COMPUTERS TAKING A QUANTUM LEAP Quantum computers will harness the - - PDF document

COMPUTING

44 • MAY 2005 • ELECTRONICS FOR YOU W W W . E F Y M A G . C O M

T

hink of a computer whose memory is exponentially larger than its apparent physical size. Or a computer that can manipulate an exponential set of inputs simulta-

• neously. The quantum computer

would be one such computer. Rela- tively few and simple concepts from quantum mechanics are needed to make quantum computers a possibil- ity. Quantum computers open up a new era for high-speed computations. They will be 1,000,000,000 times faster than current silicon-based computers. Today’s high-speed computer sitting in front of you is fundamentally no different from its 30-tonne ancestors, which were equipped with some 18,000 vacuum tubes and 805 kilometres (500 miles) of wiring! Although computers have become more compact and considerably faster in performing their tasks, the task re- mains the same: manipulate and in- terpret an encoding of binary bits into a useful computational result. A bit is the fundamental unit of information, classically represented as a ‘0’ or ‘1’ in your digital computer. Each classical bit is physically realised through a macroscopic physi- cal system, such as the magnetisation

• n a hard disk or the charge on a ca-
• pacitor. A document, for example,

comprising ‘n’ characters stored on the hard drive of a typical computer is ac- cordingly described by a string of 8n 0’s and 1’s. Herein lies a key difference be- But can it continue forever? The basic processing unit in a com- puter chip is the transistor, which acts like a small switch. The binary digits ‘0’ and ‘1’ are represented by the tran- sistor being turned off or on,

• respectively. Currently, thousands of

electrons are used to drive each tran-

• sistor. As the processing power in-

creases, the size of each transistor re- duces. If Moore’s law continues unabated, each transistor would be as small as a hydrogen atom by the year 2030. At this size, the quantum nature of elec- trons in the atoms becomes significant and generates errors in the computa- tion. However, it is possible to exploit the quantum physics as a new way to do computation. And this new way

• pens up fantastic new computational

power based on the wave nature of quantum particles. Figs 1 and 2 show the size and number of transistors over time scale up to 2030, respectively.

Particle-wave duality

We normally think of electrons, atoms and molecules as particles. But each

• f these objects can also behave as
• waves. This dual particle-wave

behaviour was first suggested in the 1920s by Louis de Broglie. This concept emerged as follows: Thomas Young’s experiment with double slits in the early 1800s shows that light behaves as a wave. But Einstein’s explanation of the pho- toelectric effect in the year 1905 shows that light consists of particles. In 1923, de Broglie suggested this dual particle- tween your classical computer and a quantum computer. Whereas the clas- sical computer obeys the well-under- stood laws of classical physics, the quantum computer uses physical phe- nomenon unique to quantum mechan- ics (especially quantum interference) to realise a fundamentally new mode

• f information processing.

Moore’s law and the future

• f computers

In 1965, Intel’s cofounder Gordan Moore noted that the processing power (number of transistors and speed) of computer chips was dou- bling every 18 months or so. This trend has continued for nearly four decades.

Quantum computers will harness the power of atoms and molecules to perform calculations billions of times faster than today’s silicon-based computers. They will also enable new revolutionary applications

COMPUTERS TAKING A QUANTUM LEAP

ASHUTOSH BHATIA

• Fig. 1: Size of transistors in a computer chip

by the year 2030

• Fig. 2: Number of transistors in a computer

chip by the year 2030

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46 • MAY 2005 • ELECTRONICS FOR YOU W W W . E F Y M A G . C O M

wave property might apply to all par- ticles including electrons. Then in 1926, Davisson and Germer found that elec- trons scattered off a nickel crystal be- haved as waves. Since then neutrons, atoms and even molecules have been shown to behave as waves. The waves tell us where the particle is likely to be found.

Bits and qubits

The basic data unit in a conventional (or classical) computer is the bit, or binary digit. A bit stores a numerical value of either ‘0’ or ‘1.’ An example

• f how bits are stored is given by a

CD-ROM, where ‘pits’ and ‘lands’ (ab- sence of a pit) are used to store the binary data. We could also represent a bit using two different electron orbits in a single atom. In most atoms, there are many electrons in many orbits. But we need to consider only the orbits available to a single outermost elec- tron in each atom.

