. The process are processor components. Disk drives store is called tautomerization. The memory states information in ever-smaller clusters of atoms. can be changed and read through the same Major inhibitions are electrical, magnetic, and technique used in electronics today: changes in quantum interferences that set limits to how electrical conduction (Timmer 2007). many transistors can fit into a given finite A team of European researchers were volume. According to Moore's Law, the density able to induce the hydrogens in of integrated chips should double every six naphthalocyanine (shown in Fig. 1) to swap months (Gershenfeld and Chuang 1998). It will locations: single-molecule storage. A tunneling become ever more difficult to maintain and microscope pushed several naphthalocyanine detect signals such as the state of a memory bit. molecules close enough to form linked orbitals. To circumvent these, scientists are exploring the possibility of molecular memory or information storage in chemical structures of single molecules. The origins of quantum computing are not too far back. It was first theorized less than 30 years ago, by a physicist at the Argonne National Laboratory. Paul Benioff was the first to apply quantum theory to computers in 1981. He theorized about creating a . Most digital computers are based on the Turing Theory (Bonsor and Strickland 2009). Fig. 1. Naphthalocyanine, a flat molecule. It Molecular memory requires chemicals can change states without any structural that can oscillate between two stable states, just changes – tautomerism (Timmer 2007). like atom clusters switching magnetic states on disk drive surfaces. Most of these molecular

Review Article 151 AU J.T. 13(3): 151-157 (Jan. 2010)

Different members of the structure can be frequencies forming harmonics. Generally a selectively switched, depending on the position quantum computer with n qubits can where current is injected in the rings. It was simultaneously be in up to 2n different states. suggested that similar arrangements can be For example a pair of qubits can be in a employed for coordinated switching of atomic quantum superposition of 4 states. Three qubits bits and enabling the state of one bit to can exist in a superposition of 8. This is in influence the response of its neighbors contrast to a normal computer that can only be (Timmer 2007). in one of 2n states at any given time. On Some scientists are now exploring operation a quantum computer manipulates quantum computing, using a computation those qubits with a fixed sequence of quantum device where direct use of quantum mechanical logic gates. The sequence of gates used is a phenomena (superposition and entanglement) quantum algorithm (West 2000). is made to perform data operations. The The state of a classical computer fundamental principle is that data can be operating on a three-bit register has a represented by quantum properties that can be probability distribution over the 23 = 8 different used to perform operations on these data. three-bit strings 000, 001, ..., 111 at any time. Quantum computers are different from other Thus it is described by eight nonnegative computers such as DNA computers (uses numbers (a, b, c, d, e, f, g, h), which add up to DNA, biochemistry and molecular biology) one. and traditional computers based on transistors Similarly the state of a three-qubit (Wikipedia 2009). An interesting development quantum computer is described by an eight- is the chemical computer. Also called reaction- dimensional vector (a, b, c, d, e, f, g, h) – a diffusion computer or BZ (Belusov- wave function. But the constraint here is that Zhabotinsky) computer, it is an unconventional the sum of the squares of the coefficient computer based on a semi-solid chemical magnitudes, | a |2 + | b |2 + ... + | h |2, must equal mixture. The data is represented by varying one. In addition, the coefficients being complex chemical concentrations. The computations are numbers can be negative as well as positive. performed by naturally occurring chemical This allows for cancellation, or interference, reactions. It is in a very early experimental between different computational paths. This is stage (Wikipedia 2009). a key difference between probabilistic classical computing and quantum computing (Wikipedia 2009). Quantum Computers It is easily seen that there are many different possible ways of specifying an eight- Quantum computing is an effort to dimensional vector, depending on the basis harness the bizarre laws that operate in the sub- chosen for the space. The basis of three-bit atomic world into practical devices that would strings 000, 001, ..., 111 is known as the revolutionize the speed at which information is computational basis. Other bases like unit- shared and processed. Scientists say they have length and orthogonal vectors can also be used. taken a big step forward towards the Ket notation is used to show explicit basis development of quantum computing, a process choice. they believe could form the basis of a new form For example, the state (a, b, c, d, e, f, g, of internet that would work at the speed of light h) in the computational basis can be written as (ABC 2009). Bits are memory components of classical a⏐000〉 + b⏐001〉 + c⏐010〉 + d⏐011〉 + computers. Each bit holds either a one or a e⏐100〉 + f⏐101〉 + g⏐110〉 + h⏐111〉, zero. The corresponding memory components where ⏐010〉 = (0,0,1,0,0,0,0,0), etc… The in a quantum computer are qubits. The memory computational basis for a single qubit in two has a sequence of qubits. A single qubit can dimensions is ⏐0〉 = (1,0), ⏐1〉 = (0,1), but hold a one, a zero, or a quantum superposition another common basis is the Hadamard basis of these two, just like music notes of different of ⏐+〉 = (1/√2, 1/√2) and ⏐–〉 = (1/√2, -1/√2).

