A bit of quantum hanky panky Physics World

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A bit of quantum hanky panky
Seth Lloyd
From
Physics World
January 2011
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Feature: Quantum-mechanical biology
physicsworld.com
A bit of quantum hanky-panky
Classical physics is usually enough to be able to understand the behaviour of biological molecules.
But as Seth Lloyd explains, photosynthetic bacteria exploit weird quantum-mechanical effects to
convert harvested light into chemical energy
Seth Lloyd is in the
Department of
Quantum Mechanical
Engineering at the
Massachusetts
Institute of
Technology, US,
e-mail slloyd@
mit.edu
In my capacity as a quantum-mechanical engineer, I
am quite experienced in quantum hanky-panky. My
colleagues and I have a toolkit of weird quantum effects
– be it entanglement, quantum superposition or tunnelling – to help us design and build quantum computers, communication systems and sensors. Until three
and a half years ago, however, I followed most biologists and chemists in regarding virtually all biological
mechanisms as being largely classical in nature. Indeed,
I had participated in the debates debunking various
theories that quantum mechanics plays an important
role in the brain. (Aside, of course, from the fact that
quantum mechanics is what guarantees the stability of
matter: a hydrogen atom governed by classical electromagnetism would collapse into nothingness in a tiny
fraction of a second.)
So when one morning in the spring of 2007 I read in
the New York Times that green sulphur bacteria were
performing quantum computation, I thought that it
must be some kind of crackpot idea. Later that day,
the quantum-computing group at the Massachusetts
Institute of Technology (MIT) held its weekly meeting, at which everyone present had a good laugh at the
notion of bacteria using quantum coherence and entanglement to assemble chemical energy from sunlight. Nonetheless, people thought it was worth taking
a closer look. Alan Aspuru-Guzik, who is now at Harvard University, had been investigating closely related
problems, and he and I were assigned the task of figuring out exactly what was going on and reporting back
to the group.
When I looked at the Nature paper (446 782) on
which the New York Times article was based, I found
that it was written not by crackpots but by a well-known
group of researchers at the University of California,
Berkeley, led by the eminent spectroscopist Graham
Fleming. Fleming’s group had carried out experiments
using ultrafast spectroscopy that appeared to show that
photosynthetic bacteria practise all forms of quantum
weirdness as they convert carbon dioxide into sugar. In
addition, the team claimed that the bacteria were using
a particular type of quantum algorithm to maximize the
Experiments using ultrafast
spectroscopy have shown that
photosynthetic bacteria practise all
forms of quantum weirdness as they
convert carbon dioxide into sugar
26
efficiency with which they transported energy from
where it was created by incoming light to the place
where that energy could be turned into chemical bonds.
The evidence for quantum coherence in the way that
the bacteria transported energy was impeccable.
Of course, for us physicists, quantum weirdness is
nothing new. We know that quantum mechanics is
strange and counterintuitive, and that the smaller
something is, the more likely it is to exhibit funky quantum behaviour. Electrons can be, and frequently are,
in many places at once; atoms have no problem behaving like waves and generating interference patterns.
Conversely, the bigger something is, the less likely it is
to exhibit quantum effects. Large objects interact so
strongly with their environment that they lose their
quantum coherence and so in “decohering” in this way
they tend to settle for more classical behaviour. After
all, a football is unlikely to appear in two places at once,
even at the feet of Lionel Messi.
Cells and other complex biological systems may not
be as big as footballs, but they exist in hot, wet environments and interact strongly with their surroundings.
This induces strong decoherence, which means that it is
usually fine to treat such systems in a classical ball-andspring way. And even when quantum mechanics must
be used to calculate rates of chemical transition, semiclassical models are often enough to explain observed
effects. It is hardly surprising then that, for many decades, biologists and chemists simply concluded that
quantum-mechanical phenomena such as coherence
and entanglement (a particularly peculiar form of quantum correlation) play little role in biological systems.
What Fleming’s paper indicated was that there are
some special biomolecules for which classical physics –
and even semiclassical physics – is not enough. Photosynthetic bacteria were the example he looked at, but
there are others too. Some species of birds navigate in a
way for which the only known explanation involves
quantum coherence and entanglement (see “The quantum of life” by Paul Davies Physics World July 2009
pp24–28). Perhaps most surprising of all, strong circumstantial evidence suggests that our sense of smell
relies intrinsically on quantum effects. In their efforts
to survive and to reproduce, it appears that living creatures are up to all sorts of quantum hanky-panky.
In search of the reaction centre
To understand how quantum mechanics can play a
role in energy transport in photosynthesis, let us
review briefly how photosynthesis works. As noted
above, photosynthesis is the process by which bacteria
and plants take energy from the Sun and turn it into
chemical energy. This transformation takes place in
Physics World January 2011
Feature: Quantum-mechanical biology
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an intricate array of protein molecules called photosynthetic complexes. The optically active pieces of
these “photocomplexes” are molecules called chromophores, from the Greek for “light carriers”.