• Fig. 3 shows two atoms represent-

ing the binary number ‘10.’ The inner

• rbits represent digit ‘0’ and the outer
• rbits represent digit ‘1.’ The position
• f the electron gives the number stored

by the atom. However, a completely new possi- bility opens up for at-

• ms. Electrons have a

wave property that al- lows a single electron to be in two orbits simul-

• taneously. In other

words, the electron can be in a superposition of both orbits.

• Fig. 4 shows two at-
• ms, each with a single

electron in a superposi- tion of two orbits. Each atom represents binary digits ‘0’ and ‘1’ simul-

• taneously. The two at-
• ms together represent

the binary numbers ‘00,’ ‘01,’ ‘10’ and ‘11’ simul- taneously. To distinguish this new kind of data stor- age from a conventional bit, it is called a quan- tum bit, or qubit. Each atom in Fig. 4 is a qubit. The key point is that a qubit can be in a superposition of the digits ‘0’ and ‘1.’ Superposition states allow many computations to be per- formed simultaneously, and give rise to what is known as quantum paral- lelism. Another example of a qubit is a photon (a particle of light) travelling along two possible paths. Consider what happens when a photon encoun- ters a beam splitter. A beam splitter is just like an ordinary mirror, however the reflective coating is made so thin that not all light is reflected and some light is transmitted through the mir- ror as well. When a single photon en- counters a beam splitter, the photon emerges in a superposition of the re- flected path and the transmitted path. One path is taken to be the binary digit ‘0,’ and the other path is taken to be the digit ‘1.’ The photon is in a super- position of both paths and so repre- sents both ‘0’ and ‘1’ simultaneously.

Superpositioning

Superpositioning means that two things overlap without interfering with each other. In classical computers, elec- trons cannot occupy the same space at the same time, but as waves, they can. Superposition in waves. Fig. 6(a) shows two superimposed waves ‘A’ and ‘B.’ If we were to add these waves together numerically, the result (S=A+B) would be a wave that looks like neither of its components (see Fig. 6(b)). However, one could retrieve ei- ther wave by subtracting out the other. (The waveform ‘S’ is shown as dotted to indicate that it is only the apparent waveform; the actual waveform is a combination of two different waves. In the quantum world, the combined waveform is a set of amplitude prob- abilities.) Superposition in link list pointers. For an example germane to computer programming, one may look at a data structure called the linked list. Each date node in the list contains a refer- ence, or pointer, to the next data node. The program traverses the list by jumping to the next data node indi- cated by the pointer. In a doubly linked list, the data node contains two pointers, one for traversing to the top

• f the list and the other for traversing

to the bottom of the list. Another way of implementing a

• Fig. 3: Two atoms representing the binary

number ‘10’

• Fig. 4: Two atoms, each with a single electron

in a superposition of two orbits. Each atom represents binary digits ‘0’ and ‘1’

• simultaneously. The two atoms together

represent the binary numbers ‘00,’ ‘01,’ ‘10’ and ‘11’ simultaneously

• Fig. 5: When a single photon encounters a beam splitter, the

photon emerges in a superposition of the reflected path and the transmitted path

• Fig. 6: (a) Two super-imposed water waves ‘A’ and ‘B’ and (b)

the sum of ‘A‘ and ‘B’ waves looks like neither of its components

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ELECTRONICS FOR YOU • MAY 2005 • 47 W W W . E F Y M A G . C O M

doubly linked list is to use a single pointer space that contains the exclu- sive-OR (XOR) or the two adjacent

• pointers. Fig. 7 shows a link list node

with pointer S that is the XOR of ref- erence A (before) and reference B (af- ter). To traverse the link list upward, the program XORs the current pointer (S) with the one it just left (B), and the result is the pointer of the next node (A). The same process works when traversing down the list. This superpositioning of node pointers is analogous to the water wave superpo- sition example above, and shows how the quantum states are maintained si- multaneously in a quantum bit.

