Computing - Kwantumcomputer
Computing: The Future may be Nearer Than
Division, teaches a class in Qubits, Quantum Mechanics,
and Computers with computer theorist Umesh Vazirani
of UC Berkeley. (Photo Roy Kaltschmidt)
to Wall Street Journal columnist Lee Gomes, you know
an idea's time has come when it "starts to be taught
to undergraduates as though it is old hat." Gomes
says that's what led him to sit in on a session of
UC Berkeley's senior-level course in "Qubits, Quantum
Mechanics, and Computers" last spring, C/CS/Physics
191 — a course otherwise known as quantum computing.
Two people the columnist heard speak that day, teacher
Michael Crommie and guest Thomas Schenkel, are both
staff scientists at Berkeley Lab, Crommie in the
Materials Sciences Division and Schenkel in the Accelerator
and Fusion Research Division (AFRD). Crommie, who
is also a professor of physics at UC Berkeley, studies
atomic and molecular structures on surfaces. Schenkel
is heading a project at Berkeley Lab to demonstrate
hardware for a quantum computer.
"In our class we start with a foundation in quantum
mechanics and only later build up to the machinery
we might use," says Crommie. Crommie teams with Umesh
Vazirani, an associate professor in UC Berkeley's
Department of Electrical Engineering and Computer
Sciences; the two created the course in concert with
K. Birgitta Whaley, a UCB professor of chemistry.
Asked about the genesis of the class, Vazirani says
that for him the motives were twofold. One was a
straightforward desire to give undergraduates a jump-start
in the field of quantum computing, a subject otherwise
taught only at the graduate level. His other motive
is more basic:
"Like others, I have thought for a long time that
quantum computing is the right way to introduce students
to quantum mechanics," Vazirani says. "If you begin
with the basic concepts that make quantum computing
work, you can grasp the fundamentals of the theory
of quantum mechanics itself."
Superposing the question
the most fundamental of all is the concept of the
superposition of states, made infamous by the parable
of Schrödinger's cat. Schrödinger's
cat is a creature who exists in a superposition of
dead and alive, until the moment an observer opens
the box and peers in (death may or may not have been
triggered by the radioactive decay of a single atom,
an unpredictable quantum event with a calculable
probability). In the vocabulary of quantum mechanics,
looking into the box is a measurement. When a system
with superposed states is measured, probabilities
collapse to certainties, in this case life or death.
introduced the paradox of the cat to argue that
quantum mechanics describes a world of atomic dimensions.
Nevertheless the notion of a cat that is both alive
and dead until a human observer looks into the
box vividly illustrates the principle of superposition
superposition and measurement are customarily confined
to the microworld, however, where their defiance
of common sense is less obvious. Like Schrödinger's
macroscopic cat, a typical microscopic system has
two (or more) discrete states, which may be the spin — up
or down — of a particle or atomic nucleus, or the
polarization — call it horizontal or vertical — of
a photon. So long as the system hasn't been measured,
both states might be equally probable; they are superposed.
Practically speaking, the quantum-mechanical system
can be in both states at once, until it is measured.
two-state system is also the basis of classical
computing, in which bits of information are manipulated
through binary arithmetic. Each bit is either a
0 or 1 — but not, in a classical system, both at once.
In a quantum computer a bit (a "qubit") is different:
it represents 0 and 1, both at the same time.
a classical system a register consisting of three
bits, say, can occupy just one of eight states,
with no uncertainty about it: the eight possible
numbers are written in binary as 000, 001, 010,
011, 100, 101, 110, or 111. Because of superposition,
however, a three-qubit register can store all eight
numbers at once. In fact whatever the number of
qubits in a quantum computer's register — say, 50 — it
can store two (states) to the power of that number.
