![NIST physicists Dietrich Leibfried and David Wineland in the laboratory where they have developed a method for correcting data handling errors for quantum computing. ©Geoffrey Wheeler](https://webarchive.library.unt.edu/eot2008/20080917110535im_/http://www.nist.gov/public_affairs/images/04PHY020_Wineland_Leibfried.jpg) |
NIST
physicists Dietrich Leibfried and David Wineland in the
laboratory where they have developed a method for correcting
data handling errors for quantum computing.
©Geoffrey
Wheeler For
a high-resolution version of this image,
contact Gail
Porter. |
A practical
method for automatically correcting data-handling errors in
quantum computers has been developed and demonstrated by physicists
at the National Institute of Standards and Technology (NIST).
Described
in the Dec. 2, 2004, issue of the journal Nature,
the NIST work is the first demonstration of all the steps
of error correction for quantum computers, a futuristic, potentially
very powerful form of computing that uses the quantum properties
of atoms or other particles as 1s and 0s for processing data.
The method was implemented using ions (electrically charged
atoms) as quantum bits (qubits). Ions are arguably the leading
candidate for use as qubits in a quantum computer.
Conventional computers
use electronic switches that are either on or off to represent
1s and 0s that then can be stored or manipulated to make calculations.
Quantum computing would use the quantum states of matter (such
as magnetic properties) as 1s, 0s—or even both at once.
The unusual features of the quantum world provide extra computational
power, offering the prospect of carrying out a massive number
of simultaneous calculations to solve problems that are impossible
to solve today. Specific applications could include code-breaking
of unprecedented power, faster database searching, fraud-proof
digital signatures and optimization of everything from communications
systems to airline schedules. But unless data-handling errors
are corrected, “noise” caused by environmental
disturbances, such as fluctuating magnetic fields associated
with electrical equipment, could diminish any gains over today’s
computers.
The new NIST method
helps to ensure the correctness of data during computations
by creating redundant data sets, or what might be called quantum
backup copies. “The basic concept is a familiar one:
If someone doesn’t understand what you say, you repeat
it several times, and eventually they’ll get it,”
explains physicist Dietrich Leibfried, who developed the approach
and helped to demonstrate its feasibility in NIST’s
Boulder, Colo., laboratories.
Direct
copying of qubits is prohibited by the rules of quantum mechanics,
nature’s instruction book for the smallest particles
of matter. Like all known quantum error correction methods,
the NIST method gets around this obstacle by exploiting a
famously spooky (the term used by Einstein) feature of quantum
mechanics that allows the “entanglement” of physically
separated atoms to link their quantum properties in predictable
ways. The atoms also are prepared in a special “superposition”
state in which they represent both 1 and 0 at the same time.
The
demonstration used three beryllium ions as qubits. One “primary”
ion is entangled with two “helper” ions as part
of a series of encoding steps. The primary qubit is essential
to the computation; the other two are expendable. Because
the three are entangled, errors in one affect the others,
a condition that is reflected in the joint quantum state of
all three qubits. If the quantum
state of the primary qubit is accidentally changed, the mistake
can be detected and corrected by reversing the steps
to decode the data, and then measuring the values of the two
extra qubits.
Unlike
other demonstrations of quantum error correction, the NIST
approach makes corrections based on actual measurements, allows
qubits to be “reset” on the fly, and could be
scaled up for use in quantum computers of practical size and
utility. Previous demonstrations by other groups have involved
correction of errors in qubits made of molecules in a liquid,
without the ability to measure or reset and reuse the extra
qubits needed to detect errors. The ability to “empty
the trash bin,” rather than simply storing mistakes
somewhere in the computer, makes the NIST approach more practical.
The NIST
error correction process could be incorporated into the programs
executed by quantum computers. In principle, the approach
could be used to maintain the fragile quantum states of ions
or atoms by repeated error correction during data processing,
an essential step toward scalable, reliable quantum computers.
The same NIST research group previously demonstrated other
essential components for a quantum computer based on atomic-ion
traps.
Error
correction is routine in today’s computing and communications
systems. For instance, a sender might periodically add up
a series of sent bit values and transmit the total to the
receiver. Once the same bits are received, the values are
also summed at the receiver and the two totals are compared.
If the totals match, there is a high probability that the
bits arrived in the correct state. If the totals differ, then
the data were corrupted, and the original bits are re-sent.
This approach would fail in quantum information systems because
measuring a qubit destroys its quantum state and effectively
stops the computation. Therefore, errors need to be detected
indirectly, as in the NIST method. It is not necessary to
know the value of the primary qubit in order to detect an
error and correct it.
To verify
that the method works, NIST scientists performed many experiments
with beryllium ion qubits and compared the corrected quantum
states to the initial and uncorrected states. The instrumentation
and procedures for manipulating qubits need to be improved
to build reliable quantum computers, but such improvements
seem feasible, Leibfried says. In addition, more ions and
a more complex approach would be needed to correct all possible
types of errors.