Review Article 152 AU J.T. 13(3): 151-157 (Jan. 2010)

Any system with an observable quantity decoherence. This effect is irreversible and A, conserved under time evolution and has at should be avoided, or highly controlled. least two discrete and sufficiently spaced consecutive eigenvalues may be used for implementing a qubit (Carey 2002). This is Candidates because such systems can be mapped onto an effective spin-1/2 system. One of the key The following are some candidates for principles that support the concept is that quantum computing: allows atomic particles to exist in two states simultaneously. Thus the • Superconductor-based quantum quantum mechanical states of an atom may be computers (including SQUID-based used to represent information and make quantum computers); quantum computers very much more useful for • Trapped ion quantum computer; complex calculations than conventional • Optical lattices; one/zero or on/off computer bits (Barenco • Topological quantum computer; 1996). Another mind-bending aspect is that the • Universal quantum automaton; quantum state atoms can be linked to other • Quantum dot on surface (e.g., the Loss- atoms, regardless of how far apart they are. DiVicenzo quantum computer); Changing one changes the other automatically. • NMR on molecules in solution (liquid Recently (January 23, 2009) scientists reported NMR); the instantaneous teleportation of information • Solid state NMR Kane quantum between two unconnected atoms that are one computers; metre apart (ABC 2009). • Electrons on helium quantum computers; A simple example of qubits for a • Cavity quantum electrodynamics quantum computer is the use of particles with (CQED); two spin states. The spin of an electron can be • Molecular magnet; in one of two spin states characterized by spin • Fullerene-based ESR quantum computer; quantum numbers: (+1/2) and (-1/2) in units of • Optic-based quantum computers ħ (= h/2π; where h is Planck’s constant). (Quantum optics); Alternatively, these are "up" and "down" spins; • Diamond-based quantum computer; or clockwise and anticlockwise spins written in • BEC-based quantum computer; • Transistor-based quantum computer - the ket notation as ⏐↑〉 and ⏐↓〉, or ⏐0〉 and ⏐1〉. string quantum computers with

entrainment of positive holes using a Quantum Decoherence electrostatic trap; • Spin-based quantum computer; Quantum decoherence is the mechanism • Adiabatic quantum computation; involved in the interaction of quantum systems • Rare-earth-metal-ion-doped inorganic with their environments, with consequent crystal based quantum computers. exhibition of probabilistic additive behavior. It gives the appearance of wave function This large list of possible candidates shows that collapse. It prevents system and environment the topic is still in its early stages. wave function’s different elements in the quantum superposition from interfering with Quantum Computing in each other. Removing or controlling decoherence is Computational Complexity Theory one of the greatest challenges. Generally this means isolating the system from its Current mathematically known factors environment. Otherwise any slight interaction about the power of quantum computers are with the external world would cause system surveyed here. Known results from computational complexity theory and the

Review Article 153 AU J.T. 13(3): 151-157 (Jan. 2010) theory of computation dealing with quantum Current Research computers are mentioned. “Bounded error, quantum, polynomial There are many institutions that are time” BQP is defined as the class of problems involved in the field of quantum computing, that can be efficiently solved by quantum both private and government. In the last decade computers. Quantum computers only run interest in quantum computing has probabilistic algorithms, so BQP on quantum mushroomed. The first big breakthrough in computers is the counterpart of BPP on constructing a computer that behaved classical computers. BQP is the set of problems according to the laws of quantum physics arose solvable with a polynomial-time algorithm. in the early 1980's when , The error probability is bounded away from California Institute of Technology, Nobel Prize one quarter. A quantum computer "solves” a winner, reasoned that the only way a system problem if its answer is right with high could exist which allowed particles to spin probability every time. If the solution is in clockwise and counterclockwise polynomial time, then BQP contains the simultaneously was to have a computer that problem. behaved the same way. This early idea of BQP is in the complexity class #P (or symmetry between a quantum mechanical more precisely in the associated class of system and a computer led to the next big #P decision problems P ), which is a subclass of breakthrough in 1994 by a scientist named PSPACE (see Fig. 2). Peter Shor at Bell Laboratories in New Jersey. BQP is believed to be disjoint from NP- He presented the first algorithm demonstrating complete and a strict superset of P. Both theoretically how a quantum computer could integer factorization and discrete log are in quickly reverse-factor large numbers. This BQP. Both of these are NP problems believed interested the United States Federal to be outside BPP, and are therefore outside P. Government because the codes that protect Quantum computers are faster than military and financial secrets are based on the classical computers; however those listed inability to do such reverse factoring. above are unable to solve any problems that classical computers cannot solve. A timeline of computer computing is shown in Wikipedia MIT and Los Alamos National (Wikipedia 2009). Laboratory (Gershenfeld and Chuang 1998)