Qubit systems

The following text describes some sys- tems currently being developed for use as qubits, the quantum version of bits. Ion traps. An ion is an atom with extra or missing electron. Being elec- trically charged, individual ions can be trapped using electric and magnetic fields. The linear ion trap shown in Fig. 8 uses four rod electrodes (light blue), which are fed an AC voltage of around

• ne kilovolt at a frequency of a few
• megahertz. This confines the ions (red

dots) along a central line. The end- rings (dark blue) are electrically charged to prevent the ions from es- caping at the ends. Finely focused lasers are used to prepare and inspect individual ions. The outer electron of each ion is ma- nipulated to be in two different orbits around the nucleus. Each ion therefore represents a qubit. As an ion scatters photons from the laser, it recoils. The recoil motion is felt by the other ions. This recoil motion is equivalent to data bus of a classical computer. Nuclear magnetic resonance (NMR). The nucleus (blue ball) of an atom can have a magnetic moment (or- ange arrow), i.e., the nucleus behaves as a tiny permanent magnet (see Fig. 9). It shows an unusual behaviour when placed in a strong magnetic field (green arrow). Owing to its quantum nature, the nuclear magnetic moment is aligned either in the same direction as or the opposite direction to the sur- rounding magnetic field. The orienta- tion of the nucleus is therefore con- fined to two distinct values and so it represents a qubit. Adjacent nuclei also affect each

• ther through their magnetic moments

in the same way as two magnets placed near each other. This interac- tion allows one nuclear qubit to con- trol an adjacent nuclear qubit. Quantum computation is carried

• ut using radio frequency fields to flip

the nuclear moments. The output data is obtained by measuring the ra- dio frequency fields generated by os- cillating moments. Quantum dots. Using advanced lithographic techniques it is possible to make small structures called quan- tum dots in semiconductor materi-

• als. Each such dot, which can be as

small as 30 nm across (around 30 times the size of an atom), can con- fine a single electron in discrete en- ergy levels. Thus the quantum dot behaves like a large artificial atom and can be used as a qubit. A user can access individual quan- tum dots using focused laser beams, which can flip the electron between two discrete energy levels or place it into a superposition of the two levels. The required interaction between qubits occurs through externally ap- plied electric and optical fields.

What is a quantum computer

In a quantum computer, the funda- mental 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 con- sequence of its adherence to the laws

• f 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’

• r ‘1,’ as in a classical bit, but also in

states corresponding to a blend or su- perposition of these classical states. In

• ther words, a qubit can exist as ‘0,’

‘1,’ or both ‘0’ and ‘1’ simultaneously, with a numerical coefficient represent- ing the probability for each state. This may seem confusing because everyday phenomena are governed by classical physics, not quantum mechanics, which takes over at the atomic level. This rather difficult concept is per- haps best explained through an

• experiment. Consider Fig. 10. Here a

light source emits a photon along a path towards a half-silvered mirror. This mirror splits the light, reflecting half vertically toward detector A and transmitting half toward detector B. A photon, however, is a single

• Fig. 7: A link list node with pointer S that is the

XOR of reference A (before) and reference B (after)

• Fig. 8: The linear ion trap uses four rod

electrodes (light blue), which are fed an AC voltage of around one kilovolt at a frequency

• f a few megahertz
• Fig. 9: The nucleus behaves as a tiny

permanent magnet. It shows an unusual behaviour when placed in a strong magnetic field (green arrow)

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quantised packet of light and cannot be split, so it is detected with equal probability at either A or B. Intuition would say that the photon randomly leaves the mirror in either the vertical

• r horizontal direction. However,

quantum mechanics predicts that the photon actually travels both paths si- multaneously, collapsing down to one path only upon measurement. This effect, known as single-par- ticle interference, can be better illus- trated in a slightly more elaborate ex- periment outlined in Fig. 11. In this experiment, the photon first encoun- ters a half-silvered mirror, then a fully silvered mirror and finally another half-silvered mirror before reaching a detector, where each half-silvered mir- ror introduces the probability of the photon traveling down one path or the

• ther.

