AAWSAP DIRD Quantum Computing and Utilizing Organic Molecules in Automation Technology December 10 2010
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Defense
Intelligence
Reference
Document
Defense Futures
10 December 20 10
! COD: 10 December 2010
DIA-08- 1102-005
Quantum Computing and
Utilizing Organic Molecules in
Automation Technology
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Quantum Computing and Utilizing Organic Molecules in
Automation Technology
The Defense Intelligence Reference Document provides non-substantive but
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Prepared by:
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Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
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Contents
Summary........................................................................................................................ 5
Introduction ................................................................................................................... 7
Ultrafast Computing Power in Aerospace Applications ................................................... 7
Making Digital Circuits Faster..................................................................................... 8
Applications of Quantum Computers ........................................................................ 10
The Closed Box and Fault Tolerance ......................................................................... 11
Scalability ................................................................................................................ 12
Universal Logic ......................................................................................................... 12
Initialization and Measurement................................................................................ 13
The Quantum Dot Approach ................................................................................. 13
Electrostatic Quantum Dots in Graphene .............................................................. 14
Quantum Dots in Graphene Nanoribbons ............................................................. 15
Graphene Disc in Single-Layer Graphene ............................................................. 16
Graphene Disc in Bilayer Graphene ...................................................................... 17
Manipulation of Spin Qubits in Graphene Quantum Dots Relative to GaAs ........... 18
Spin Relaxation and De-phasing in Graphene Quantum Dots ............................... 19
Spin Relaxation Due to Spin-orbit Interaction ...................................................... 20
Research with Graphene Quantum Dots ............................................................... 21
Summary of Additional Inorganic Technologies ....................................................... 21
Photon Technologies ............................................................................................ 21
Ion and Atomic Trap Technologies ....................................................................... 22
Nuclear Magnetic Resonance (NMR) Technologies ............................................... 22
Superconducting Technologies ............................................................................. 22
DNA-based Designs for Molecular Computers ........................................................... 23
DNA Background .................................................................................................. 23
Error Suppression Mechanisms in DNA Self-Assembly .......................................... 28
Self-assembly with DNA-based Microfluidic Devices ............................................ 31
DNA Origami ........................................................................................................ 32
Engineering DNA-Based Logic Gates .................................................................... 35
Logic Operation by Deoxyribozymes .................................................................... 35
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Deoxyribozyme-based Boolean Automata ............................................................ 39
Robotic Bases (The DNA Robot) ........................................................................... 40
DNA Nanomotors.................................................................................................. 41
The Nano Walker; a Spider-like Approach ............................................................ 43
Discussion ................................................................................................................ 45
Conclusion ................................................................................................................ 46
References ................................................................................................................ 48
Figures
Figure 1. Hexagonal structure of graphene..................................................................... 14
Figure 2. Quantum dot in graphene nanoribbon.............................................................. 15
Figure 3. Left; Energy diagram for quantum dot in single-layer graphene. Right; Bound
state levels as function of dot radius............................................................. 16
Figure 4. (a) Color scale plot of the transconductance. (b) One of the vertices of the
honeycomb structure at Vsd = 800 µV: Charge stability diagrams for series-
coupled quantum dots...................................................................................... 16
Figure 5. Quantum dot in bilayer graphene..................................................................... 17
Figure 6. Bilayer graphene tunneling device structure................................................. 18
Figure 7. Qubit piano........................................................................................................19
Figure 8. Long distance coupling of three graphene qubits ............................................ 19
Figure 9. A DNA nanomachine driven by repeated sequential addition of DNA control
strands.............................................................................................................. 23
Figure 10. Recombinant DNA molecule with restriction enzyme cleavage and sticky end
ligation....................................................................................................... 25
Figure 11. Two symmetric DNA nanomotifs and the crystals grown using them .......... 26
Figure 12. (top a-e) The XOR Cellular Automaton and Its Implementation by Tile-Based
Self-Assembly............................................................................................. 27
Figure 12 (continued). (bottom a-e) AFM Images of Algorithmic Self-assembly of
Sierpinski Triangle Crystals ........................................................................... 28
Figure 13. Error Suppression with the PTM Method ........................................................ 30
Figure 14. Simulation results of growth in (A} the OTM, (B) the PTM, and (C} the LTM.30
Figure 15. Three Types of Error in DNA Tile Self-assembly (a) Growth error (b) Facet
error (c) Nucleation error. Red lines indicate the mismatched sides .......... 31
Figure 16. Micro-fluidic device for DNA tile self-assembly............................................ 32
Figure 17. (A) Schematic diagram of a 16-column microfluidic DNA synthesizer
(B) Close up schematic of the column array............................................... 33
Figure 18. Design of DNA origami ................................................................................ 34
Figure 19. Several DNA origami folding paths.............................................................. 34
Figure 20. Functional design of a DNA based logic gate............................................... 37
Figure 21. Simplistic rendering of a DNA logic gate...................................................... 38
Figure 22. Basic gate structures, derived from allosterically regulated deoxyribozyme
E6, for playing tic-tac-toe against a human opponent................................ 39
Figure 23. First Generation (MAYA I) DNA-based Logic Circuit that plays tic-tac-toe ... 40
Figure 24. A single molecule DNA-based nanomotor driven by photons....................... 42
Figure 25. AFM Scan of walkers as they follow a track pattern places on the surface.. 43
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Figure 26. The Nano walker made at Columbia University is a protein molecule
decorated with three legs--single-stranded DNAzymes, synthetic DNA
molecules that act as enzymes and catalyze a reaction............................. 44
Figure 27. Deoxyribozyme-based molecular walker and origami prescriptive landscape.
..................................................................................................................................... 45
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Quantum Computing and Utilizing Organic Molecules in
Automation Technology
Summary
Powerful onboard computing hardware is a desired option for future space travel. Without
large data processing capability, the copious amounts of data acquired during flight from
astronomical sensors as well as crew and vehicle sensors will need to be sent back to
earthbound machines for processing, introducing delays measured in hours for routine
calculations. Current commercial computer hardware trajectories in silicon substrate
semiconductors are not likely to produce a radiation-hard or small and portable
supercomputer without significant mission-specific alteration. Alternatives to traditional
computing technology include computers based on entangled quantum states and molecular
computing hardware based on DNA molecules.
Included in th is review is significant introduction to the necessary elements of quantum
computing and a summary of the state-of-the-art technologies. Following is background on
DNA and production of engineered DNA chains. Finally, DNA logic gates are presented along
with a treatment of nanomachines that will repair DNA circuitry. Forecasts of technology
development in the 10-20 and 40-year horizons are included along the way, as well as
summary discussion and a conclusion.
The first operating quantum computers capable of solving real-world problems will
commence within 10 years and be based on ion trap technology. This is entirely based on the
amount of research resources dedicated to the problem and the fact that there appear to
only be eng ineering challenges remaining. Atomic and ion traps require very substantial
cryogenic and EM shielding systems and are not practical for space travel.
Pure photonic technologies available today have difficulty with both miniaturization and
scalability. However, the amount of active work in the field makes a disruptive advance likely
in the 10-year t imeframe . Optical computers will likely be rea li zed in the 20-year horizon;
however, the very powerful promise of quantum computing will still have issues with photon
loss in any solid state device. The 40 -year horizon will see photon technologies play an
essential but supporting role in distributed quantum computing. Realized all-optical non
quantum systems will have radiation tolerance advantages over current semiconductor
technology and are likely to augment or even replace general - purpose computing devices for
space travel.
Hybrid designs uti lizing arrays of quantum dots and photon communication channels will be
an option for space travel supercomputing on the 40-year timescale. These systems operate
at attainable temperatures without cryonics, and require no more shield ing than humans. It
is likely that spintronics will be an essential ingredient.
Simple organic computing based on DNA tiles will be realized in the next 20 years. On the
40-year time horizon, useful DNA-based devices will be essential space exploration tools.