Two to the power of 50 is well over a quadrillion.
of this scaling it was long thought that a quantum
computer, if one could be constructed, would have
vast memory capacity. But although superposition
opens a "huge space in which a relativity small amount
of information can be spread out, operated upon,
and collapsed at will," Vazirani says, most of it
is unavailable for ordinary data storage.
"Operations in this enormous space allow us to peek
at the private world of Nature, which is extremely
complex but pretends to be otherwise," he says. As
a result, it may be possible to perform some kinds
of mathematical operations with a quantum computer
that can't be done in any other way.
Schenkel of AFRD describes one of the most spectacular: "In 1994, Peter Shor of Bell Labs came
up with an algorithm for factoring very large numbers
with a quantum computer," Schenkel says. "The difficulty
of factoring is at the core of modern methods of
Research Division are working with an electron-beam
ion trap to develop a quantum computer based on single-electron
transistors. (Photo Roy Kaltschmidt)
paper and pencil, it would take most people about
an hour of trial-and-error long division to find
the only two numbers, or factors, that when multiplied
together equal the five-digit number 29,083 (they
are 127 and 129, a unique solution except for 1 and
29,083 itself) — although it takes only a minute
to go the other way, that is, to arrive at 29,083
by multiplication. (This example is taken from an
article by Adriano Barenco et al; see Additional
information below.) Likewise, classical computers
are good at multiplying large numbers rapidly, but
bog down trying to factor large numbers.
"When Shor suggested that with his algorithm and
a quantum computer you could factor a very large
number in a very short time, he let loose a storm
of activity," says Schenkel. Soon, finding a practical
way to realize what had until then seemed like a
purely mental exercise had assumed new importance
in research labs around the world.
A tangled web of calculation
says, "Beginning with understanding a qubit,
the quantum mechanical behavior of a two-state or
two-level system" — electrons orbiting an atom can
have many energy levels, with an electron jumping
between two of them serving as a qubit — "we ask
how does a qubit evolve in time? How do we measure
it? What is a measurement?"
last is a question that particularly troubled Albert
Einstein, who asked, "Is it enough that a
mouse observes that the moon exists?")
the best part: if qubits are prepared in the right
way, the computer can perform a calculation on
all of them virtually at once. Crucial to this
capacity is the concept of entanglement, an intimate
relationship that may exist between two or more separate
quantum systems. Quantum entanglement is almost as
well known as Schrödinger's cat, in the form
of the so-called Einstein-Podolsky-Rosen paradox,
or EPR (which was an expression of Einstein's unhappiness
with the implications of the quantum theory he helped
version of EPR goes this way: suppose two photons
are prepared together so that they have opposed
polarization, so if one is horizontal, the other
is vertical. The states of each are superposed,
so initially there is no way to distinguish them
by polarization. The two photons are allowed to
separate to an arbitrary distance — one could fly to the moon, even "to infinity
and beyond" — but because the systems are entangled,
when a measurement is performed on one, the state
of the other is instantly determined as well.
objections to quantum-mechanical explanations of
this scenario were many, including the apparent
violation of relativity when information appears
to travel from one place to another faster than the
speed of light. But the effect is real; it has been
measured over many kilometers and forms the basis
for a number of communication and "teleportation" schemes.
In quantum computing, entanglement is what allows
the states of many qubits to be related so that measurement
of one instantaneously measures them all.
"Once the students understand the theory of two-state
systems, we look at how we might use it to embody
qubits in the real world," Crommie says. "There are
lots of possibilities, but we picked just a few:
spin is one, of an electron or an atom — what do
you need to do to really put an electron into a superposition?
How do you entangle it? The energy levels of atoms
are another: how to take a real atom, measure its
levels, superpose them, evolve the system in time.
Another is polarization of photons: how to manipulate
and use it."