Once a photon strikes the mirror along either of the two paths after the first beam splitter, the arrangement is identical to that in Fig. 10, and so one might hypothesise that the photon will reach either detector A or detector B with equal probability. However, the experiment shows that in reality this arrangement causes detector A to register 100 per cent of the

• time. That is, the pho-

ton always reaches detector A, never de- tector B! If a single photon travels vertically and strikes the mirror, then, by compari- son to the experiment in Fig. 10, there should be an equal probability that the photon will strike either detector A or detector B. The same goes for a pho- ton traveling down the horizontal

• path. However, the actual result is

drastically different. The only conceivable conclusion is therefore that the photon somehow traveled both paths simultaneously, creating an interference at the point of intersection that destroyed the possi- bility of the signal reaching detector

• B. This is known as ‘quantum inter-

ference’ and results from the su- perposition of the possible pho- ton states, or potential paths. So although only a single photon is emitted, it appears as though an identical photon ex- ists and travels the ‘path not taken,’ only detectable by the in- terference it causes with the

• riginal photon when their paths

come together again. If, for ex- ample, either of the paths is blocked with an absorbing screen, detector B begins regis- tering hits again just as in the first experiment! This unique characteristic, among others, makes the current research in quantum computing not merely a continuation of today’s idea of a computer but rather an entirely new branch of thought.

Quantum parallelism

A one-bit memory can store one

• f the digits ‘0’ and ‘1.’ Likewise,

a two-bit memory can store one of the binary numbers ‘00,’ ‘01,’ ‘10’ and ‘11’ (i.e. 0, 1, 2 and 3 in base ten, respec- tively). But these memories can store

• nly a single number (e.g., the binary

number ‘10’) at a time. As described earlier, a quantum superposition state allows a qubit to store ‘0’ and ‘1’ simultaneously. Two qubits can store all the four binary numbers ‘00,’ ‘01,’ ‘10’ and ‘11’ simul-

• taneously. Three qubits store the eight

binary numbers ‘000,’ ‘001,’ ‘010,’ ‘011,’ ‘100,’ ‘101,’ ‘110’ and ‘111’ simulta- neously. The table shows that 300 qubits can store more than 1090 numbers simulta-

• neously. That’s more than the num-

ber

• f

atoms in the visible universe! This shows the power of quantum computers: just 300 photons (or 300 ions, etc) can store more num- bers than there are atoms in the uni- verse, and calculations can be per- formed simultaneously on each of these numbers.

A brief history of quantum computing

Quantum theory is not new. It started with Max Planck’s discovery of the en- ergy quantum and Einstein’s discov- ery of the photon. We might trace the invention of the modern computer back to 1956 when Bardeen, Brattain, and Shockley won the Nobel prize for the invention of the transistor. The idea of a quantum computer

• riginated in 1980 when P. Benioff

thought about the Turing machine (de- veloped in 1935 by Alan Turing) in terms of quantum states. Whereas the convention Turing machine computes by punching holes in a linear strip of paper, the Benioff’s quantum Turing machine (QTM) has strips of paper with multiple paths, each with a prob- ability of traversal. The QTM has ex- ponentially many paths, not all equal probably, but all possible. Two years later, Richard Feynman showed that because of these diverse paths a classical computer would slow down exponentially in attempting to

• Fig. 10: A light source emitting a photon along a path

towards a half-silvered mirror

• Fig. 11: A more elaborate experiment where the

photon first encounters a half-silvered mirror, then a fully silvered mirror and finally another half-silvered mirror before reaching a detector

Numbers Stored by Qubits

Qubits Stores simultaneously Total number 1 (0 and 1) 21 = 2 2 (0 and 1)(0 and 1) 2×2 = 22 = 4 3 (0 and 1)(0 and 1)(0 and 1) 2×2×2 = 23 = 8 : : : 300 (0 and 1)(0 and 1)........(0 and 1) 2×2......×2 = 2300

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ELECTRONICS FOR YOU • MAY 2005 • 49 W W W . E F Y M A G . C O M

traverse an exponentially growing number of paths; that is, a classical computer would not be able to simu- late quantum processes. Berthiaume & Brassard proved in 1994 that QTMs are theoretically faster than Turing machines, partly due to the parallelism of quantum comput-

• ing. Shor was able to demonstrate this

fact the same year by factoring large integers in polynomial time. Shor’s al- gorithm was the first significant prob- lem solved by a quantum approach to excel classical computers. Grover showed in 1996 a quantum algorithm to search unsorted databases in the square root of the time it would take a classical computer to find an

• entry. It is said that to search for your

name in the entire text of the Library

• f Congress would take classical com-

puters around 100 years, but a quan- tum computer could find your name in a little under half a second. The Turing machine, designed around a machine traversing a strip