These could take the form of orbital-del ivered wireless sensors searching planetary/asteroid
features or for essential compounds such as high concentrations of water. DNA computers
will also be realized on the 40-year timeline . Their advantage over solid state devices will be
the ability to repair nanoscale elements damaged in normal use or by cosmic radiation.
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These will not be the fastest systems in the astro-arsenal, but self-repair may make them
the most robust.
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INTRODUCTION
Computers today are not what they used to be. In the 17 th century, a computer was merely a
person who performs computations. In this sense, the first computers were universally
programmable and were ultimately utilizing organic (DNA) hardware architecture. The
modern sense of a computer as a machine that manipulates input to produce deterministic
output emerged from the work of Turing in the 1930s. A Turing machine consists of four
parts: tape containing cells of symbols, read head, action table, and state register. In
operation, the state register is initialized, the first cell of the tape is read by the head, the
table translates the symbol into an action in the state register, and the tape is advanced to
read the next symbol. The read, action, advance tape loop is repeated until the program
ends.(1) Any calculation a modern digital computer can perform can be accomplished using a
Turing machine .a
Modern digital processing hardware, first used in the ENIAC in the 1950s, is based on logic
gates. All functions of a computer consist of the basic logic elements AND, OR, NOT, etc.
These are accomplished electronically by producing logic gates, combinations of transistors
that perform the logic function on input data. A common exercise in didactic digital logic
pedagogy is to design all of the basic logic gates using only NANO or NOR gates; thus, any
hardware element that can execute the NAND function can build a complete computer.b
Optimum designs are regularly more elegant than combining a single two-input gate, but it is
sufficient as proof of principle for any architecture to be able to produce an inverter and a
simple logic gate (AND/OR).
The quest for faster computing can be accomplished by making current hardware
architecture faster, or by designing new hardware based on different architecture that solves
the calculation in fewer steps. The current treatise concentrates on the latter, dramatically
changing the architecture of modern computers to perform calculations in a different manner.
Two methods are explored: that of creating logic gates, and that of creating a general Turing
machine. The second of these is explored in the context of quantum computing with an
emphasis on organ ic molecules as a core technology. Designs of logic gates utilizing DNA are
covered. Background on all these areas of research is included first. Finally, DNA machines
that can assemble and repair DNA technology are outlined.
ULTRAFAST COMPUTING POWER IN AEROSPACE
APPLICATIONS
The history of manned spaceflight does not include powerful computers as integrated
companions; space-borne supercomputers have so far been reserved to the world of science
fiction. The main issue on space stations has been radiation hardness, while the main issue
on vehicles such as the space shuttle has been safety. The amount of testing required for a
microprocessor to be certified for space precludes the most current technology from
becoming astro-worthy. Indeed, the most powerful general purpose computers riding in the
shuttle are the laptops the astronauts bring with them.
• The complete history of computers up until the 1950s is a fascinating story. A good summary of this history is ava ilable
in the Wikipedia entries for "computer" and " Turing machine" among other places. The model of a Turing machine
presented is simplified .
b The didactic exercise is usual ly followed by a laboratory exercise on breadboards and measurement of the truth table .
NAND gates are popular because they are particularly simple to manufacture with current technology.
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The first challenge to overcome in supercomputing in space is radiation causing temporary
and permanent errors in calculation. The current approach is to make the solid state
components radiation-hard, a time-consuming and costly process. An alternate approach is
to use multiple commercial-off-the-shelf (COTS) components in parallel architecture.
George's group at the University of Florida pursued this approach with earthbound success. (2,
3) A good question arises that if 50 years of space travel hasn't required one onboard
supercomputer, why start now? It seems NASA asked this question as well and, after years
of preparation, cancelled the space test of the technology in late 2009.
Regardless of the need for current missions, one can imagine many future applications where
it would be more convenient to data process on long space missions without downloading
data to Earth-based system and uploading the results. This is especially true for long
duration spaceflight where communication delays could be minutes to hours (Mars ~13
minutes, Jupiter ~45 minutes, and Neptune ~4 hours). Spacecraft active in the 40-year
horizon will require supercomputing technology on-board to process all of the data to be
acquired during flight. This includes astronomical data as well as ship and crew data. c
Example missions include Mars with a goal to analyze the planet using thousands of semi
autonomous sensors or millions of independent, wirelessly communicating nanomachines
("magic dust"). In such scenarios, it is not necessarily numbers that need lots of crunching,
but algorithms that need to be run on powerful systems that could be non -traditional in their
design; for example, massively parallel.
MAKING DIGITAL CIRCUITS FASTER
In consideration of the underlying physics in the electrodynamics of transistor operation, the
scale of the constituent elements dominates the type of analyses required. In the
macroscopic regime, constituents are measured in microns or larger, properties are
dominated by well-defined statistical averages in bulk matter, and non-classical effects due
to the underlying fact that all particles involved in the interactions are really fluctuations
within a relativistic quantum field can safely be ignored. For 40 years making a fast transistor
was primarily accomplished by avoiding saturation between states in an arrangement known
as emitter coupled logic (ECL, pronounced "ek-el"). The ECL family of logic circuits could
achieve sub-nanosecond switching times and dominated the leading-edge of high-speed
computing up until the early 1990s. The drawback of ECL was that without reaching
saturation, no depletion zone existed within the individual transistors and thus current flowed
through much of the device hardware instead of the usual small leakage current associated
with gates in a defined state. ECL's large current flow makes cooling and power requirements
challenging, especially for space-based platforms where heat dissipation is an issue.
Saturation technologies, primarily MOSFET-based, surpassed the speed of high-current
devices when the footprint of individual elements became small enough that a change
between depletion states could be quickly stabilized, given the comparably slow drift
velocities of primary charge carriers. These CMOS-family technology devices are the current
state-of-the-art in integrated circuits, and device speed increases, until recently, were
dominated by making the circuit elements smaller (see below). Intel produces high volume
!Cs with circuit elements size at 32 nm, and has demonstrated memory elements in 22 nm
c The scenario of several massive data acqu isition channels was presented at the Workshop for Technology Brea kthroughs
fo r Human Space Exploration , June 17 th 2010, NASA Headquarters, Washington DC . Navigation is and will continue to be
handled by traditional computing mach ines - it is only rocket science that needs to be solved for navigation purposes.
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pitch.d By comparison, atomic diameters range from around 0.1 nm to 0.5 nm, with silicon
~0.2 nm, or only a factor of 100 smaller.
As circuit elements decrease in size, the number of atoms making up the bulk materials
decreases and ignoring individual quantum effects becomes problematic. This is the
mesoscopic scale. At this size, quantum effects can introduce noise into the circuit as the
unpredictablee nature of the underlying wave functions. Once the circuit size shrinks to only a
few atoms, quantum effects will emerge from the noise domain to dominate the electrical
behavior. It is thought that exploiting rather than avoiding quantum phenomena may prove
useful in this regime for inorganic technologies.
Following Moore's law, in less than 10 years inorganic circuit elements will be less than 5x5
molecules in 2-D extent. (Molecular machines built of organic components, primarily DNA,
are discussed in a later section.) Shrinking traditional silicon-based general-processing
technology to this microscopic scale is one motivation for developing new types of machines
based on quantum phenomena, but it is not the on ly one. Smaller circuit elements decreased
the settling time of transistors and thus gates on CPUs, allowing increasing clock speed (the
CPU can execute the next instruction with shorter delay from the last instruction). CPUs
today get most of their performance with parallel architecture, executing several instructions
at once in different pipelines. Using smaller circuitry in general consumes less power, and
this allows more parallel elements to be packed into a reasonable wattage package. The
march toward smaller circuitry is continuing unabated so plann ing for the eventual quantum
dominant characteristics is essential.
