RAYMOND LAFLAMME鈥橲 computer sits in a low, unassuming building at the heart
of Los Alamos National Labs in the high deserts of New Mexico. No more than a
kilometre away is Blue Mountain, a Department of Defense computer the size of
small office block that last year claimed the title of the world鈥檚 fastest
computing machine with a record 1.6 trillion operations per second.
Laflamme鈥檚 computer is just as impressive but in a very different way. It
occupies a grey vat the size of a beer keg and it has less number-crunching
power than a pocket calculator. Bathed in magnetic fields powerful enough to
wipe out credit cards at 20 paces, this vat is the prototype of a calculating
machine so weird and magical that until a few years ago scientists were not even
sure that it was possible to build one at all.
This is one species of quantum computer. And not just any old species: its
proud parent boasts that it can handle all of 5 bits of quantum information, an
achievement that qualifies it for the title of the world鈥檚 most powerful.
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Laflamme belongs to an elite band of researchers who have built their own
quantum computers and even got them to run esoteric programs. Nobody has been
able to make a quantum computer do anything even approaching a 鈥渞eal鈥� world
application. Which is why the work of Laflamme and his colleague David Cory of
the Massachusetts Institute of Technology is so exciting. In June, they
announced that they had used a quantum computer to simulate the behaviour of a
real, physical thing: a quantum particle in a container. It is the first time a
quantum computer has simulated a physical system of any kind. And for this
emerging field, it represents a coming of age.
Laflamme and Cory鈥檚 work is a textbook example of how quantum computing
works. As with any conventional computer, information must be entered, processed
and then read out. But in a quantum computer, the way this is done is far from
conventional.
Quantum information is very different from the stuff that ordinary computers
chew on. Conventional computers store and manipulate information in the form of
bits鈥攅ach bit can take the value of a 0 or a 1. In an electronic circuit,
these 0s and 1s are represented by bunches of electrons or switches that are on
or off. But the quantum version of bits is far more exciting and ethereal.
Parallel existence
In quantum computers, quantum bits (qubits) can take a value of 0 and 1 at
the same time. This phenomenon is called a superposition of states and it
happens all the time at the subatomic scale. Take a proton, for example, which
spins like a top with its axis pointing either up or down. Unlike a top,
however, a proton in a superposition of states spins in both directions at
once鈥攁lmost as if it had two existences simultaneously. As long as the
superposition survives, these two states exist together. If the up and down
states represent 0s and 1s, a quantum computer can perform the neat trick of
carrying out two calculations at the same time.
Things get stranger still. Qubits can be linked together by a phenomenon
known as entanglement. This is no ordinary bond: entangled protons are so deeply
connected that they share the same set of existences, regardless even of the
distance between them.
This makes things even more exciting. A single proton can be in a
superposition of two states, say a 0 and a 1. But when two protons become
entangled, their total number of shared existences adds up to four (00, 01, 10
and 11). When three become entangled, the number of existences rises to eight
(000, 001, 010, 100, 110, 101, 011 and 111) and with four entangled protons,
there are 16 existences and so on. The curious thing is that a quantum computer
processes each existence separately, no matter how many are involved. So a
32-qubit computer requiring only 32 protons would be able to carry out
4 294 967 296 (232) calculations at the same time.
That, at least, is the theory. In practice, today鈥檚 physicists cannot play
with more than a handful of qubits at the same time and even then they face huge
challenges.
But even a few qubits turn out to be useful. The device that Cory and
Laflamme have used is based in Cory鈥檚 lab at MIT. It is a less powerful version
of the one at Los Alamos and it uses only 2 qubits to do its work. At its heart
is half a test tube of rusty brown liquid called 2,3-dibromothiophene. The
molecules in this liquid are the quantum equivalent of computer chips because
they carry out the calculations.
Entangled pair
Their structure is extremely important because they contain only two hydrogen
atoms. Each molecule consists of a ring of four carbon atoms and one sulphur
atom, with two bromine atoms and two hydrogen atoms sticking out from this ring
(see Diagram).
The two hydrogen atoms鈥攐r at least their nuclei, two
protons鈥攁re the ones that take part in the quantum calculation. These two
protons are able to form an entangled pair and the properties of this pair can
be measurable.
The system that Cory and Laflamme decided to simulate is a quantum particle
trapped in a specially shaped container, like a bowl. The special shape limits
the number of states the particle can have to four and physicists call it a
truncated quantum harmonic oscillator (QHO). The question that Cory and Laflamme
set out to answer is this: what is the energy of these four states?
This is where the link with dibromothiophene becomes clearer: both the
truncated QHO and the two protons in the molecule can have four states. But the
question immediately arises: how can two protons in a molecule behave like a
single quantum particle in a container?
Instead of thinking about the individual properties of a system, physicists
often prefer to think of the total energy of the system, an entity they call the
Hamiltonian of that system. The Hamiltonian of a ball rolling down a mountain,
for example, would be the sum of its rotational energy, kinetic energy and
gravitational potential. In fact, in this case, the Hamiltonian actually
describes the shape of the mountainside. Armed with this information, a
researcher could calculate the ball鈥檚 future path and speed of descent with as
much precision as the laws of physics allow.
