June 2009

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(a) Scanning electron microscope image of Sandia National Laboratories’ dual quantum dot structure fabricated in silicon (the dots suggest the approximate location of the electron position); (b) schematic cross section of the quantum dot structure showing the position of the single electron locations; and (c) schematic representation of spin manipulation using rotation and precession of two different spins. |

A three-year science and technology project is aiming to transform abstract quantum theories into actual quantum products. A goal of the effort is to create the world’s first silicon spin-based quantum bit, which would be a major advancement in the development of quantum computing. Additionally, the work includes its own theoretical piece that addresses the design of a quantum error correction circuit. Applications include enhancing the basic understanding of spin device physics for potential spin-based microelectronics and determining the feasibility of certain aspects of silicon quantum bits for future research and use (*SIGNAL* Magazine, June 2008).

Scientists at Sandia National Laboratories, a Department of Energy (DOE) facility,

The researchers also are studying the error-correction capabilities possible in quantum computing and how to make the nanostructures isolate a single spin. “We’re really trying to isolate a single electron—or in our case actually two electrons—to make them talk to each other and sense the spin, which is a very challenging thing to do,” explains Dr. Malcolm Carroll, principal investigator for the project.

Spin is a quantum mechanical property that describes an electron’s angular momentum. Carroll is reluctant to make a classical analogy to describe spin because it is a truly quantum mechanical phenomenon. Spin is important to quantum computing because of its relationship to decoherence time. The longer it takes for decoherence to occur, the more computer operations can be conducted. It is believed that a much longer spin decoherence time can be established than a charged decoherence time, thereby increasing the number of operations possible.

In addition, sensing spin is important because information can be encoded in it. “The specific implementation we’re using doesn’t do this exactly, but other people have encoded information in spin up and spin down,” Carroll says. The work is equivalent to labeling the spin up as 0 and the spin down as 1. To determine the information in the qubit, users have to read out the spin.

To make the project’s goals a reality requires a combination of disciplines such as materials science, electrical engineering and fundamental physics. Sandia researchers are drawing from all of those fields as they pursue their main interest of using quantum information science for DOE interests.

One such application is microelectronics. As devices’ geometries continue to become smaller, quantum effects begin to dominate their operation. Related to that effort is Sandia’s use and capabilities in advanced computing architectures. Tom Tarman, deputy program manager for the Quantum Information Science and Technology Grand Challenge, explains that the laboratories “are heavy users of computing machines for DOE applications, and the potential represented by quantum computing is pretty compelling.” He says researchers on the project need to understand how quantum sciences in general can be applied to the types of problems worked on at Sandia and other DOE laboratories.

Another goal is to contribute to the quantum information science research community. “We’re interested in these things for our applications as a DOE laboratory, but of course our objective as well is to push the state of the art,” Tarman shares.

The project can provide new data because its research into silicon and spin is cutting-edge. Spin qubits have been created in the past in a different material, gallium arsenide. The nanostructures the Grand Challenge team is building are based on one of the designs that was successful in gallium arsenide. At least one example of a qubit in silicon already has been demonstrated, but that did not rely on spin.

Carroll says that the reason gallium arsenide was used instead of silicon before is that silicon is a more disordered system. Silicon has more frequent and prevalent trapping sites for electrons that interfere with their movement. “The specific work in silicon is important from the perspective that there are predictions that if this can be done in silicon, the spin decoherence will be considerably better than what has been observed in gallium arsenide,” Carroll explains. “If it is better, this will open up many more opportunities in terms of actually demonstrating those first quantum circuits and functionality that we ultimately want to achieve.”

One of the areas where quantum computation shows promise is in the optimization of problems, which directly relates to the number of problems that computing organizations at laboratories must handle. Personnel at those locations dedicate significant amounts of time to developing algorithms that classical computers can use to solve problems or come up with reasonable approximate solutions to optimization problems. Tarman says that, “Quantum computing would be a potentially significantly faster and more efficient way to compute optimal solutions to certain problems.” Scientists are studying the potential of quantum computers and physical qubit alternatives, he adds.

Quantum computing stores information in qubits. These differ from classical bits because while either can hold the value 0 or 1, qubits can be put into a state known as superposition. The readout value from a qubit in superposition still comes back with those values, but it will read out to a 0 of a certain probability. “What you’ve encoded in the qubit is probability amplitudes for both possible states of the qubit,” Tarman explains. “The algorithm acts on these probability amplitudes, which are then determined when you read it out later. You read the qubit out as a 0 or a 1 with the given probability determined by the probability amplitudes.”

Silicon double quantum dot qubits use electron spin to encode quantum information and contain control and readout electronics to manipulate and measure qubit states. |

Another concept associated with qubits is the notion of entanglement, which is captured in the circuit or algorithm that is working on an input. An entanglement sets up a correlation among qubits so that operations performed on one qubit also could affect the state readout from the other qubit. When multiple qubits are entangled, the information is spread out across more bits, which is beneficial for error correction.

