Can We Build a

Large-Scale Quantum Computer Using Semiconductor Materials? B.E. Kane

Abstract The following article is based on the Symposium X presentation given by Bruce E. Kane (University of Maryland) at the 2004 Materials Research Society Spring Meeting in San Francisco. Quantum computing has the potential to revolutionize our ability to solve certain classes of difficult problems. A quantum computer is able to manipulate individual two-level quantum states (“qubits”) in the same way that a conventional computer processes binary ones and zeroes. Here, Kane discusses some of the most promising proposals for quantum computing, in which the qubit is associated with single-electron spins in semiconductors. While current research is focused on devices at the one- and two-qubit level, there is hope that cross-fertilization with advancing conventional computer technology will enable the eventual development of a large-scale (thousands of qubits) semiconductor quantum computer.The author focuses on materials issues that will need to be surmounted if large-scale quantum computing is to be realizable. He argues in particular that inherent fluctuations in doped semiconductors will severely limit scaling and that scalable quantum computing in semiconductors may only be possible at the end of the road of Moore’s law scaling, when devices are engineered and fabricated at the atomic level. Keywords: quantum computing, semiconductors, spintronics.

Introduction One of the most exciting questions facing the physics and materials science communities today is whether it will be possible to construct a large-scale quantum computer.1 Such computers are (currently theoretical) machines which manipulate and process single quantum states in the same way that conventional computers process ones and zeroes. The field of quantum computing has flourished since the realization by Peter Shor in 1994 that quantum computers—if they could be built—could solve certain cryptographic problems that are completely in-

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tractable for any conventional computer.2,3 Since then, a wide range of systems have been explored in search of the best “qubit,” or two-level quantum state, on which to base a scalable quantum computer technology. This exploration is still in its infancy: experiments today are typically performed on one or two qubits, while the solution of significant cryptographic problems would require on the order of 10 4 qubits. There is currently no consensus as to which of the many qubits under scrutiny

will be most easily scaled. A good candidate qubit must be a two-level quantum state (such as a spin-1/2 particle) in which it is possible to manipulate and measure the state. Ideally, the qubit should have a very long lifetime relative to the time necessary for performing logic and measurement operations. The lifetime relevant here, usually called the decoherence time, is the time it takes for the information encoded onto the qubit to be lost, typically through interactions of the qubit with its surrounding environment. The first elementary quantum logic operation on single qubits was performed in an ion trap,4 a system in which single ions are electromagnetically confined in a vacuum and are manipulated and measured with laser pulses (see Figure 1 in the article by Davidovich in this issue). This system is currently the leader in terms of the number of qubits manipulated, and several ideas have been proposed for making much larger ion-trap quantum computers.5 Solid-state devices can also potentially perform quantum operations, raising the possibility that in the future thousands of quantum devices could be fabricated in much the same way that conventional transistors are made for contemporary microprocessors. Success in this arena was first made in superconducting devices,6,7 and there is hope that quantum computing can be performed in semiconductors with the recent demonstration of single-electron spin measurement 8 and controlled coupling9,10 in semiconductor devices. Perhaps one of the most exciting possibilities for achieving scalable quantum computing is to do quantum computing in silicon—the material at the heart of current computer technology. It turns out that the lifetimes of electron and nuclear spins are extremely long in silicon,11,12 making it a nearly ideal material in which to perform quantum computing. Several designs for quantum computers have been proposed to take advantage of these favorable properties.13–15 In what follows, I will discuss the proposals for quantum computing in semiconductors, paying particular attention to how materials and fabrication issues will affect the ability to scale simple devices into large quantum information processors. In virtually every quantum computer design receiving significant attention, materials issues will play a critical role in the scalability of the devices (even in ion traps—where the qubits are in a vacuum—the properties of the electrodes can affect qubit coherence). I will argue that the fundamental impediment to large-scale quantum computation in semiconductors is the inherent variability

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Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials?

of the devices arising from materials and fabrication. It is likely that quantum computer scaling will not be possible unless this variability is mitigated and devices can be tailored nearly perfectly at the atomic level. While this assessment is certainly bad news for quantum computer development in the near term, it increases the importance of research at the “end of the road” of Moore’s law scaling, where devices are fabricated with essentially atomic precision. Advances in this area may not only lead to maximally scaled conventional computers, but also to the entirely new vista of quantum computing.

SWAP:The Simplest Two-Qubit Quantum Logic Operation In a conventional computer, complex operations are built up from simple Boolean logic operations such as AND and NOT. In a quantum computer, quantum algorithms are built up from elementary operations on the qubits. The simplest two-qubit operation in a quantum computer is a “SWAP,” illustrated in Figure 1. At time t  0, two qubits are in well-defined states, designatedaandb(this is a common notation typically used for spin quantum states, but it can be applied to any two-level quantum system). At some later time, interactions between the two qubits are turned on. If the form of the interaction and its duration are appropriate, then the states of the two qubits can be completely interchanged, or “swapped.”

Figure 1. Schematic illustration of a quantum “SWAP” operation. Two qubits (Qubit 1 and Qubit 2) are initially non-interacting. When interactions are turned on, the qubits are coupled to one another. With appropriate interactions, and for an appropriate duration of the interactions, the qubits are interchanged, leading to a SWAP operation. While SWAP can readily be interpreted classically, SWAP (which results when the interaction duration is halved) leaves the qubits in a nonclassical entangled quantum state that can be used as the elementary operation of a universal quantum computer.