Chromophores give colour. In plants and bacteria,
most chromophores are chlorophyll molecules (from
the Greek for “green leaf”): the chlorophyll in the
leaves of plants absorbs light in the blue and red parts
of the spectrum, reflecting the green. Other chromophores include carotenes. As their name suggests,
carotenes are what make carrots orange; they also
make tomatoes red. Lots of different types of chromophores are involved both in gathering light and
in preventing light from damaging the cell. Chromophores can act both as tiny photocells and as a kind of
microscopic suntan lotion.
The light that is absorbed by these chromophores
creates an excited quantum state called an exciton. An
exciton is a composite quantum system consisting of
a negatively charged electron bound to a positively
charged hole. A hole is the absence of an electron – if
you like, it is the place in a molecule from which the electron was “dug up”. A hole behaves like a particle: it has
mass and charge, and it can move around. Similarly,
excitons can move from chromophore to chromophore,
and that is exactly what they do as they make their way
from where they were created, via a large number of
photocomplexes, to a special photocomplex called the
reaction centre where their energy can be put to use.
By using femtosecond laser spectroscopy on a photoPhysics World January 2011
complex called the Fenna–Matthews–Olson (FMO)
complex that is found in the green sulphur bacteria
Chlorobium tepidum (figure 1), the Fleming group had
shown in its Nature paper that excitons can slosh
back and forth between chromophores in a quantummechanically coherent way via quantum tunnelling. Although these original experiments were performed at
liquid-nitrogen temperatures, recent work by Greg
Engel at the University of Chicago and Greg Scholes
at the University of Toronto have confirmed that this
coherent tunnelling persists even at room temperature.
So where does quantum computing come in? The
sole mention of it in Fleming’s 2007 Nature article was
a brief conjecture that the bacteria might be using a
particular quantum technique called a quantum search
algorithm. They suggested that this allows the absorbed
energy to find its way through the photosynthetic complex to the reaction centre where it can be turned into
chemical energy. Quantum search algorithms, which
were discovered by Lov Grover at Bell Labs in 1996,
allow quantum computers to search through an unstructured database with N entries in a time proportional to the square root of N, whereas the best classical
algorithms can only do the same job in a time proportional to N. The Fleming group conjectured that the
way that the exciton was finding its way to the reaction
centre was by implementing such an algorithm.
It seemed a neat solution to the decades-old mystery of how excitons can find their way to a reaction
centre with only minimal energetic cues to tell them
Mysterious ways
Light absorbed by
chlorophyll molecules
creates bound
electron–hole pairs,
the movement of
which we need
quantum mechanics
to understand.
27
Feature: Quantum-mechanical biology
physicsworld.com
Dennis Kunkel Microscopy, Inc./Visuals Unlimited/Corbis
1 Brilliant bacteria
Chlorobidium tepidum bacteria grow in dense mats over hot springs in places such as the
Yellowstone National Park in the US. Light that they absorb creates excitons – bound
electron–hole pairs – that follow a “quantum walk” as they travel to where their energy is
converted to chemical energy.
where to go. Unfortunately, the conjecture is false.
Quantum search algorithms are rather specific beasts,
and the dynamics of excitons sloshing back and forth
between chromophores, while definitely quantum
mechanical, simply did not support quantum search
algorithms because it involves a very specific form of
Hamiltonian, or energy functional, that FMO definitely does not possess.
While investigating the properties of the quantum
excitonic sloshing, however, Aspuru-Guzik and I realized that the exciton was in fact performing a different
type of quantum algorithm called a quantum walk. A
quantum walk is the quantum version of a classical
random walk, in which a particle, or “walker”, takes
steps in randomly chosen directions, like a drunk staggering back and forth along a street. Such a particle will
end up exploring its entire neighbourhood and eventually finding its destination, but it does not do so very
efficiently. A quantum walk takes advantage of the
weird quantum fact that a quantum particle need not
take just one path through the neighbourhood – it can
take all paths simultaneously. Where the particle ends
up derives from the interference between the paths.
Because of this interference, a quantum walker can
make its way to its destination much faster than a classical random walker ever could. For some configurations of paths, such as a tree with N branches, the time
it takes a classical walker to explore the tree is proportional to N, whereas a quantum walker would take a
time that is proportional to the logarithm of N.
Either God is
one great
quantummechanical
engineer or
gazillions of
bacteria did
not die in vain
28
Doing the quantum walk
Starting from the Fleming result, we then used the
experimentally determined Hamiltonian to perform a
simulation of how the exciton in a Chlorobium tepidum
bacterium makes its was through the photocomplex.
As expected, we found that its journey does indeed
follow a quantum walk. However, it is not just any old
quantum walk. The chromophores inhabit a complex
chemical environment, and fluctuations and disorder
from this environment buffet the exciton while it is on
its way to the reaction centre. To understand the effects
of this buffeting, Aspuru-Guzik and I, together with
Masoud Mohseni and Patrick Rebentrost from Harvard, constructed a quantum equation that describes
how the exciton responds to the influence of its environment (New J. Phys. 11 033003). (Independently,
Martin Plenio’s group at Imperial College London and
the University of Ulm developed a similar equation.)