Is it really possible?
nitty-gritty of practical hardware is where classroom
guests like Schenkel come in. As a member of AFRD's
Ion Beam Technology Program, Schenkel has devoted
much of his research to devices called electron-beam
ion traps, which produce low-energy, highly charged
ions — atoms that have shed many of their orbiting
A pair of single-electron transistors only a few
nanometers apart. Each acts as a sensitive electrometer
to register single-ion impacts and also allows measurement
of spin-dependent transport, to read out the spin
states of implanted dopant ions
the several uses for highly charged ions, one in
particular fires Schenkel's imagination. In 1998
he read a paper by Bruce Kane in Nature proposing
a silicon-based quantum computer . "Kane said 'I
can do it in silicon!' and everybody said 'Wow,'
because that meant, unlike other schemes, these quantum
devices would be scalable."
says, "One project is a prototype single-electron
transistor," which would encode information in the
electron spin of a dopant atom embedded in silicon. "We
want to make the current through the transistor depend
on the spin of a single electron in a single atom.
The expectation is that if we can make one transistor,
we can make millions."
any quantum phenomenon, electron spins eventually
become entangled with their environment, leading
to "decoherence" that can obliterate quantum effects. "The
time for coherence of a single atom of phosphorus
or antimony implanted in silicon is quite long, about
60 milliseconds" — which may not seem all that long
until one considers the possibility of virtually
instantaneous computation. "Maintaining coherence
could be done with controlled pulse interactions,
like a juggler keeping a bunch of plates spinning
on poles. Except in quantum computing you have to
do it without looking at the plates. Once you look
at them — make a measurement — they all collapse."
The goal is to plant single atoms in very precise
positions in silicon that will be sculpted lithographically.
Single atoms are hard to detect unless highly ionized,
but the electron-beam ion trap readily makes phosphorus
plus-13 (lacking 13 of its 15 electrons), bismuth
plus-45 (lacking 45 of its 83 electrons), and other
highly charged ions suitable for use with silicon.
These are implanted by drilling a extraordinarily
narrow passage through or near the tip of a scanning
microscope; the tip images the surface of the wafer
and positions the ion beam at the desired location
The tip of the scanning microscope (lower right)
is used to position the beam, which is aimed through
a narrow hole in the cantilever (upper right). The
ion implanter has been used to spell out LBL in letters
measuring only 6 by 14 micrometers; individual ions
can be detected within the implanted dots.
group has used the implanter to spell out the letters "LBL" with
dots in resist on a silicon substrate, each dot aligned
to within 10 nanometers (billionths of a meter) inside
a rectangle 6 by 14 micrometers (millionths of a
meter) on a side. This placement resolution is at
the upper limit for qubits based on electron spin,
but while isolated single ions are easily detected
within the dots, single ions haven't yet been implanted
"Our ion implanter is a unique way to implant atoms," says
Schenkel. "We want to implant just one, but we haven't
done the killer experiment yet." Nevertheless he
expects to achieve the goal of demonstrating a layered
single-electron transistor, with metal gates on the
surface to control input and output, by August 2005.
Not long thereafter he expects to demonstrate a full-blown
single-electron MOSFET (metal-oxide semiconductor
field-effect transistor), a qubit as down to earth
as the workhorse transistors in a desktop PC.
But it may take a thousand qubits for a quantum
computer to perform dramatically better than classical
supercomputers, and the obstacles are formidable.
The more qubits that must interact with one another,
the faster irreversible decoherence is likely to
says, "Some people say quantum computing
is impossible, the problems are just too hard. Others,
like myself, say quantum computing is inevitable.
If you let loose the rules of quantum mechanics on
information, you get a far more general theory of
information than the classical theory. We have lots
of time to figure out how to get there."
a faith he shares with Mike Crommie, Umesh Vazirani,
and Birgitta Whaley, and their students in C/CS/Phys
191 — who at semester's end made presentations
on such topics as quantum error-correction in fault-tolerant
memory hierarchies, how to realize Josephson-junction
qubits, and a host of other practical schemes. It's
a faith that even the Wall Street Journal seems to
story has been adapted from a news release -
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