In March 1997, quantum computing was brought one step closer when addition of two numbers was performed by using Nuclear Magnetic Resonance to flip the nuclear spins of the organic molecule, alanine – an alpha amino acid. The atoms were then embedded within a large molecule and used the direction of their spins to represent data. In detail, the core of the experiment was a tiny amount alanine or actually the trillions of atoms within. This was possible because in this sample of atoms, most are found pointing in any random direction. However a very small percentage was found pointing in a specific direction. The spins of the randomly pointing atoms Fig. 2. The suspected relationship of BQP to cancel each other. This allows an NMR other problem spaces (Wikipedia 2009). machine to recognize the small percentage of atoms that are pointed in the same direction.

Review Article 154 AU J.T. 13(3): 151-157 (Jan. 2010)

These atoms that are found in plurality spins of the embedded atoms' nuclei. The spins constitute one quantum bit, or qubit. could be flipped by radio signals, and the The alanine molecule yields three qubits neighboring atom interactions could be because it has 3 atoms of carbon that each followed by an electrode. This would enable correspond to a different NMR frequency, and linked qubits to perform operations. Such a the atoms are also linked in a manner that they design could supposedly contain thousands of could be used for addition. The scientists used qubits that would be manipulated by existing two of the carbon atoms to accomplish the electronics. addition of one and one. In this experiment, the Stoneham (Hogan 2003) proposed to hardware was the atoms, and the software was manipulate electron spins rather than nuclear the radio pulse used to manipulate the atoms. spins. Embedded atoms are to be randomly “Each pulse made one atom in the pair (the distributed within the silicon and laser light is “target”) shift the orientation of its spin, in a to be employed to manipulate electron spin. way that depended on both the duration of the Qubits would be connected with "control pulse (say one-hundredth of a second for a atoms" that can be excited by specific laser- quarter turn) and on the orientation of the light frequencies, just like the qubit electrons partner atom, the “control”. When the program (Hogan 2003). was finished, the final spin state of the atoms, gave the answer- two, in this case” (Hogan 2003). The ability to apply this concept to The Institute for Microstructural sorting, picking a telephone number from a list Science in Ottawa, Canada of four other numbers was mentioned (Hogan (Burkard 2000) 2003). Researchers built a spintronic transistor that plays a major role in the quest for quantum University College London computing. Although simple spintronic devices (Hogan 2003) such as diodes have already been created, the transistor is the first to use electron spin to Making quantum computers practical is control current that passes between gates. The the goal of University College London transistor made from a “quantum dot", a tiny materials scientist Marshall Stoneham. He semiconductor, acts as a gateway that controls received ₤3.7 million to produce a quantum electrons by blocking them or letting them device that calculates efficiently, functions at pass. This allows the storage of information higher temperatures than competing machines, that also can be read and erased by and can be assembled with existing equipment. manipulating spin inside the dot (Burkard Current quantum computers can store and 2000). manipulate quantum bits (qubits) either by exploiting an ion's energy state or using the spins of atomic nuclei to represent 0 or 1. University of Michigan However, ion manipulation approach on a (Steeh 2003) quantum computer requires it to be extremely large; a nuclear-spin-based device requires An important milestone on the way to magnets cooled by liquid helium. The latter creating viable quantum computers, laser- cannot handle qubit increases past a certain cooling of individual atoms, have been point as the noise from neighboring molecules demonstrated. Christopher Monroe (Steeh can mask the resulting signal. 2003) stated that quantum computers using A design for a silicon-based quantum individual atoms for information storage computer was proposed by an Australian require special conditions, such as keeping the researcher Bruce Kane (Hogan 2003), who atoms cool and electronic suspension in a theorized that phosphorus-impregnated silicon vacuum. The experiment conducted at the could yield a device that stores qubits in the Michigan University used electronic fields to