One of the benefits of quantum computing is the ability to operate on the entire input space that is encoded in a collection of qubits. In classical computing, one operation runs on one bit, and no more can be done. Entanglement allows operation on more than one individual location. Carroll explains that, “Relying on the quantum nature of the spin behavior, the idea is that through entanglement, if you operate on one spin you actually can have some effect on multiple spins simultaneously. Through this entanglement, it is proposed that you can produce more efficient algorithms.”

Quantum superposition and quantum entanglement work together on quantum computers to execute an algorithm, and some quantum algorithms would require fewer operations than in classical algorithms. According to Tarman, some algorithms can be executed more efficiently on a quantum computer because the two properties are at work.

When Richard Feynman first introduced the idea of quantum computing in the 1980s, the thought was that one application for quantum computing was the study of quantum mechanical systems that were intractable with classical computing, such as some properties of materials. Some problems, including quantum simulations, scale exponentially on classical computers. So if researchers need to model a system of 100 atoms, it would require on the order of 2^{100 }operations to model that on a classical computer. A quantum computer would require on the order of 100 operations. However, according to Tarman, a problem in the early days was that when people thought about quantum computers for those sorts of applications, quantum computing was quickly dismissed because decoherence errors would cause algorithms to crash.

Then researcher Peter Shor developed an error correction algorithm for quantum information, which in principle allowed people to preserve quantum information with much higher fidelity in a logical qubit. It then would run continuous error correction on the quantum information and therefore would make that quantum information useful for quantum computation.

Despite error correction, quantum computers’ algorithms do not always ensure that the final answer is correct. “Sometimes the recipe for getting the solution using a quantum algorithm requires that you solve [the problem], but because the answers are probabilistic, you must check the solution, and then you may have to run it again,” Carroll says. “You might actually say they’re by design more errant [than classical computers], but the computation is so much faster that you can afford to run it a couple of times until you get the right answer.”

Quantum computers and classical computers could be co-processors in certain situations, and could be used to ensure correct answers. For example, a quantum computer could quickly find an algorithm, which then could be entered into a classical computer for verification.

Carroll says his team will judge success in several ways, but the obvious one is actually to demonstrate a silicon spin qubit. “That would be a very big result for the community,” he states. Another success will be the development of a better understanding of what it will take to build a logical error-corrected qubit. Several theoretical studies have been done on the topic, but none on how it would be wired. Thoughts about the limitations of electronics that control the quantum bits introduce challenges and more reality into the design.

Carroll also touts achieved success, such as the recent progress with silicon quantum dots. Sandia personnel have demonstrated quantum dots in silicon dioxide. “We have moved forward and shown on the particular lateral quantum dot of wires that we put down that you can put down a quantum dot that is not dominated by disorder,” Carroll explains. “That’s a small but important step forward.” He says the fact that they used the same geometry that was done in gallium arsenide is particularly significant.

Quantum dots are quantized electrons confined in a space where quantized means that the energy of the electron takes on discrete values. A classic analogy compares this phenomenon to playing a drum. Tapping a drum creates certain modes of vibration that are allowed on the drum surface. This turns out to be the case for all particles in nature if they are confined in a small enough region. The electron’s wavelike nature takes on only certain allowed modes. Each of those modes has a different energy.

In a silicon DQD, nanoscale conducting wires sit close together on top of the silicon dioxide. The wires can be used to isolate little puddles of electrons and then ultimately squeeze down the number of electrons in the puddle to single electron occupation.

The quantum dots being studied at Sandia are related to complementary metal oxide semiconductor (CMOS) technology. One connection is that CMOS fabrication technologies are being used to build the nanostructures that form the quantum dots. From an application perspective, if quantum circuits prove beneficial, they would develop in parallel with classic CMOS electronics. The classical circuitry actually would be used to control and manipulate the quantum circuitry. The quantum circuit would augment existing classical hardware.

Lessons learned from quantum dot research could improve the understanding of some effects that are being observed in CMOS electronics as the semiconductor scales become smaller. “As they scale down in size, the quantum effects become increasingly important even for classical transistors,” Carroll says.

Working with quantum dots is not simple, however, because they have to be kept at 0.1 degree above absolute zero on the Kelvin scale. This is because of spacing of allowed energy levels. “You do not want the electrons to be thermally excited into any higher energy levels, so the thermal energy has to be small relative to the spacing of energy levels in the quantum dots,” Carroll explains. “It turns out that the energy level spacing in these quantum dots is not particularly big, and that’s why you have to cool to these very cold temperatures.”

Another success for the project is the beginning of work on cryogenic CMOS circuit-assisted charge readout. Spin information is deduced indirectly through charge sensing—that is, spin to charge transduction—so it is important to be able to sensitively measure a single or even less than a single charge fluctuation in the quantum dot systems. The real success, according to Carroll, is the steps taken to assist the charge measurement with cryogenic electronics. “We’ve put forward a design, and we’re testing these circuits and they appear very promising,” he says.

**WEB RESOURCE***Quantum Information Science and Technology Grand Challenge: www.sandia.gov/QIST*