It is common to use the analogy of the laser to elucidate the application developments
possible with quantum computing. In one sense, the laser is just another hardware
technology that makes light. Earlier light technologies include organic-fueled fire ( ~50,000
BC), incandescent bulbs (early 19th c.), and fluorescent chambers (mid-19 th c.). The light
source to utilize is not governed by the highness of the technology, but by requirements of
the application. One can read by laser light, but older and cheaper incandescent light will
provide superior perceptible illumination to a page. Traditional semiconductor-based
computing is cheap and plenty powerful for controlling navigation or driving ship status
displays.
The laser analogy is further revealing in that it is quantum effects producing a special kind of
light that is coherent. Coherent light is single wavelength with all photons travelling in the
same direction .f This coherence is a natural consequence of conservation of momentum in
the absorption/emission process. (4) Coherent light is very useful for some applications that
require low dispersion; for example, bouncing a beam off of a mirror on the moon, or the
more pedestrian pinpoint highlight of a projected PowerPoint presentation.
The practical uses of the laser are not universally bigger or smaller, faster or slower, or more
or less energy efficient than the other hardware technologies that produce light, they are just
different. Similarly, when we think of what hardware and applications will arise for quantum
computing, they too are not necessarily bigger, smaller, or faster than traditional methods;
they are just different, and many could not be accomplished with traditional technologies. (5)
d Pitch is the distance between repeat circuit elements. What is most interesting about the 22 nm technology is that it was
produced with 192 nm lithography.
• At the mesoscopic scale, individua l wave functions are not prepared a priori or controlled in their propagation . Some of
the noise components are correlated .
'Laser light is actually very narrow bandwidth rather than single-valued.
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APPLICATIONS OF QUANTUM COMPUTERS
Although smaller circuitry and supercomputing is a motivator, the driving application behind
quantum computing is cryptography. First, there is cracking cipher codes. The vast majority
of secured communications utilize a method known as publ ic-key cryptography . In this
method, the code is based on the prime number factors of a very large integer which is
publically available. The private key is one of the integer factors and this allows the receiver
of information to decipher the code easily. The strength of this technique is that traditional
computer algorithms will take a long time to guess the correct factors of the public key, on
the order of months. 9 Traditional brute force methods require a number of steps that
increase as an exponential function of the size of the public key. However, in 1994 Shor
presented a quantum algorithm that would only require a polynomial number of steps, thus
dramatically decreasing the requ ired time to factor, assuming a quantum computer would
ever be physically realized. (6) This speedup is primarily due to the nature of quantum
waves; specifically, they can follow several parallel paths instead of the usual stepwise
procedural execution of instructions. This acceleration by superposition concept is more
easily understood in a random search of data. Consider an algorithm that has a 50%
probability to locate a specific phone number in a database of N phone numbers by a random
search . The procedural algorithm on average will require O.SN inquiries to locate the correct
number. A quantum algorithm on the other hand can be devised that accumulates
information by examining multiple numbers with each step. Such a scheme has been shown
to reduce the number of examinations required to .JN. (7, 8) The superposition of states
allows examination and processing of several tape cells simultaneously in a Turing-inspired
machine.
Second, there is quantum communication. Once public key encryption is easily broken by the
quantum computer, a new cipher needs to repla ce it. The canonical quantum commun ication
experiment defines a sender, Bob, and a receiver, Alice. In most scenarios, Alice and Bob
communicate over a distance using entangled particles and a trad itional open line. The open
line relays information about measurement settings, but is useless to an observer without
access to the entangled wave function (entanglement is discussed below, and the open line
information is an analogue to the public key of current ciphers). The other advantage of this
setup is that almost any disturbance in the commun ication line between Alice and Bob would
destroy entanglement and thus the information would be lost instead of intercepted.
Additional archetypical participants in a communications experiment/scenario follow the
English alphabet: Charlie (or Chuck if his intent is malicious), Dave, Eve, etc. Quantum
communication is thus an application replacing one performed by a general purpose
computing machine ; the classical and quantum systems do not operate in similar fashion
other than the function of securely transmitting information. Additionally, quantum
communication has been suggested as a method to connect isolated quantum systems
without disturbing closed box requirements like classical interventions would. (9, 10)
Beyond cryptography is a third application, quantum metrology, where time and/or distance
are measured to an extremely high accuracy . A fourth obvious application is simulation of
quantum systems. (11, 12)
9 Or hours if one has farms of supercomputers. The point is that the value of most communication is much smaller than
the cost to decipher by brute force. Th e 128-bit web standard is a compromise between security and speed.
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THE CLOSED BOX AND FAULT TOLERANCE
In traditional silicon transistor circuits, once a bit is set to 1 or O by a gate or other device
locking the output voltage, that value is expected to remain through subsequent clock cycles
until deterministically changed.h Additionally, traditional circuits behave by the same rules for
each clock cycle; that is, as more information is processed, repeated gate operation does not
deteriorate the bit latching mechanism. This behavior is achieved by constantly providing
energy to the circuits. Any interruption in this constant need for power from the outside and
the integrity of the information in the computing circuit is lost. 1
A fundamental principle of quantum mechanics is that any external influence on a system
necessarily disturbs the state of that system. This influence could be external disruption or
internal leakage - either interaction will change the internal quantum state. This destructive
process is known as decoherence. External influences will disturb the system and thus the
circuits need to be isolated from the rest of the universe, also known as the 'closed box'
requirement.
Trial to trial variations in a quantum circuit produce an increasing deviation from an initial
phase as the wave function evolves. This trial-to-trial deviation causes decoherence on a
timescale termed T2*. Although a single trial in a quantum circuit could retain coherence
longer than T2*, absent external influence the isolated internal circuit components must
eventually come to thermal equilibrium through random processes: this occurs on timescale
TL Moreover, the closed box cannot be perfect since a useful device requires some kind of
input and output, thus some small interaction with the external environment is necessary.
Random interactions with the environment from this isolation 'leakage' will dephase internal
signals on timescale T2. These three time constants that describe the internal signal decays
are very similar to the same named quantities in nuclear magnetic resonance (NMR). NMR is
indeed a technology path under development for quantum circuits. Each technology and
hardware design will be characterized in its isolation from external and internal influences by
T2* (stable repeatability), Tl (resistance to entropy), and T2 (isolation from the rest of the
universe).
No design can be completely free of decoherence and the next consideration is how much
decoherence is acceptable, or more precisely, what is the fault tolerance threshold for
successful operation? Fault tolerance isn't much of a consideration in traditional processing
architecture,i although it is a major consideration in storage and communication of
information. To illustrate fault tolerance, consider a scheme of hard disk storage
configuration where each 8-bit byte is written across 9 disks in a stripe-set configuration
(one bit per disk, read in parallel). The extra disk holds parity information about the byte.
Consecutive bytes shift the location of all bits one disk so the parity information isn't all
stored on the same disk.k In the event one disk fails, each byte can be reconstructed from
the other 8 disks using a software algorithm that automatically starts when the disk failure is
detected. The broken hardware ca n be replaced and the data reconstructed while the system
is operating in this slower 'limp' mode. Th is storage system is said to be fault tolerant. The
h For those new to quantum phenomena, it may seem redundant to use the phrase "deterministically changed ." The
phrase emphasizes the point that absent any error, classical circuits are always changed by intent, while quantum circuits
include the element of random occurrence .
; Here we refer to the processing circuits themselves. Some types of memory and long term storage can of course hold
information in isolation indefinitely.
J A non-determ inistic result in processing hardware causes a fatal error in current designs.
k The bitwise stripe-set is instructive on the principle at hand, but for engineering considerations, more complex
configurations are used in practice. See Wikipedia " RAID " for actual data distribution schemes .
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drive failure detection and algorithm takeover in the readout phase is the error correction
scheme.