Thanks to the efforts of Klaus Schulten at the University of Illinois at Urbana-Champaign in the US,
Thomas Renger at the University of Linz in Austria, as
well as Fleming and Rienk van Grondelle at the VU
University in Amsterdam in the Netherlands, the molecular structure – including the quantum dynamics – of
photosynthetic complexes such as FMO is known
precisely, which meant that the parameters of our
model could be taken entirely from experiment. In
addition, the form of the interaction between FMO and
its environment is also known, so that the only free variable left in our model was the strength of that interaction, which can be thought of as corresponding to an
effective environmental temperature.
The quantum equation we developed predicted that
at low effective temperature the exciton would take a
coherent quantum walk through the FMO complex.
Because of disorder in the environment, however, this
coherence – rather than leading to more efficient transport – would give rise to destructive interference that
would make transport less efficient, a phenomenon
called Anderson localization. But as the effective temperature of the environment was raised, the resulting
“fuzzing out” of quantum coherence would reduce the
degree of destructive interference, thus yielding high
efficiency as long as sufficient coherence remained to
speed the quantum walk on its way. We dubbed this
effect environmentally assisted quantum transport, or
ENAQT. Finally, at still higher temperatures, quantum
coherence would be almost completely destroyed, drastically decreasing the efficiency of the walk.
Our predictions were borne out by detailed computation (figure 2): at low effective temperatures, the exciton became stuck, taking hundreds of picoseconds to
get through the FMO complex to the reaction centre, if
it got there at all (the lifetime of the exciton is about a
nanosecond). As the effective temperature increased,
the exciton became unstuck and the time it took to
make it through the FMO complex decreased dramatically. Indeed, at the optimal effective temperature, the
probability that the exciton reached the reaction centre
was 100%, while the time of transport was almost as little as 5 ps. But when the temperature again rose above
the optimal temperature, the probability of success fell
once more, thus slowing the transfer time, which eventually reached as much as 500 ps.
Given that our model had essentially no free parameters – there was nothing left for us to tweak – we were
excited to find that it predicted the optimal temperature to be just room temperature; in other words, the
actual operating temperature of the bacteria. Moreover, the optimum was robust: for a range of several
tens of degrees around the optimum, efficiency and
time of transport were close to their optimal values.
From this one can conclude that (depending on one’s
Physics World January 2011
physicsworld.com
2 Quantum walk
1.0
efficiency
0.8
200
100
0.6
50
0.4
20
0.2
0.0
10–4
transfer time (ps)
500
Biophotonics
Optical Filters for Fluorescence Systems
10
5
0.01
1
100
effective temperature
104
106
Certain photosynthetic bacteria transform energy from the Sun into chemical
energy by first converting photons into excitons – an electron bound to a hole. In
Chlorobium tepidum bacteria, these excitons move via a “quantum walk” into an
array of protein molecules known as a Fenna–Matthews–Olson (FMO) complex.
Simulations reveal that, at low temperatures, it takes several hundred picoseconds
(red curve) for an exciton to reach the key “reaction centre” at the heart of the FMO
complex. As the temperature rises, the process eventually becomes 100% efficient
(blue curve) and the time taken falls to just 5 ps. As the temperature rises further,
however, the efficiency drops and the process takes hundreds of times longer.
Physics World January 2011
Emission Filter
(Notchfilter, Bandpass Filter)
Eyepiece
Light source
(Lamp, LED, Laser)
Dichroic Beamsplitter
Excitation Filter
Objective
Excitation Light
Emitted Fluorescence Light
Specimen
Optics Balzers AG Balzers/Liechtenstein
Optics Balzers Jena GmbH Jena/Germany
religious persuasion) either God is one great quantummechanical engineer or gazillions of bacteria did not
die in vain.
Natural computers
Since this initial breakthrough, we and other researchers
have discovered that bacteria and plants are using other
quantum information-processing techniques. Purple
sulphur-breathing bacteria that live near hot ocean
vents, for example, employ sophisticated quantumcoding techniques to make excitons last longer and to
speed their passage to the reaction centre. Green plants
are not immune to the blandishments of quantum coherence either: the energy levels and interaction rates
of their chromophores are apparently carefully tuned
to allow quantum effects to enhance excitonic transfer
rates. We suspect that a wide variety of biological mechanisms, particularly those related to interactions with
light, should show the same sort of environmentally
enhanced quantum efficiency displayed by photosynthesis. Quantum hanky-panky has run amok.
Meanwhile, the discovery that living systems are using
the techniques of quantum computing to improve their
chances of reproducing has had one important benefit
for me personally. For years, when I would give talks on
quantum computing, an audience member might pipe
up with the objection that quantum computing is impossible because if it were possible, then nature would
have already produced a quantum computer via natural
selection. This is a spurious argument. After all, nature
failed to discover the laser. (Of course, one could always
argue that nature evolved human beings, and human
beings then discovered the laser.) Now, however, I can
reply to those naysayers that nature did indeed evolve
quantum computers in the form of the photocomplexes
of bacteria and plants. And – even better – those naturally occurring quantum computers have been working
■
away for more than a billion years.
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