• f paper, is hard to use as a focus to

manipulate new ideas in program- ming and electronics. In 1993, Yao showed that the same effect could be accomplished by using quantum cir-

• cuits. These circuits are equivalent to

digital logic circuits, but use quantum

• principles. Classical circuits use Bool-

ean logic, either state ‘0’ or ‘1,’ for inputs and outputs. Quantum circuits use these states simultaneously: the inputs of a quantum circuit are both ‘0’ and ‘1.’ These algorithms are constructed and proved in theory, but in June 1998 Gershenfeld and Chuang built the first quantum computer at the Massachu- setts Institute of Technology (MIT). It was based on the principles of nuclear magnetic resonance. There are other types of quantum computers that may be built, but it is characteristic in that it uses molecules in a liquid CPU of chloroform for logic gates. In December 1998, Anton Zeilinger made a fantastic accomplishment. He was able to quantum teleport a beam

• f light around 90 cm (3 feet) across

his laboratory. This feat was achieved using a principle called ‘quantum en- tanglement.’

Entanglement and quantum teleportation

The quantum property of entangle- ment has an interesting history. Einstein, who claimed that “God does not play dice with the universe,” used the property of entanglement in 1935 in an attempt to prove that quantum theory was incomplete. Albert Einstein, Boris Podolski and Nathan Rosen knew that the state vec- tors of certain quantum systems were correlated, or ‘entangled’ with each

• ther. If one changes the state vector
• f one system, the corresponding state

vector of the other system is also changed, instantaneously and indepen- dently of the medium through which some communicating signal must travel. Since nothing could travel faster than the speed of light, how could one system arbitrarily far apart affect the

• ther? Einstein called this ‘spooky ac-

tion at a distance’ and it required a philosophy of reality contrary to sci- ence as then known. He preferred the idea that some unknown or ‘hidden variables’ were contributing to the ef- fect, and since they weren’t known, quantum theory must be incomplete. In 1964, John Bell proved that there could not possibly be any hidden vari- able, which meant that spooky action at a distance was a fact. Alan Aspect later (1982) performed an experiment in which he showed that Bells’ Theo- rem, as it was called, had experimen- tal validity. Either some faster-than- light speed communication was hap- pening or some other mechanism was at work. This basic concept has made all the difference between classical ideas of reality and quantum ideas of reality. Throughout all of history previ-

• usly, all physical phenomena were

dependent on some force, and some particle to carry that force, and there- fore the speed of light restriction ap-

• plied. For example, electrostatic forces

are carried by the electron, gravita- tional forces are carried by the gravi- ton, etc. However, with entanglement, quantum systems are correlated in some way that does not involve a force, and the speed of light restric- tion does not apply. The actual mecha- nism of how one system affects the

• ther is still unknown.

Collapse of the state vector. When two quantum systems are created while conserving some property, their state vectors are correlated, or entangled. For example, when two photons are cre- ated, and their spin conserved, as it must, one photon has spins of ‘1’ and ‘–1.’ By measuring one of the state vec- tors of the photon, the state vector col- lapses into a knowable state. Instanta- neously and automatically, the state vector of the other photon collapses into the other knowable state. When

• ne photon’s spin is measured and

found to be ‘1,’ the other photon’s spin

• f ‘–1’ immediately becomes known
• too. There are no forces involved and

no explanation of the mechanism. Quantum teleportation. The prin- ciple of entanglement enables a phenomenon called ‘quantum teleportation.’ This kind of teleportation does not involve moving an entity from

• ne physical location to another, as may

be found in many popular science fic- tion stories, but a destruction of the

• riginal and recreation of an exact rep-

lica at another location.

The power of quantum computers

As the technology evolves, several fac- tors work together to push us toward quantum computing, and push out the classical silicon-based chips. These fac- tors are scaling in size, energy con- sumption, economics of building lead- ing-edge computers and new applica-

• Fig. 12: Quantum teleportation

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tions that are available with quantum computers that cannot be executed with classical computers. At the current rate of chip miniaturisation, energy efficiency and economics, the classical computer of the year 2020 (if it could happen at all) would contain a CPU running at 40 GHz (or 40,000 MHz), with 160 GB (160,000 MB) of random-access memory (RAM), and run on 40 watts of power.