But imagine turning this idea on its head. Think of the ball as a kind of
specialised computing machine that, by its own action, calculates the future
values its speed and direction. To enter data into this 鈥渃omputer鈥�, raise the
ball to certain height. The computer 鈥減rogram鈥� is the Hamiltonian (the shape of
the mountainside) and to set it running, simply let the ball go. The position,
velocity or energy of the ball can then be determined simply by measuring it.
The laws of physics themselves will have performed the arithmetic. But here is
the important point: since these laws are always the same, the result holds true
for any system that shares the same Hamiltonian, regardless of how different it
might seem to our eyes.
This is exactly how Laflamme and Cory鈥檚 experiment works. The Hamiltonian of
two protons in dibromothiophene can be made to appear the same as the
Hamiltonian of a truncated QHO but only when viewed in the right way. The trick
is to prepare the protons in the correct way so that the experiment 鈥渟ees鈥� the
right answer.
It鈥檚 a bit like using one mountainside to simulate another. Although the two
mountains may look entirely different, the trick is to find part of one mountain
that has exactly the same twists and turns as the other. If you make
measurements in this area only, your experiment 鈥渟ees鈥� the right answer
regardless of the shape of the rest of the mountain.
Of course, the difficult part of the experiment is preparing the protons and
making the measurements. For this the team turned to the well-trusted techniques
of nuclear magnetic resonance (NMR), the same ideas that produce extraordinary
images of the human body. 鈥淢agnetic resonance has a deep history of controlling
quantum systems,鈥� says Cory.
An NMR machine works by applying a powerful
magnetic field to the liquid, which defines a direction for the experiment.
Since protons have an intrinsic spin, this forces them to become aligned either
with the field (up) or against it (down).
The protons can be manipulated further by bombarding them with radio waves.
The sequence and pattern of radio waves adds energy to the system and orients
the protons relative to the measuring device so that it 鈥渟ees鈥� only a certain
aspect of the protons鈥� Hamiltonian. If the Hamiltonian looks exactly like that
of a truncated QHO, then the relative energy of the protons鈥� states will be same
as those in a truncated QHO.
Nodding protons
Measuring proton states is not as hard as it sounds. Just like spinning tops,
the protons nod or precess as they rotate. In theory, this precession should
induce a current in any nearby coil of wire so a measurement of this current is
also a measure of the state of the protons. Of course, actually measuring the
precession of one or two protons is well-nigh impossible, which is why Cory and
Laflamme look for the combined signal from the many trillions of protons in half
a test tube of dibromothiophene. For modern magnetic resonance machines, this is
child鈥檚 play. 鈥淲e can piggyback on other people鈥檚 technological advances,鈥�
admits Laflamme.
The results were convincing. A simple analysis showed that the output from
Cory鈥檚 NMR machine was actually four signals superimposed. Each of these
represents one of the possible states that a truncated QHO can adopt. And the
ratio between them鈥攖heir relative energies鈥攚as exactly the ratio
that a physicist would have calculated conventionally (Physical Review
Letters, 28 June, vol 82, p 5381).
The success of the quantum processor has raised Cory鈥檚 expectations for the
long-term potential of quantum computing. 鈥淨uantum information processing will
become an integral part of our understanding of quantum physics,鈥� he says.
And other researchers have taken note. David Wineland of the National
Institute of Standards and Technology in Boulder, Colorado, has been working on
building quantum information processors from a series of carefully trapped ions.
鈥淚t鈥檚 a really nice experiment,鈥� Wineland says of the recent simulation. 鈥淭hese
guys have led the way, but the field as a whole is faced with scaling this up to
large problems.鈥�
Quantum computers based on NMR techniques cannot be made much more powerful.
NMR machines measure the average state of a large number of molecules, so a
certain proportion of the molecules will be in the wrong state to start with and
so produce the wrong answer. When only a handful of qubits are involved and the
number of parallel existences are few, the right answers can be distinguished
from the wrong ones.
But as the number of existences increase, making this distinction becomes
steadily more difficult and eventually impossible. 鈥淲e have no way of
differentiating between those that started out in the wrong state and those that
started in the right state,鈥� says Cory. The practical limit for quantum
computers based on nuclear resonance techniques is only about 10 qubits so other
more exotic techniques will be needed for larger scale computing
(New 杏吧原创,6 June 1998, p 36).
One obstacle looms large, no matter the number of qubits. Quantum information
processors leak information because superpositions are extremely fragile and
tend to collapse into a single state, a process known as decoherence. When this
happens, the calculation is ruined. This severely limits the complexity of
simulations that can run on a quantum computer because the longer it runs, the
more likely any result is to be ruined by decoherence.
Cory and Laflamme ran into exactly this problem when they were trying to
simulate a more complex system called a driven anharmonic oscillator, which is a
bit like a ball in a bowl being driven by, say, the wind. This requires longer
processing before the pick-up coils can read the output of the simulation. While
this is going on, decoherence degrades the output signal until it is unreadable.
Such an effect isn鈥檛 all bad, however: the researchers now plan to use quantum
information processing to study the phenomenon of decoherence itself.
Even with the problem of decoherence, the future looks bright. 鈥淚 don鈥檛 think
we鈥檝e found the magic prototype for quantum computers yet,鈥� admits Laflamme,
鈥渂ut we can start to explore the quantum world in a way that no one has done
before.鈥� All in all, that鈥檚 not a bad prognosis for some ageing NMR technology
and a spoonful of rusty liquid.