In a quantum system the error correction is accomplished in a similar manner; that is, the
state of a qubit is defined across multiple subspaces of the logic space and then several
measurements are performed on the subspace that do not disturb the state itself. The
original state can be reconstructed by the partial measurement. As an illustrative example
consider the one-qubit space defined by an electron spin-up or spin-down. First, re-define
this 1-d state in an oblique three-dimensional system such that spin-up is in the (+x,+y,+z)
octant, and spin down is thus in the (-x,-y,-z) octant. If one measures x as positive the
original state was up; measuring x and y both positive provides additional assurance the
state was actually up. Measuring x and y different allows z as a tie-breaker. In this example
system, 33% error rates are allowed. Of course realizable systems are more complex and
only tolerate error rates in the 3% range. This difference is mainly due to the need to disturb
the system as little as possible in what is known as a quantum non-demolition measurement
(a QND measurement). (13, 14) In summary, fault tolerance is possible if a QND mechanism
to measure qubits can be demonstrated.
SCALABILITY
Once a closed box has been constructed, the next consideration in successful quantum
information processing (QIP) technology is whether circuit elements are scalable. That is,
whether elements shown to perform as quantum bits can be combined into larger circuits at
a reasonable cost of resources (computation time, decoherence time, physical space, or
required power). The exact nature of the required engineering scale-up is specific to each
technology.
The unit of QIP (quantum information processing) is the qubit. 1 Different from digital logic,
quantum mechanics increases the information content in N qubits through superposition.
That is, quantum waves can travel through several paths and contain a superposition of
states, increasing the amount of information in each channel. Furthermore, any system of N
qubits can have degrees of entanglement. This entanglement makes the simple example
state (1,0,0) different from (1,0,0) with (x,0,0) entangled, different from (1,0,0) with (1,0,x)
entangled, etc. When there are 4 qubits, entanglement can occur with 2, 3 or all 4 bits, as
well as 2 with 2. The logic space quickly grows to Bunyanesque proportions and is easily
outside of the rea lm of simulation or even representation by Nor even N2 classical bits.
Considering that one could start with qupits or qudits (see footnote I) it is quickly obvious
that quantum computers have enormous computational potential when scalable.
UNIVERSAL LOGIC
The very large number of possible states of a quantum computer spans what is known in
mathematics as a Hilbert space, a generalized version of Euclidean space with arbitrary
(finite or infinite) dimension (Euclidean space having 3 dimensions). The concept of a
universal logic requires that this large Hilbert space be accessible with a finite set of control
operations. For most designs these control operations are small in number and are the
quantum analogues of digital gates performing operations on qubits.
1 For pedagogy, the discussion is limited to qbits ; however,
p and d states could also be used as a basic unit (qpits or
qdits) thus greatly expanding the possible Information content In a single channel.
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Two special schemes that operate differently than digital analogues of gate-based technology
are adiabatic and cluster-state quantum computation . In an adiabatic design, the answer is
the ground state of a complex network of interactions and the interactions are slowly turned
on to evolve qubits from the initial state to the final ground state . In the cluster-state
scheme, the system is placed in a particular state through use of a small set of control gates
and the output is repeatedly measured using arb itrary basis (the fault-tolerance mechanism).
In the adiabatic case, the computation is 'programmed' in the setup of interactions. In the
cluster-state case, the calculation produces a superposition of states that need several
measurements to ensure correct interpretation. Both schemes have been shown to be
equivalent to gate-based circuit technologies. (15-17)
INITIALIZATION AND MEASUREMENT
Implied in the discussions above is the ability to set the quantum computer into a known
initial state, measure various states dur ing computation if needed, and output the final state.
These processes can be tricky while maintaining isolation and low entropy. The initialization
and measurement techniques are discussed with each technology.
The Quantum Dot Approach
A major obstacle in the quest to design and construct a radically new kind of inorganic
quantum computer has been finding a way to manipulate the single electrons that are likely
to constitute the new machines' qubits . The ability to manipulate and alter a single electron
without disturbing the trillions of electrons in the immed iate surroundings has become a
research focus for many studies. (18) (19)(20) A cand idate is to utilize properties of the
intrinsic spin of the electron. In 1925, Austrian physicist Wolfgang Pauli proposed that an
electron in a quantum state can assume only one of two states-"spin-up" or "spin down."
(21) One approach to manipulate spin state and electrical charge independently for use in
quantum computing has arisen in the quantum dot.
Quantum dots (QDs) are tiny islands within a solid state lattice where electrons experience
charg ing effects as well as quantum confinement, like an electron in an energy level around a
nucleus. (22) Besides fundamental insights into matter, these artificial atoms can also work
as building blocks for the control of electronics at the single electron level. The so called
single-electron transistors are able to switch on and off electron transport through a dot by
means of electrical gates using the effect of Coulomb blockade.
Conversely, one can use spin rather than charge to control electrical conduction in
mesoscopic-scale electronics; such "spin-controlled electronic devices," and their
development and study, are termed spintronics. (23) Exploiting the spin degree of freedom,
a quantum dot can act as a spin filter (24)(25)(26) or as a spin-blockade device. (27)
Quantum dots have been proposed as host for an electron - spin qubit. Arrays of such
quantum dots with tunable tunnel-couplings between them would work as a universal
quantum computer. (28) Recent progress in this field using GaAs-based two-dimensional
electron gases is impressive (29), though decoherence can arise from spin -orbit and
hyperfine interaction with the nuclear-spin(s) of the host material (30) (31) (32). These
decoherence effects can be reduced by using a lattice structure with low magnetic moment.
Carbon has near zero magnetic moment due to the six each paired protons and neutrons in
carbon isotope 12C; a small net magnetic moment comes from the natural 1% contamination
of 13C.
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Electrostatic Quantum Dots in Graphene
The graphene form of carbon, a hexagonal sheet array single atom thick, is a candidate
substrate for quantum dots. However, two fundamental challenges need to be overcome
before graphene can be used to form and operate spin qubits. First, it is difficult to create a
tunable quantum dot in graphene because of the absence of an energy gap in the band
spectrum. Electrons in such low energy gap materials exhibit Klein tunneling, and
complicating efforts to confine particles (33) (34) (35). Second, due to the valley degeneracy
that exists in graphene, (36)(37)(38) it is non-trivial to form two-qubit gates using
Heisenberg exchange coupling for spins in tunnel-coupled dots. Attempts have been made to
solve the first problem, such as to use suitable transverse states in graphene ribbons to
confine electrons (39), to combine single and bilayer regions of graphene (40), or to achieve
confinement by using inhomogeneous magnetic fields. ( 41) The second problem has only
been realized recently, and scientists have created a method to confine the electrons in a
unique valley through suitable transverse states in a ribbon of graphene which appears to
overcome these limitations. (42) The approach as used in GaAs quantum dots ( 43) is not
possible due to Klein tunneling.
Figure 1. Hexagonal structure of graphene.
Several ways are possible to induce a gap in bulk graphene. In general, quantum
confinement can lead to the opening of a gap in ribbons (44) (45) (46). Within the tight
binding approximation of graphene, armchair boundary conditions can lead to an insulator
and gate-tunable quantum dots (Figure 2).
Another promising direction is to start with bulk grapheme and induce a gap via the
interaction with a substrate. (47)(48)(49) Three quantum dot architectures that allow for
bound states tunable by electrostatic fields are: (i) graphene nanoribbons with armchair
terminated boundaries, (ii) discs in single-layer graphene, and (iii) discs in bilayer graphene.
Special emphasis is given on the ability to controllably break the valley degeneracy, a
prerequisite for two-qubit spintronic gates (50) (51) in graphene.
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Quantum Dots in Graphene Nanoribbons
Graphene ribbons are one dimensional stripes of graphene. They can be considered as
unfolded carbon nanotubes. Graphene ribbons were proposed by Nakada et al in 1996 (52).
