BERKELEY,
CA  Researchers in the Department of Energy's Lawrence
Berkeley National Laboratory and the University of
California at Berkeley have simulated the process
by which a quantum computer could calculate to high
precision an important basic property of two small
molecules. Simulated quantum calculations of the
groundstate energies of water (H2O) and lithium
hydride (LiH) are the first of this kind ever done
for specific molecules.
Alán
AspuruGuzik, Anthony Dutoi, Peter Love, and Martin
HeadGordon report on their work in the 9 September
issue of the journal Science.
HeadGordon is a staff scientist in Berkeley
Lab's Chemical Sciences Division and a professor
of chemistry at UC Berkeley; AspuruGuzik
is a postdoctoral fellow and Dutoi a graduate
student in the HeadGordon group. Love is
a senior applications scientist on the staff
of D Wave Systems, Inc. in Vancouver, B.C. The researchers developed a quantumcomputational
algorithm and ran it on a classical computer to demonstrate
that quantum computers comprised of only tens or
a few hundreds of quantum bits (qubits) could calculate
significant information about real molecular systems
to high accuracy.
Thus a relatively small quantum computer could surpass
the most powerful quantumchemistry calculations
possible with today's classical supercomputers.
"What
we have done is demonstrate  by using a quantum
algorithm to determine the states of minimum energy
for two real molecules that quantum computing can
deliver on the promise of giving highly accurate
practical solutions to interesting chemical problems," says
AspuruGuzik.
Confronting virtually unsolvable problems
The HeadGordon group concentrates on calculating
the electronic
structure of molecules from first principles  that
is, from a
quantummechanical description of the states of all
the particles in the
system. Electronic structure calculations allow scientists
to predict
how molecules react with other molecules and are
key to understanding
and controlling their physical and chemical properties.
The practical challenge of such calculations was
famously expressed by
Paul Dirac in 1929, who remarked of quantum mechanics
that "The
underlying physical laws necessary for the mathematical
theory of a
large part of physics and the whole of chemistry
are thus completely
known, and the difficulty is only that the exact
application of these
laws leads to equations much too complicated to be
soluble."
Indeed,
exact solutions of the Schrödinger
equation, the fundamental
expression of quantum mechanics, are so complicated
that classical
computers are only able to exactly solve very small
molecules, about the
size of water, because the time needed for computation
increases
exponentially with size. Practical calculations on
real molecules are
performed using approximations such as density functional
theories.
These are useful and usually accurate, but nonetheless
are still
approximations, which can sometimes fail. As long
ago as 1982 Richard
Feynman suggested that an easier way to calculate
a quantum system might
be by using quantum computers.
Unlike classical computing, where each bit represents
either a 0 or a 1
but not both at once, a quantum bit simultaneously
superposes 0 and 1
and only resolves (or "collapses") to a
single value when measured.
While a classical computer operates serially, essentially
dealing with
one bit after another, a quantum computer's qubits
interact to form very
large computational spaces that, when measured, quickly
deliver the
solution to a complex problem.
Various physical systems have been used to perform
quantum computations,
but no one has yet built a quantum computer large
enough to compete with
classical computers. Hardware is only part of the
challenge. Another is
devising practical algorithms that can run on quantum
computers; in
principle these can be run  if much more slowly
 on classical
simulations of quantum computers, provided only a
few qubits are involved.
AspuruGuzik
calls this the Russian doll approach: "You
begin with the
physical system you want to describe  that's the
biggest doll, with
the most information. Inside that is the basic equation
that describes
the system. Inside that is an 'emulation' of the
system using a quantum
computer. And inside that is a simulation of the
quantum computer on a
classical computer."
The limits to computation
Classical supercomputers are hardly tiny; rather
they are limited by the
number of operations they can manage within a reasonable
time. Only very
small molecular systems have been solved exactly
from first principles,
because the orbital states of each particle in the
system must be
represented in what's known as a basis set, which
in a molecule with
many electrons is very large indeed. As the size
of the system
increases, the number of calculations  and thus
the time needed to
solve the problem  increases exponentially (the
larger the number
gets, the faster it grows).
Using quantum algorithms on a quantum computer,
however, the number of
calculations (and thus the time) grows only polynomially
 faster than
linearly, but still "efficiently"  as
the size of the basis set grows.
AspuruGuzik
says, "We chose to calculate water
and lithium hydride
because threeatom water is a goodsized molecule
with a small basis
set, while twoatom lithium hydride is a small molecule
but has a
comparatively large basis set."
Two factors were key to the group's success. One
was finding an
efficient way to achieve the essential starting point
of any
calculation, an approximation of the groundstate
energy sufficiently
close to the actual state  the process of "preparing
the state that
you will simulate," as AspuruGuzik puts it.
The researchers showed that
by using a method called adiabatic state preparation
(ASP), even a
relatively crude initial estimate was practical.
"'Adiabatic'
in this context means reiterating approximations
of the
state slowly," he says. "How fast you
can prepare the state is
determined by the gap between the ground state of
the molecule and its
lowest excited state. We found a way to keep this
gap large." The
researchers confirmed the accuracy of the ASP method
by calculating the
ground state of the twoelectron hydrogen molecule
(H2).
Even more important was their adaptation of a quantum
algorithm called a
phase estimation algorithm (PEA), proposed by Daniel
Abrams and Seth
Lloyd six years ago. The original version required
a readout register
of about 20 qubits  prohibitively large for early
quantum computers.
By modifying PEA so that it performed recursively,
approaching greater
accuracy with each repeated calculation, the researchers
reduced the
size of the readout register to a manageable four
qubits.
Don't try this at home
Applying these and other measures, the researchers
were able to simulate
a quantum computer's calculation of the ground states
of water and
lithium hydride with accuracy to six decimal places.
A real quantum
computer could have performed the same calculations
almost instantly.
Its classical simulacrum, however, was an order of
magnitude less
efficient than the best conventional methods now
available, leading the
authors to emphasize that "while possible as
experiments, such
simulations are not competitive as an alternative" to
what people
already do on classical computers.
"In other words, we're saying don't try this
at home," says
AspuruGuzik. "What we've done is illustrate
the truth of the conjecture
that to exceed the limits of classical computing,
quantum algorithms
running with at least 40 to 100 qubits are needed."
The members of HeadGordon's group at Berkeley Lab
and UC Berkeley
continue to explore new theoretical approaches and
define more specifics
for the design of practical algorithms to enable
quantum chemistry on
quantum computers. Making the vast power and speed
of quantum computers
available to industrial customers is the goal of
Vancouver's DWave
Systems, Inc., the HeadGordon group's research partner
and sponsor in
the work.
"Simulated quantum computation of molecular
energies," by Alán
AspuruGuzik, Anthony D. Dutoi, Peter J. Love, and
Martin HeadGordon,
appears in the 9 September 2005 edition of Science.
More about Martin HeadGordon's group is at
http://www.cchem.berkeley.edu/mhggrp/. More about
DWave Systems, Inc.,
is at http://www.dwavesys.com/.
Berkeley Lab is a U.S. Department of Energy national
laboratory located
in Berkeley, California. It conducts unclassified
scientific research
and is managed by the University of California. Visit
our website at
http://www.lbl.gov.
Contact: Paul Preuss, (510) 4866249, paul_preuss@lbl.gov