The research was
supported in part by the Advanced Research and Development
Activity and the National Security Agency.
As a
non-regulatory agency of the U.S. Department of Commerce’s
Technology Administration, NIST develops and promotes measurement,
standards and technology to enhance productivity, facilitate
trade and improve the quality of life.
How
Error Correction Works
The NIST quantum
error correction method is a way of using a set of three atomic
qubits to detect and correct data-handling errors in one of
the qubits.
![Quantum computing Illustration](https://webarchive.library.unt.edu/eot2008/20080917110535im_/http://www.nist.gov/public_affairs/images/Quantum_error_spinstates_we.jpg) |
An
ion’s quantum state can be spin up (top), spin
down (middle) or a superposition state, represented
graphically as any one of many possible spin directions
in between up and down (bottom). Superposition states
in which the spin is depicted as horizontal will be
measured as spin up 50 percent of the time and spin
down 50 percent of the time.
Click
here to download a higher resolution version of this
image. |
Three
beryllium ions (charged atoms) are held in a tiny, micrometer-sized
electromagnetic trap, where their quantum states are manipulated
with ultraviolet laser beams and their physical movement is
controlled with electrodes. One ion is the primary qubit containing
the data essential to a computation; the other two are “helper”
qubits.
An ion’s
quantum state includes properties such as the orientation
of its “magnetic moment” (which can be thought
of as a little compass needle inside the ion, with north and
south poles). For quantum computing purposes, this is called
the “spin,” because a spinning electrical charge
is one way to create a magnetic moment. The digital values
1 and 0 are represented by the direction of the spin. “Spin
up,” corresponding to 0, has a greater energy than “spin
down,” corresponding to 1.
Atoms can exist
in both states at once, a condition called “quantum
superposition,” and, therefore can represent both 0
and 1 at the same time. On a sphere representing all possible
spin states, a superposition can be visualized as a tilt of
the north-south axis, at an angle that depends on whether
the state is closer to (i.e., has a greater probability of
being) 0 or 1. When a qubit is measured by probing it with
a laser, the state collapses to 0 or 1, with a rate of occurrence
that depends on the angle of the ion’s tilt (or the
probability of its being 1 or 0). For example, when the ion’s
axis points directly to the side (i.e., the axis is horizontal),
the qubit will have an equal probability of collapsing to
spin up or to spin down. For each single experiment it will
collapse to one of the two states; but if the experiment is
repeated 100 times, the qubit will, on average, collapse to
spin down 50 times, and to spin up 50 times
In the NIST error
correction procedure, the primary qubit is prepared in a superposition
of spin up and spin down. Then the data in this qubit are
“encoded” in the set of three qubits by putting
the three ions through a series of processing steps, or what
a scientist would call “quantum logic gates.”
This has the effect of correlating the quantum properties
of all three qubits so that an action on one produces a predictable
outcome on the others. One type of logic gate places the two
extra ions in superposition states. Another type of logic
gate has the effect of entangling the three ions, so their
quantum states are related to each other in a particular choreography.
Overall, these processing steps place the entangled system
in a superposition of several possible quantum spin states
of the three atoms.
Scientists then
use lasers to purposely introduce errors—spin flips,
or reversals—into all the qubits simultaneously, as
might occur in a real computer due to environmental disturbances.
The exact nature of the errors occurring in a single run of
the experiment depends partly on the length of the laser pulse
hitting the ions, and partly on the unusual features of quantum
mechanics, which, like a coin toss, produces results that
can be predicted only in terms of probabilities, as described
earlier. So, from run to run, different errors might occur,
and the correction steps described below would be adapted
to the situation in that particular run. (Scientists can rigorously
characterize the performance of the error-correcting procedure
by using well-characterized laser pulses so they know exactly
what type of “error” occurred.)
Then the quantum
logic operations are performed in reverse order to “decode”
the data in the entangled system. The process is designed
so that the qubit state needed for the computation is transferred
back to the primary qubit, and the error information is contained
in the two extra qubits. These two then are measured by hitting
them with a different laser pulse that either makes them fluoresce
(like a light bulb that turns on) if they are spin down, or
remain dark if they are spin up. This procedure forces their
states to collapse to one of four possible outcomes (spin
up/spin up, spin down/spin up, spin up/spin down, spin down/spin
down), depending on the error that occurred.
At the time of
measurement, the primary qubit is disentangled from the helper
qubits and left in either its original superposition state
or one of two slightly altered versions of that state, rotated
around a particular axis. The final values of the two helper
qubits herald which of these cases occurred, so that corrections
can be made if needed. For instance, the routine is designed
so that, if both extra ions are spin down, then the spin of
the primary qubit was flipped around a particular axis and
can be corrected with a precisely timed laser pulse to undo
that flip. The two extra qubits then can be reset and used
again to detect and correct future errors.
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