Nakada used the same single orbital tight-binding model that successfully portrays two
dimensional graphene as a semimetal; graphene ribbons are either metallic or
semiconducting depending on their crystallographic orientation and width. More realistic
calculations using the Hubbard model in a mean field approximation and density functional
calculations show that zigzag ribbons are insulating due to the magnetization of their edges
with opposite spin orientation in each edge. It has been found that this anti-ferromagnetic
insulator phase has a hidden underlying ferroelectric order that can be described as excitonic
insulator whose order parameter is the spin-resolved dipole operator, the analog of the spin
current operator (53). Long (gl µm) graphene nanoconstrictions display gapped behavior:
conduction is suppressed by several orders of magnitude for a wide range of gate voltages
around the Dirac point, and for tens of millivolts of source-drain bias (54) (55).
Figure 2. Quantum dot in graphene nanoribbon. A ribbon of graphene with semi-conducting
armchair boundaries is schematically shown. Two barrier gates (blue) define the rectangular
size of the quantum dot (with width W and length L). A back gate (red) allows one to shift the
energy levels in the dot. Two or more quantum dots of this type can be easily put in series in a
single nanoribbon.
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u
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Figure 3. Left; Energy diagram for quantum dot in single-layer graphene. Right; Bound state
levels as function of dot radius.
Graphene Disc in Single-Layer Graphene
Single layer graphene is attracting attention because its charge carriers are massless,
relativistic particles (56). The relativistic effects result from a unique, zero-gap band
structure that leads to quantum states described by the two-component Dirac-Weyl equation.
This allows relativistic physics to be explored in a solid state system and has many potential
applications ranging from high frequency electronics (57) to quantum computing (58).
Graphene dots can be formed from external potentials or nanocrystals but this work is only
concerned with external potentials. The physics of nanocrystals has been discussed recently
(59) (60) and is different from the situation treated here. The quantum states, in external
potentials are quasi-bound: they have a low amplitude oscillatory tail and are similar to the
scattering resonances stud ied in undergraduate physics. A perpendicular magnetic field
enhances the localization of these states (61) and true bound states can occur in graphene
dots defined by a spatially non-uniform field (62). So a magnetic vector potential has a
localizing effect that tends to cancel the delocalizing effect of a scalar potential.
dl/dVg1(nS)
(a) 0 0 ,◄ 0.8
(b) /[pA]
800
1900
550
1880
5'
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>E
- 500 - 1860
-::.";l, >~
1&40
450
1820
400
300 400 500 600 1380 1400 1420 1440 1460 1480
V91 [mV] V91 [mV]
Figure 4. (a) Color scale plot of the transconductance. (b) One of the vertices of the honeycomb
structure at Vsd = 800 1,1V: Charge stability diagrams for series-coupled quantum dots.
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Graphene Disc in Bilayer Graphene
Bilayer graphene is the two-layer analog of the single layer. The two sublattices are coupled
by the so-called Bernal stacking. A voltage V between the two layers breaks inversion
symmetry (like the mass term ti in the single layer) and opens a gap proportional to the
voltage. In addition, the combination of a top gate and a back gate allows tuning the gap and
the average potential U(r) independently.
A central issue, from a computational electronics perspective, is to quantitatively study the
condensed state. In materials-based device models, one has an underlying Hamiltonian, such
as an ab initio Hamiltonian .m
In principle, the excitonic condensate emerges from the interacting particles described by the
Hamiltonian. It is shown that both true bound states and quasi-bound states occur,
depending on the form of the potentials. In add ition, there is a third and most interesting
possibility where the character of the states depends on the parameters of the potentials and
can be controlled at will. A confinement-de-confinement transition then occurs in which the
character of the states changes from oscillatory to exponential as in the Klein paradox for
particles with mass. This gives a way of probing the Klein paradox experimentally in a solid
state system and numerical studies of the quantum states in a realistic dot model show it is
feasible. Further, the same effect could be used to fabricate a graphene dot which has true
bound states. This only requires a uniform magnetic field and a gate which can be made
lithographically, a geometry that is much easier to fabricate than the non-uniform magnetic
field geometry.
The relativistic nature of the transmission, exactly 100%, does not depend on E and Vo is a
consequence of the zero mass. If the particles had mass mo, the energy-momentum relation
would be (E - V) 2 - p 2c2 = mo 2c4 and the amplitudes of the wave function components in
equations of motion would depend on k or k' and mo . Then the right side amplitude in
equations would be different from the left side amplitude, so a reflected wave would have to
be introduced to satisfy the boundary condition at x = 0 and the transmission coefficient
would not be 100%.
bilayer aph · ne op gat
f
+ + + + + + + +
Figure 5. Quantum dot in bilayer graphene .
m Ab initio Hamiltonian is one derived from first principles.
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Figure 6. Bilayer graphene tunneling device structure. Two sheets of graphene
are separated by a one-nanometer thick insulating of graphene.
Manipulation of Spin Qubits in Graphene Quantum Dots Relative to GaAs
For universal quantum computing, single-qubit and two-qubit manipulations are necessary.
Single-qubit rotations of spin qubits are naturally done by electron spin resonance (ESR) (63)
and by electric- dipole-ind uced spin resonance (EDSR) (64). The Rabi frequency faabl at which
the qubit rotates, for instance, in the ESR experiment (65) is proportional to the electron spin
g-factor, faabi = gµsBac/2h where µs is the Bohr magneton and Bae the external oscillating
magnetic field used to rotate the spin. Notably, the electron spin g-factor differs for different
materials . In GaAs quantum dots, it has been measured to be lg I < 0.43 (66) whereas, in
graphene quantum dots, it has been determined to be close to lg I = 2. (67) Thus, it is
possible to rotate t he electron spin in graphene quantum dots using ESR about five times
faster than in GaAs quantum dots using the same field strength of the external oscillating
magnetic field. This is an important gain because all qubit manipulations need to be done
fast to avoid decoherence and implement fault-tolerant quantum computing (68).
Another important advantage of graphene spin qubits is related to the small band gap in
graphene nanoribbons . (For a ribbon width of about 30nm, the band gap can be estimated to
be of the order of 60 meV.) This fact yields additional flexibility for two-qubit operations.
Two-qubit operations are usually done via the Heisenberg exchange interaction (69). The
tunneling matrix element can, however, be easily tuned by increasing or decreasing the
overlap of the wave functions of the electrons in the two quantum dots. In graphene or any
small band gap semiconductor, this manipulation can be done in two distinct ways: either
through tunneling via conduction band states (i.e., normal tunneling) or through tu nneling
via valence band states (i.e., Klein tunneli ng) . This has been predicted for graphene
nanoribbons and experimentally realized in carbon nanotube quantum dots in (70)(71).
The most important physical consequence of this additional flexibility is the appearance of a
new type of long-distance coupling between graphene spin qubits as illustrated in Figure 8.
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By means of Klein tunneling, two distant qubits can be strongly coupled without touching the
states of intermediate qubits that might be located between the two. Thus, a ribbon of
graphene hosting many spin qubits in a line can be viewed as a qubit piano where any two of
them can be entangled with leaving the states of the others unchanged; see Figure 7.
Interestingly, this feature, i.e., the availability of non-local interactions, is important for
quantum error correction since it raises the threshold for fault-tolerant quantum computing
(72).
Figure 7. Qubit piano . Illustration of many spin qubits in a line hosted within a
graphene nanoribbon. Quantum dots are red bars and barrier regions are blue
bars. Different spin qubits that are strongly coupled to each other via Klein
tunneling are marked with the same color.
Figure 8. Long distance coupling of three graphene qubits.