• Scaling. The computing world is

full of innovations, and many of them involve more powerful and smaller

• chips. Chip capacity has doubled every

18 months, according to Moore’s Law, but the chip size remains constant. The number of transistors on a single chip is also rising exponentially. It seems that if miniaturisation continues at the cur- rent rate, a bit will be represented by a single atom by the year 2020. This trend inevitably leads us into the microworld

• f quantum effects, where classical rules

no longer apply.

• Energy. The speed of chips is also

rising exponentially. Faster, more densely packed and closer transistors cause thermodynamic problems. Quantum computers are reversible, and therefore there is theoretically no net energy consumption. Quantum reversibility means that quantum computers drive themselves forward in infinitesimal (reversible) steps, much the same way that mol- ecules of perfume would diffuse from a perfume bottle. Quantum computer programs are not ‘run,’ but are said to ‘evolve,’ as they process the program’s inputs to outputs. Incidentally, reversibility also means that the inputs

• f a quantum computer can be implied

from the outputs; the program can be run backwards to get the inputs.

• Economics. Besides the energy fac-

tors at the micro level of computing, there are large-scale economic factors pushing us to a more energy-efficient means of computing: five per cent of the entire national power production is consumed by computing machinery. With fossil fuels continuing to dwindle, fission power in disfavour with the public and fusion power still many decades away, the drain com- puters impose on our power supply could become significant. Japan, in its bid for software and hardware global dominance, has allocated huge funds for quantum computer research.

New applications

Encryption technology. The speed of quantum computers also explores the encryption schemes that rely on im- practicably long times to decrypt by brute force methods. Encryption schemes that may take millions of years to guess and check can be de- feated by quantum computers that may reach a solution within a year. Ultra-secure and super-dense com-

• munications. It is possible to transmit

information without a signal path by using quantum teleportation. There is no way to intercept the path and ex- tract information. Ultra-secure commu- nication is also possible by super-dense information coding, which is a new technology in its own right. Quantum bits can be used to allow more infor- mation to be communicated per bit than the same number of classical bits. Improved error correction and er- ror detection. Through similar pro- cesses that support ultra-secure and super-dense communications, the ex- isting bitstreams can be made more ro- bust and secure by improvements in error correction and detection. Recov- ering the information from a noisy transmission path will also be a lucra- tive and useful practice. Molecular simulations. Richard Feynman showed in 1982 that classical computers cannot simulate quantum effects without slowing down exponen- tially; a quantum computer can simu- late physical processes of quantum ef- fects in real time. Molecular simula- tions of chemical interactions will al- low chemists and pharmacists to learn more about how their products inter- act with each other, and with biological processes (such as a drug’s interaction with a person’s metabolism or disease). Pharmaceutical research offers a big market to such applications. True randomness. Randomness plays a significant role in applications with a heavy reliance on statistical ap- proaches (e.g., simulations, code mak- ing, randomised algorithms for prob- lems solving and stock market predic- tions). Today’s computers cannot gen- erate true random numbers. The ran- dom number generators on them are pseudo-random generators, i.e., there is always a cycle or a trend. Quantum computers can generate true random- ness, thus giving more veracity to pro- grams that need true randomness in their processing.

Obstacles

The field of quantum information pro- cessing has made numerous promising advancements since its conception, in- cluding the building of two- and three- qubit quantum computers capable of some simple arithmetic and data sort-

• ing. However, a few large obstacles

still remain that prevent us from build- ing a quantum computer that can re- place today’s digital computer. Among these difficulties, error cor- rection, decoherence and hardware ar- chitecture are probably the most formi-

• dable. Error correction is rather self-

explanatory, but what errors need cor- rection? The answer is primarily those errors which arise as a direct result of decoherence, or the tendency of a quan- tum computer to decay from a given quantum state into an incoherent state as it interacts, or entangles, with the state of the environment. These inter- actions between the environment and qubits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus errors in computation.

The author is a scientist-B at Defence Research & Development Organisation (DRDO), Delhi

300 qubits can store more than 1090 numbers

• simultaneously. That’s more than the number of

atoms in the visible universe! This shows the power

• f quantum computers.