Review Article 155 AU J.T. 13(3): 151-157 (Jan. 2010) confine a crystal of two atoms (each a different (Lerner 2001). One interesting progress in this isotope of the same element). The quantum direction is the IBM BlueGene project (Win computing atom was cooled to almost absolute 2007). Apart from these, answers to many zero through direct laser cooling of its questions in many areas of physics, , neighboring atom. This process removes and most other areas of science, unwanted motion in the atom crystal without would become available. affecting the internal state of the other atom; an important step in scaling a trapped atom computer with information qubits stored in the Limitations quantum states of individual atoms. Based on the cooling experiments, Can practical quantum computers of Monroe and two colleagues, David Kielpinski useful size be actually built in our universe? of MIT and David Wineland of the National Are the theoretical constructs, the physics of Institute of Standards and Technology (Steeh quantum mechanics and our concept of the 2003) proposed a quantum computer algorithms that run them entirely correct? architecture model. They described a “quantum These are nagging questions. There is no charged-coupled device” (QCCD) composed of agreement yet about the best way to build a many paired atoms connected through quantum computer. For example Chuang and electrical charges of invisible “springs” and is Gershenfeld experiments at MIT used atoms or scalable to large numbers of qubits (Steeh charged ions in an electromagnetic trap. But 2003). IBM tested superconducting materials that can generate quantum bits. For quantum computers to live up to the Applications expectations, a quantum computer capable of 100,000 calculating atoms would be required. The applications for quantum computing The ultimate limitation with quantum are endless. Computer systems that are capable computing is making it practical. Creating the of simultaneously processing billions of data conditions for Nuclear Magnetic Resonance, bits would revolutionize every area of science employing laser light or the need for magnets and mathematics. It would be possible to parse cooled by liquid helium to control electron in minimal time, enormous amounts of spin, are still limiting factors. information organized in databases. Boeing has interest in preventing eavesdropping or jamming of aircraft electronic signals by using Conclusion quantum computers. Another area is super accurate calibration in time keeping and Quantum computing has the future satellite positioning. potential to reinvent not only computers, but As with any radically new technology, most fields of science. At the moment it is governments are strongly interested in terms of thought of as a “scary science,” because it national security. A computer with this represents things that are not fully understood processing power level could reverse factor any yet and could open doors of scientific level of modern encryption in real time, as well understanding that is unprecedented. as create levels of encryption unfactorable by Scientists are now able to perform current computing systems. mathematical computations through controlling Biochemists are interested in high the spin states of an electron within an atom or performance computing to simulate protein molecule. By information actually being stored folding after generation in cells. It would then at a subatomic level, quantum computing will be possible to change the individual amino achieve unprecedented speed in processing acids in the protein and also alter its shape, power, capable of processing billions of bits of consequently modifying how the protein acts. information at once. This would be vital in developing new drugs

Review Article 156 AU J.T. 13(3): 151-157 (Jan. 2010)

When the ultimate limitation of making it Gershenfeld, N.; and Chuang, I. 1998. practical is overcome, quantum computing will Quantum computing with molecules. MIT. reinvent entire fields: including , Available: engineering, weather, space flight and http://www.media.mit.edu/physics/publicati mathematics. ons/papers/98.06.sciam/0698gers Will a quantum hyper-computer take henfeld.html. over the world? Will it simulate a human Hogan, J. 2003. Computing: Quantum bits and being? Is there a possibility of it becoming a silicon chips. Nature 424(6948): 484-6. power-hungry despot that can enslave the Lerner, E.J. 2001. Cellular architecture builds whole world. Who knows? next generation supercomputers. IBM Think Research. Available: http://www.researchweb.watson.ibm.com/20 References 010611_cellular.shtml. Steeh, J. 2003. Michigan researchers achieve ABC. 2009. US scientists move toward speed- quantum entanglement of three electrons. of-light Internet. Australian Broadcasting Univ. Michigan, Ann Arbor, MI, USA. Corporation (ABC). Available: Available: http://www.abc.net.au/news/stories/2009/01/ http://www.eurekalert.org/pub_releases/2003- 23/2473402.htm. 02/uom-mra022603.php. Barenco, A. 1996. A short introduction to Timmer, J. 2007. Shifting atoms in single quantum computation. CQC introductions: molecules memory. Available: Quantum computing. Available: http://www.arstechnica.com/news.ars/post/200 http://www.qubit.org/library/intros/comp/co 70902 –shifting-atoms-in-single-molecule- mp.html. memory.html. Bonsor, K.; and Strickland, J. 2009. How West, J. 2000. The quantum computer - An quantum computers work. Available: introduction. Available: http://www.computer.howstuffworks.com/q http://www.cs.caltech.edu/~westside/quantu uantum-computer.htm. m-intro.html. Burkard, G. 2000. Spintronics and quantum Wikipedia 2009. Quantum computing. dots for quantum computing and quantum Available: communications. University of Basel, http://www.en.wikipedia.org/wiki/Quantum Switzerland. Available: _computing.htm. http://theorie5.physik.unibas.ch/qcomp/qco Win, D.T. 2007. The IBM BlueGene mp.html. (Supercomputer) project - Capability in Carey, D. 2002. Quantum computing FAQ. science applications (Molecular dynamics Available: and protein folding). AU J.T. 10(4): 237-47. http://www.rdrop.com/~cary/html/quantum_ c_faq.html.

Review Article 157