Spin Relaxation and De-phasing in Graphene Quantum Dots
Why can we expect stable spin qubits in graphene quantum dots? There is hope that spin
relaxation and dephasing will be very weak in graphene for the following reasons: (i) Carbon
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is a light element with atomic number 6. Hence, its atomic spin-orbit interaction is weak as
compared to heavier elements. However, such a statement should be taken with care
because, in the solid state, spin-orbit coupling is oftentimes dominated by bulk inversion or
structure inversion asymmetry. Therefore, crystal structures of light elements can (under
certain circumstances) exhibit rather strong spin-orbit coupling.
Prime examples are carbon nanotubes where theory predicted a substantial spin-orbit
coupling (a few hundred µeV) due to the curvature of the tube (73) (74 )(75) which has been
nicely confirmed in recent transport experiments on carbon nanotube quantum dots (76).
Since the surface of graphene is less curved than that of carbon nanotubes, the spin-orbit
coupling in graphene - due to ripples - should still be rather weak (roughly ten times less
than the spin -orbit coupling due to curvature in carbon nanotubes (77)). (ii) Carbon has two
stable isotopes: 12C and 13C. The natural abundance is 99% 12C and 1% 13C. Since 12C
has nuclear-spin O and 13C has nuclear-spin 1/2, the electron spin of the qubit can only
interact with 1% of the nuclei via hyperfine interaction. This ratio can even be further
decreased because it is possible to artificially make 12C-enriched graphene.
Spin Relaxation Due to Spin-orbit Interaction
The spin-orbit coupling arises from the band structure and is enhanced by ripples in the
graphene sheet. The orbital motion is influenced by scattering centers and ripple-induced
gauge fields. Spin relaxation due to Elliot-Yafet and Dyakonov-Perel mechanisms and gauge
fields in combination with spin-orbit coupling are discussed. In intrinsic graphene, the
Dyakonov-Perel mechanism and spin flip due to gauge fields dominate and the spin-fl ip
relaxation time is inversely proportional to the elastic scattering time. The spin-relaxation
anisotropy depends on an intricate competition between these mechanisms.
As Pauli noted, when an electron is in a quantum state it can simultaneously be partially in
the spin up state and partially in the spin down state. During this phenomenon known as
"superposition states" an electron can exist in a free spin cycle oscillating between the up
and down states. A qubit based on the spin of an electron could have nearly limitless
potential because it is neither strictly on or off. Recently, researchers at Princeton University
discovered how to manipulate a single electron without disrupting any surrounding electrons
(78) . By utilizing an interferometer technique where one or two electrons are trapped in
microscopic corrals that are created by applying voltage to miniscule electrodes, "spin qubits"
were formed. This effort is ground-breaking in that previous research utilized techniques
where the electrons were exposed to microwave radiation.
The previous method was ineffective to manipulate individual spin qubits because the
microwave was incapable of isolating to only a single electron. Whereas commonly used
single-spin rotation mechanisms rely on gigahertz frequency magnetic fields, the coherent
rotations between S and T + demonstrated here occur on a nanosecond time scale set by the
Zeeman energy and are solely driven with local gate-voltage pulses. As a result, it will be
feasible to scale this quantum control method to a large number of spin qubits operating in
close proximity. In addition, it is possible that the spin-flip mechanism employed here, which
relies on coupling to the nuclear-spin bath, could be harnessed under the appropriate
conditions to create a nuclear-spin memory (79).
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Research with Graphene Quantum Dots
Graphene is an ideal candidate for spin qubits due to its low intrinsic spin-orbit coupling and
the sparse amount of nuclear spins. We discussed bound states in gate-tunable graphene
quantum dots realized in both graphene nanoribbons and gapped single- layer and bilayer
graphene. In contrast to quantum dots rea lized in edged graphene flakes, gate-tunable
quantum dots are defined electrostatically rather than by the physical edge of a graphene
sample. Th is allows one to controllably break the valley degeneracy, a prerequisite for spin
based quantum computing, e.g., by using a magnetic fie ld. We have also discussed quantum
manipulation of spin qubits in such dots, as well as recent theoretical studies on the
consequences of spin-orbit interaction and hyperfine interaction with nuclei for sp in
relaxation and sp in-decoherence . Both theoretical and experimental efforts have focused on
single-layer graphene quantum dots. The next major area is likely to be bilayer graphene.
Bilayer graphene is potentially superior to sing le-layer graphene due to the creation of a
tunable bandgap by electric fields which allows for an all electrical control of graphene
quantum dots .
These new capabilities may be a boon for spintron ic quantum information processing.
Single-qubit gates, based on single- spin electron spin resonance, have ach ieved sign ificant
breakthroughs. Fast ( ~200 ps) two-qubit operation has been demonstrated, but single-qubit
operations on a similar time scale still remain a challenge. A proposed new configuration of
two-spin encoding of the qubit, where a sing le and a triplet state play the role of the 0 and 1,
shows promise. With this type of qubit, the interferometer, demonstrated by the Princeton
researchers, could be used for single-qubit gates on a nanosecond t ime sca le. Alternatively,
fast qubit rotations in a slightly different singlet-triplet qubit can be obtained by align ing
nuclear spins to create different nuclear polarizations in the two dots. Fast single-qubit and
two-qubit gates ava ilable in the same syst em allow for efficient quant um error correction and
could provide an important head start in the battle against decoherence. However, no two
qubit gates for this type of qubit, which would involve four spins, have yet been
demonstrated. Util izing graphene as a structural basis for quantum computing, coupled with
other carbon based materials such as self-assembling DNA, motifs, may lead the
revolutionary development in quantum computing.
SUMMARY OF ADDITIONAL INORGANIC TECHNOLOGIES
The advancement of quantum computing schemes is the subject of sign ificant investment
and development over the past two decades. Recently, Ladd reviewed inorganic technolog ies.
(5) Ladd proposes that ion traps are the most probable technology based on their long T2,
but then concludes that a comparison between the technologies is incomplete without further
development on all front s. The current treatise concentrates on organic technology but
summarizes here the work of Ladd and others for completeness.
Photon Technologies
Using the polarization state of a photon is an appealing approach to store, communicate, and
manipulate qubits. Photons do not requ ire a vacuum or very low temperature for fa irly good
isolation from thermodynamic interactions. They do require special, non-linear media for
robust, reliably predictable manipu lation. A major advance in 2001, known as the KLM
scheme, showed that a scalable quantum computing was possib le using linear optics and
single-photon detectors and sources. (80) The major hurd le, according to Ladd, is photon
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loss within waveguides, and is equivalent to decoherence time in other quantum hardware. n
The size of quantum gates is currently on the order of cm; this hurdle becomes less as gate
size decreases. It is finally concluded that photons will likely be used in a hybrid technology
with another quantum element serving as the basis for gates and other interactions. This
scheme is known as distributed quantum computing, where elements can be separated by
significant distance. This distance is either large by comparison with gate or gate array size,
or actually large (km) in a communications network.
Photonic technologies are a very active development area: the raw number of publications
found for "photon computers" or "photon computing" shows more entries for 2009 than for
2008 and 2007 combined.° Furthermore, many devices operate at or near room temperature
and most do not require expensive cryogenic systems (temperature below He boiling point),
making them inexpensive to research versus other technologies. These objective measures
make breakthroughs more likely, and in 10 years all-optical computing should be addressing
problems that cannot be accomplished via classical systems. In 40 years, manufacturing
engineering will decrease the cost of these devices and they will be an option for many
computing tasks in the space environment.
Ion and Atomic Trap Technologies
Individual atomic ions can be trapped in free space by nanoscale electrodes, while atoms can
be trapped in an optical lattice created by lasers. In the ion systems, manipulation of
electrode voltages move ions around the lattice and interact them with each other. In atomic
systems, modulation of the optical lattice and/or external optical interference is used to
manipulate the atoms. Ladd concludes that scaling is the primary hurdle in trap-based
technologies.
