AAWSAP DIRD, Quantum Computing and Utilizing Organic Molecules in Automation Technology,…

UNCLASSIFIED/ ,<FOR. OFFI@IAL l!ISI!! 8HLY Defense Intelligence Reference Document Defense Futures 10 December 2010 !COD: 10 December 2010 DIA-08-1102-005 Quantum Computing and Utilizing Organic Molecules in Automation Technology UNCLASSIFIED/ /FOR 066iliCili.t.k WS& 8,.Llf UNCLASSIFIED//FOR OFFICIAL USE ONLY Quantum Computing and Utilizing Organic Molecules in Automation Technology The Defense Intelligence Reference Document provides non-substantive but authoritative reference information related to intelliqence topics or methodoloqies. Prepared by: Technology Warning Division (DW0-4) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: AAP Person 73 COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2010 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications \AAWSA) Program. Comments or questions pertaining to this document should be addressed to AAP Person 1 l AAWSA Program Manager, Defense Intelligence Agency, ATTN: JUIAF - DI/DWO-3, Bldg 6000, Washington, DC 20340-5100. UNCLASSIFIED/ /FOR AlililGII.L W&lii &PtLY 1 UNCLASSIFIED/}Fdk OFFICIAL U.!r:: BHL\I 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 UNCLASSIFIED//FAR 055iliCl.\k W&E 8HLY 2 UNCLASSIFIED//P91t 9PPl@IAL l:ISIE 8HLY 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 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 Figure 13. Error Suppression with the PTM Method........................................................ 30 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 UNCLASSIFIED//EAR OEEICI Pk Wlili BHLY 3 UNCLASSIFIED//FOR: 8ffl@IAL U.!I! 014Li 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 UNCLASSIFIED//FOR AliliiliCIAk W&i 9PU::J.f 4 UNCLASSIFIED//FOR. 8FFI@IAL l!ISI!!! er~t I 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 this 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 engineering 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 timeframe. Optical computers will likely be rea lized 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 utilizing 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 shielding 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-delivered 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. UNCLASSIFIED/ j FOR OFFICIAL 031!!! l>flt I 5 UNCLASSIFIED//FAQ OFFI€i1Al 1481: 8Ht'I" These will not be the fastest systems in the astro-arsenal, but self-repair may make them the most robust. UNCLASSIFIED//FOR OPPICil<t U:!I!! 8HLY 6 UNCLASSIFIED//P91t 9PPl@IAL l!ISI!!! 9HL'I INTRODUCTION Computers today are not what they used to be. In the 17th 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 organic 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 available 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 usually 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. UNCLASSIFIED/lfQB OFFICIO! I!Si OPIL¥ 7 UNCLASSIFIED//POR: OPPICIAL USE OIILI 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 acquisition channels was presented at the Workshop for Technology Breakthroughs for Human Space Exploration, June 17th 2010, NASA Headquarters, Washington DC. Navigation is and will continue to be handled by traditional computing machines - it is only rocket science that needs to be solved for navigation purposes. UNCLASSIFIED//FOA OFFICil.t.k W&E 8HL1/ 8 UNCLASSIFIED//FOR: 8FFl@IJIIL tt9I!!! er•t I 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 only 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 planning 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-19th 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, individual 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. UNCLASSIFIED//FOR OFFI&Iit.k W&E OHkY 9 UNCLASSIFIED//POK: OPPIClltL U.!r:: Oflt I 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 public-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 required 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 replace it. The canonical quantum communication experiment defines a sender, Bob, and a receiver, Alice. In most scenarios, Alice and Bob communicate over a distance using entangled particles and a traditional 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 communication 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. The 128-bit web standard is a compromise between security and speed. UNCLASSIFIED//POK: 9ffl@IAl W&li 8P◄IL¥ 10 UNCLASSIFIED//EAR OEFIClt.k WSIE ertt I 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. This 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-deterministic 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. UNCLASSIFIED// FOR OFFICIAL YSE 8P.k¥ 11 UNCLASSIFIED//fQR OFFICI0k WSE 8HLI 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. UNCLASSIFIED//FOR &FFl&I.Tik WSE &Hk\f 12 UNCLASSIFIED//FOR. 8FFI@IAL l!ISI!!! er~t I 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 arbitrary 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 during 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 immediate 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 charging 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. UNCLASSIFIED//fdk OFFICIAL U:!I!!! 9HL'I 13 UNCLASSIFIED//EOA QFFl&Il.l Y81: 8HtY 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. UNCLASSIFIED//FOR AEEICIAk W&i &Ptllf 14 UNCLASSIFIED//FOA 8FFl&I.t.k WSli 8,.k\f 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. UNCLASSIFIED// FOR OPPICIJ!tt U:!I!! 8HL\S 15 UNCLASSIFIED//FOR. 8FFI@IAL l::181: 8HL'I E C 11 IUo 2Ll u <l -........, V I I II I 10 11 loll -R 0 R r 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 studied 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. (a) 800 5' E - -::.";l, 550 500 450 400 dl/dVg1(nS) /[pA] (b) 0 0 ,◄ 0.8 1900 1880 > E - 1860 >~ 1&40 1820 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. UNCLASSIFIED//POft. orr1e1s11t l::181: 8,.LY 16 UNCLASSIFIED//FOR. OFFI@IAI: l48E OHi:¥ 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 addition, 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 = mo2c4 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. UNCLASSIFIED/;'FOR. 8FFl@IAL U9I!! eHt I 17 UNCLASSIFIED//FOR OFFICIAL USE ONLY 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-induced 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 the 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 tunneling via valence band states (i.e., Klein tunneling). 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. UNCLASSIFIED/,'FOA OFFI&il.t.L W&li 8,.LY 18 UNCLASSIFIED//FOA QFFIEJIAL YSI!!! 9Ht'I" 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 UNCLASSIFIED//EAR OFFICIO I. flii 0Plk¥ 19 UNCLASSIFIED//FOR: OPPIClltt U.!I! Oflt I 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-flip 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). UNCLASSIFIED//fdk OFFICIAL U.!I! OHL¥ 20 UNCLASSIFIED//FOR: 8Pfl@IAL YSli &Pn,¥ 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 realized in edged graphene flakes, gate-tunable quantum dots are defined electrostatically rather than by the physical edge of a graphene sample. This allows one to controllably break the valley degeneracy, a prerequisite for spin­ based quantum computing, e.g., by using a magnetic field. 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 spin­ relaxation and spin-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 single-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 spintronic quantum information processing. Single-qubit gates, based on single-spin electron spin resonance, have achieved significant 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 single 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 time scale. Alternatively, fast qubit rotations in a slightly different singlet-triplet qubit can be obtained by aligning nuclear spins to create different nuclear polarizations in the two dots. Fast single-qubit and two-qubit gates available in the same system allow for efficient quantum 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. Utilizing 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 significant investment and development over the past two decades. Recently, Ladd reviewed inorganic technologies. (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 fronts. 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 require a vacuum or very low temperature for fairly good isolation from thermodynamic interactions. They do require special, non-linear media for robust, reliably predictable manipulation. A major advance in 2001, known as the KLM scheme, showed that a scalable quantum computing was possible using linear optics and single-photon detectors and sources. (80) The major hurdle, according to Ladd, is photon UNCLASSIFIED//EAR OEEICIOI IPiii QNLlf 21 UNCLASSIFIED//FOA OFFIEIAk W&lii 0NLY 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