More detail of such hurdles in trap technologies is revealed in a year earlier (much longer)
review by Haffner. (81) Ion-trap-based gate operations are shown to have arbitrarily high
fidelity, or higher fidelity than required for fault-tolerant computation. The current bottleneck
in trap technology versus classical systems is the trapping frequency of a few hundred
microseconds, even though massive parallel operations are possible. Haffner concludes that
there are no fundamental barriers to scaling trap-based computing, but the technology is
challeng ing and will progress as evolution rather than revolution. This is encouraging given
that 40 years ago 20-nm transistors seemed challenging, but without fundamental
operational barriers.
Nuclear Magnetic Resonance (NMR) Technologies
NMR storage and manipulation has been shown in liquid media up to a dozen qubits. Liquids
are preferred because of their longer T2. However, thermal motion in the liquid state made
scalability an issue. Moving to solid state NMR to address thermodynamic issues dramatically
decreases T2. Ladd concludes that NMR technologies are a good testing ground for fault
tolerant algorithm development, but of little practical use for quantum computing.
Superconducting Technologies
Superconductivity is the flow of electricity without resistive losses. Similar to the laser, this
macroscopic phenomenon has quantum mechanical origins. When cooled below a critical
n A waveguide is the equivalent "wire" that isolates the transmission of photons between interaction and storage devices .
0 Web of Science database, Inquired 30 June 2010 .
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temperature, some materials such as copper form a lattice that allows electrons to pair and
flow as a bosonic charged (2e) particle. The components of superconducting circuits can be
fabricated with current technology; however, decoherence times are limited to several
microseconds maximum due to the large size (100 micrometers) of the circu it elements and
thus large number of charge carriers in a qubit device ( ~10 10 ). Additionally, the current qubit
device designs only operate at the scale of l0's of mK. Superconducting elements,
specifically Josephson junctions, may play a role in hybrid designs such as the distributed ion
traps of Haffner (81), but are currently not seen as a stand-alone technology for quantum
computation.
DNA-BASED DESIGNS FOR MOLECULAR COMPUTERS
While traditional silicon-based circuits reach their fundamental atomic limitation, researchers
search for alternative mediums for computation. The most logical solution to overcome this
restriction in silicon-based integrated circuit architectures resides within our own bodies,
deoxyribonucleic acid (DNA). Living organisms also carry out complex physical processes
under the direction of digital information. Biochemical reactions and ultimately an entire
organism's operation are ruled by instructions stored in its genome, encoded in sequences of
nucleic acids. When the workings of bimolecular machines inside cells that process DNA and
RNA are compared to Turing's machine, striking similarities emerge: both systems process
information stored in a string of symbols taken from a fixed alphabet, and both operate by
moving step by step along those strings, modifying or adding symbols according to a given
set of rules.
Set strand
'Open '
r
'Closed'
Unset strand
Figure 9. A DNA nanomachine driven by repeated sequential addition of DNA control strands (82).
DNA Background
Watson and Crick may have never realized the full potential of the double helical structure
they identified nearly 60 years ago, (83) for little was known about this amazing molecule
that harnesses life. Biochemists in the late nineteenth century had found that these nucleic
acids, long-chain polymers of nucleotides, were made up of sugar, phosphoric acid, and
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several nitrogen-containing bases consisting of deoxyribonucleic acid (DNA). By the late
1940s the scientific community widely accepted DNA as the carrier of genetic information.
But, it wasn't until 1977 that Fred Sanger developed the first dideoxynucleotide chain
termination bottom up assembly method for DNA. (84) This technique would later usher in a
new age of nucleic acid research and open the door for the modern era of biotechnology.
With the advent of the Polymerase Chain Reaction (PCR) (85) technology a virtual treasure
trove of capabilities now exist for genetic and biochemical engineers to create customized
DNA strands. This revolutionary process has created a multidisciplinary field of work within
nanotechnology that intersects at the crossroads of computer science, biochemistry, material
science, and engineering. This section on DNA-based nanosystems and computing will
introduce several state of the art research applications and concepts currently being
employed to produce DNA-based devices.
It is crucial to formulate a basic understanding of the structure and chemical principles of the
DNA molecule to fully grasp its potential as a building material for DNA-based nanosytems.
For the lay reader we have constructed a simplistic outline to illustrate the general principles
of the DNA molecule that hold true to their biochemical properties as they apply to bottom
up nanostructure assemblies.
1. DNA consists of two long polymers made of simple units called nucleotides, with
backbones made of sugars and phosphate groups joined by ester bonds. These two
strands run in opposite directions to each other and are therefore anti-parallel. The
double strands of DNA form a double helical structure.
2. The information in DNA is stored as a code made up of four chemical bases: adenine (A),
guanine (G), cytosine (C), and thymine (T). The order, or sequence, of these bases
determines the information available for building and maintaining an organism. These
nucleotides bind through a chemical bonding process known as Watson and Crick base
pairing . A bonds with T, and G bonds with C - a given sequence of such nucleotides will
always bond with the complementary sequence.P
3. In its double helical configuration, DNA is a relatively rigid molecule. This rigidity can be
further enhanced by bundling several double helixes to form DNA lattices and tiles to
form synthesized nanoarchitechtures (87)(88)(89).
4. The Watson and Crick base-pairing principles have created predictable binding affinities in
bench top applications. This knowledge of the intra- and inter-molecular physical
properties of the DNA molecule enable the programming of desired interactions within the
sequences to produce a customized sequence of DNA.
5. The ease in sequencing DNA based on the Sanger technique, which today has evolved
into advanced automated processes, have made designer DNA strands readily available.
Customized strand lengths or oligonucleotides (strands typically 100-200 base pairs long)
can be easily ordered from various sequencing services or produced within the lab at
relatively low costs with high throughput and quality.
6. Today biotechnologists can employ a library of unique restriction enzymes that can cut
the DNA strand between specific nucleotides leaving "sticky ends", or single stranded
P Sometimes transcription errors will result in an incorrect bond , such as A with G. These are single nucleotide
polymorph isms, or SNPs (pronounced "snips"). SNPs are not uncommon in the human genome and have important
imp lications in disease; however, in the current treatise we consider such "wrong" pairings to be errors that need
correction .
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overhangs at the end of the double helix (Figure 10). These fragments can be exploited to
create a recombinant molecule of DNA by;
a. Inserting or removing a specific sequence of DNA.
b. Attaching a fluorescent molecular beacon.
c. Amplifying the sequence through the PCR process.
5,• ~ - - - - GA_A_T_T_C_ _ _--<1 3s•'
l
Original DNA 3 _ CT TA A G _
molecules
5' GAATTC
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Figure 10. Recombinant DNA molecule with restriction enzyme cleavage and sticky end ligation.
7. By carefully using the recombinant tools and technologies available to genetic engineers,
one can properly program a customized Watson-Crick base-paired DNA motif that will
self-assemble in solution. This method of self assembly is preferred on small scale
applications due to the difficulties experienced when assembling nanoscale objects
through the traditional top down method. Assembly of DNA motifs with t he aid of various
branched DNA strands with sticky ends can be directed by the geometry and connectivity
of the varying motifs. Once the structure is assembled a range of DNA lattices can be
produced (Fig ure 11) .
25
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Figure 11. Two symmetric DNA nanomotifs and the crystals grown using them. {a)
and {d) show a symmetric cross motif and a three-point-star motif, respectively.
Images {b) and {e) are atomic force micrographs showing the crystal structure,
and (c) and (f) are fluorescence microscopy images of DNA 2D crystals assembled
from the DNA motifs {86).
8. Another widely accepted bottom up method to construct DNA nanosystems is through a
process known as strand displacement or branched migration . This assembly method
displaces one DNA strand and selectively replaces it with a strong complementary strand
which usually consists of more Watson Crick base pairs. This method can be utilized to
correct sequence errors made during strand synthesis and DNA tile assembly and in
complex logic gates, and for controll ing DNA motors.
In 1996, Winfree devised a theoretical proposal that addressed how crystal morphology and
patterning can be programmed by tile design in an inherently asynchronous assembly
process, in which it was addressed by the abstract Tile Assembly Model (aTAM) . (90) Winfree
explored how physical parameters, such as tile concentration and temperature, affect crystal
growth and influence error rates, based on reversible t ile association and dissociation rates
(91). This work was built on previous efforts by Wang 's (92)(93) embedding of computation
in geometrical tiles showing that two-dimensional (20) self-assembly of DNA can perform
Turing-universal computation. This implies that any algorithm can in principle be embedded
in, and guide, a potentially aperiodic crystallization process. In this "algorithmic self
assembly" paradigm, a set of molecu lar "Wang tiles" is viewed as the program for a
particular computation or molecular fabrication task.
Later collaboration between Winfree and Seeman resulted in the first successful fabrication of
a two-dimensional DNA lattice structure that utilized the mathematical principle of tiling (94) .
The self named DX (double crossover) molecule has two double helical motifs that are rigidly
bound together by several single strands that are organized in a double crossover pattern
forming a rigid structure of DNA. These DNA strands are oriented in a parallel direction. This
method allows for the production of DNA based lattices by exploiting the use of sticky ends at
four ends. These ends can then be further constructed to bu ild up a scaffold of DNA based on
26
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the complementary binding of the Watson-Crick base pairs that correspond to each sticky
end. In this way, a lattice structure can be built upon the base structure by synthesizing
additional DX motifs to construct what is known as a "DNA tile." These tiles can be further
utilized as a scaffold for additional molecular structures.
In order to envision the aTAM tiling process, it is easy to picture various tiles with different
numbers written on the sides, indicating matching rules where two tiles would stick only if
their contacts matched. Additional matching interactions can be arranged in a manner that
adjacent tiles can strongly hold the next one in place, but a single interaction creates a weak
bond. Figure 12 illustrates an instantiation of the algorithmic self assembly process, in which
sets of four species tiles that represents XOR ( exclusive OR) function to create a Sierpinski
triangle pattern. The so called seed structure is used to input the initial values that
commence the algorithmic self assembly process. However, it must be noted that random
nucleation events may occur. Nevertheless, algorithmic self-assembly has created a means
to emulate cellular automata.
A
l =2:
I =0:
z = xEBy
output - z z ~
i nputs - x ~y ~
D *
E - - -
y
....
.....
--·--
........ ~-~ ---
-
Figure 12. (top a-e) The XOR Cellular Automaton and Its Implementation by Tile-Ba sed Self- Assembly .
(bottom a-e) AFM Images of Algorithmic Self-assembly of Sierpinski Triangle Crystals.
27
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Figure 12 (continued). (top a-e) The XOR Cellular Automaton and Its
Implementation by Tile-Based Self-Assembly. (bottom a-e) AFM Images of
Algorithmic Self-assembly of Sierpinski Triangle Crystals.
In theory, this process allows scientists the ability to build a computer from nanoscale
material with DNA tiles (95). The experimental success of this trial demonstrated that 2D
algorithm ic self -assembly offers new capabilities for computation and construction, as well as
a new range of physical phenomena and experimental challenges as well.
Error Suppression Mechanisms in DNA Self- Assembly
Molecular self-assembly is an emerging technology that will ultimately enable the fabrication
of great quantities of complex nanoscale objects such as computer circu its at very low costs.
Because the DNA-tile-based bottom-up assembly technique relies on the logic of
programming self-assembly, it requires a situation where sticky-end binding specificity is
infallible. Realistically, however, correctness of matching between tiles cannot be guaranteed
due to the thermodynamics and kinetics of DNA tile self-assembly. This process alone results
in occasional erroneous assembly steps. The number of assembly errors increases with the
number of tile types, and accruing errors render large scale complex computation practically
infeasible.
Assembly errors can be classified into three types: 1.) Growth errors. 2.) Facet errors. 3.)
Nucleation errors. Growth and facet errors are the errors that occur on the growth front of an
existing assembly, while nucleation errors deal with the spurious initiation of assembl ies. A
growth error occurs when a DNA tile with one or more mismatched sticky ends is embedded
in the assembly. A facet error occurs on the flat surface (facet) of the aggregate when two
DNA tiles attach on a growth front (facet) side by side, and thus stabilize each other's
binding . This is considered an error because the identity of these tiles may not be correct
with respect to the computation being performed. Nucleation er rors are similar to facet errors
in that a number of tiles spontaneously assemble a cluster by stabilizing each other through
28
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binding. This then seeds ordinary, but meaningless computation. Growth errors, facet errors,
and nucleation errors all occur because of tiles that make only weak contacts with the
assembly (Figure 15). These erroneous tiles must fall off in order for correct growth to
proceed. One approach is to design the lattice such that each tile is first stabilized by the
arrival of another tile before it secures itself in place.
Prior analysis predicted that the error rates of tile assembly can be reduced by optim izing
physical parameters such as tile concentrations and temperature. In order to suppress
different types of errors, several methods have been proposed based on the idea of
increasin g the amount of time required to lock in erroneously assembled tiles. In order to
min imize the errors, several methods have been proposed. Unfortunately, some of these
methods cannot effectively suppress all types of errors. For example, the tile proof reading
model first proposed by Winfree and Bekbolatov (96) can correct errors in growth if an
incorrect tile attaches in the next position. This error correction technique uses redundancy
to correct errors. In this method, each tile is replaced in the system with four tiles, arranged
in a 2 X 2 block. The compact resilient tile model as proposed by Reif (97) attempts to
reduce the increase in scale of the final pattern produced by self-assembly. While both of
these methods are effective in reducing errors, they are only lim ited to those errors produced
by growth. However, the error suppression models Protected Tile Mechanism (PTM) and
Layered Tile Mechanism (LTM) proposed by Fujibayashi and Murata can suppress all three
error types illustrated in Figure 15. (98)(99). The functional method of suppression in these
models is the control of sticky end hybridization. In these mechanisms the implementation of
the DNA tiles is altered by the introduction of a structural motif protection strand and
protection tiles (see Figure 13 and Figure 14 ). In this technique, the protection strand is a
single oligomer that covers the input side of the tile. Each sticky end remains uncovered and
it works as the toehold for initiating a branch migration process that removes the protection
strand . The combination of a tile and a protection strand is called a "protected tile," or just
"tile" when it is clear from context, and "foundation tile" refers to the unprotected
foundation tile. The output sides of all t iles are unprotected, thus the growth front always
displays unprotected sticky ends. As seen in Figure 13 the protected tiles associate to the
growth front by the exposed 3-nt sticky ends first, then branch migration results in strand
displacement on each of the matching input arms; if both arms are matched, the protection
strand is completely displaced, and it dissociates. In Figure 14, this method undergoes Monte
Carlo simulation to evaluate its suppressive properties. Surprisingly, it was discovered that
the PTM and LTM suppression methods can prevent nucleation errors as well as growth and
facet errors.
29
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Figure 13. Error Suppression with the PTM Method.
f' a
Figure 14. Simulation results of growth in (A) the OTM, (B) the PTM, and (C) the LTM.
30
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(a )
Mismatched
~ Facet
c)
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Figure 15. Three Types of Error in DNA Tile Self-assembly (a)
Growth error (b) Facet error (c) Nucleation error. Red lines
indicate the mismatched sides.
Self-assembly with DNA-based Microfluidic Devices
Thus far we have explored DNA computing through methods based on linear DNA molecule
hybrid izations (100) and "DNA tiles" with four "sticky ends"(101) . While it has been proven
experimentally that DNA tiles have much stronger computational power compared to linear
DNA strands (102)(103), the suppression of assembly errors is the central problem of the
DNA-tile-based nanotechnology. Even though several error reduction methods have been
proposed thus far, many of them only con
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