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Things get far more interesting if the duration of the SWAP interaction is reduced by a factor of two, producing the SWAP operation. The states of the individual qubits are indeterminate after this operation, in the sense that a measurement of the qubits yields an equal probability of being eitheraorb. Nevertheless, the overall state of the system is still well defined: in quantum computing parlance, the qubits have become “entangled.” Entanglement is a property of many particle quantum states in which correlations between particle states are well defined even though the states of individual particles are not. It is the ability to create such entangled states that is at the core of the power of quantum computing. It is known that entangling operations like SWAP, combined with single-qubit operations (analogous to the classical NOT), are sufficient in combination to perform any quantum computer algorithm on arbitrarily many qubits.16 Quantum information can in principle be moved throughout large arrays of qubits only coupled to their neighbors by performing multiple SWAP operations. Thus, the problem of creating a large quantum computer can essentially be reduced to making large numbers of qubits with controllable coupling to their neighbors.

Implementing Quantum Logic Using Gated Electron Spins and the Exchange Interaction While these ideas can be applied to a wide variety of potential qubits, they are particularly well suited to systems of electron spins, since electrons are spin-1/2 objects. Pairs of electrons must satisfy the Pauli exclusion principle. A consequence of this is that symmetric and antisymmetric states of electron pairs must differ in energy when the electron wave functions overlap. This effect, called the exchange interaction, has precisely the desired effect of causing the transitions betweenEandFstates that are necessary to produce the SWAP operation between two qubits. Just as important, because the exchange interaction is absent when the electrons’ wave functions do not overlap, it can be controlled, or gated, by an electrostatic voltage that moves the electrons in and out of contact with one another. Electrostatic gates on field-effect transistors (FETs) play a similar role in moving electrons in and out of a conducting channel. The difference is that while an FET gate moves many thousands of electrons in the channel, the gate in a quantum computer performing a SWAP operation must manipulate only a single pair of electrons. While controlling the motion of individual electrons with gates is certainly a challenging task, it is also necessary to measure their

spin state at the end of the calculation. Quantum algorithms take advantage of entangling operations to create very complicated electron states, but all of the information is gleaned from measurements of the qubits, which always produce either aaor abmeasurement of the state. While this is seemingly a difficult task, since the only direct probe of an isolated electron spin is the tiny magnetic field that it generates, recent success has been demonstrated in measuring a single-electron spin in a nanostructured device at low temperature.8 In this experiment, a gated GaAs/AlGaAs heterostructure device was fabricated to create a sensitive electrometer close to a quantum dot that can confine a single electron. The key to these measurements is “spin-to-charge conversion,” in which an electron is cleverly manipulated so that its spin state can be determined from its position. Because an electron is charged, the presence (or absence) of an electron in a small device is relatively easy to determine with the electrometer.

Implementing Quantum Logic in Semiconductor Devices There are currently a wide range of proposals for semiconductor-based quantum computers. In the following, I will concentrate on “all-electronic” proposals, where applied voltages are used to control the exchange interaction between electrons, since these architectures have perhaps the most similarity to conventional electronic devices and are consequently receiving the most attention. Optical control has been incorporated into several architectures,17,18 but these approaches will have additional impediments to scaling. To use the exchange interaction to perform quantum logic in semiconductors, two things are required: a method must be devised to create an array of isolated single electrons, and a gate must be incorporated to turn on and off the exchange interactions between neighboring electrons. The earliest proposal, and the one that is currently receiving the greatest attention from experimentalists, was put forth by Loss and DiVincenzo in 1998.19 They proposed confining electrons in quantum dots created in GaAs/AlGaAs heterostructures.20 Confining single electrons in this manner has recently been achieved experimentally in modulation-doped heterostructures.21,22 Typically, many electrons are distributed at the GaAs/AlGaAs interface, and negative voltages are applied to the gates (conducting electrodes patterned on the semiconductor surface) to deplete the electrons beneath them (Figure 2a). Isolated electrons can be produced in regions between gates if appropriate biases

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Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials?

Figure 2. (a) Quantum-dot quantum computer architectures are usually based on a two-dimensional electron gas, further defined by nanoscale top gate electrodes. (b) Bias applied to the top gates can confine single electrons at potential minima. (c) Architectures for quantum computing typically require gates to confine the electrons (solid areas) and additional gates (hatched area) that control coupling between adjacent quantum dots to control the exchange interaction. (d) Some silicon-based architectures use donors to confine single electrons, but they also need a top gate to modulate the exchange coupling.

are applied (Figure 2b). Needless to say, the dimensions of the gates (shown in plan view in Figure 2c) must be very small (typically 100 nm) to fabricate these types of devices successfully. To implement a SWAP operation in these quantum-dot devices, a pulse is applied to a gate lying between two electrons (Figure 2d). This pulse momentarily turns on the exchange interaction, and—if it is done for the appropriate length of time—a SWAP operation is performed on the two spins (Figure 3). Extensive modeling has been performed on this system to determine the voltages and durations of pulses applied to the gates that are necessary to produce a logic operation.16,23 Because the tails of the electron wave function fall off rapidly away from the potential minima, the quantum dots must be very close together (again, 100 nm), and the strength of the exchange interaction is very sensitive to

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the voltage applied. With realistic quantumdot geometries, however, it is possible to achieve quantum logic operations in less than 1 ns, substantially less than the relaxation time of the electron spins, estimated to be on the order of 1 ms.8 This approach to quantum logic can potentially be applied to any material in which it is possible to apply voltage to gates to induce single-electron quantum wells. While it is probably best suited to GaAs/AlGaAs heterostructures, where the state of the art in single-electron device nanofabrication is the most advanced, it has also been discussed in other systems, including Si/SiGe heterostructures15 and carbon nanotubes.24 From a materials perspective, Group IV semiconductors have several important advantages over their III–V counterparts: Group IV semiconductors all have stable spin-0 nuclear isotopes, potentially allowing the refinement of these materials to re-

move an important source of decoherence in spin systems. Also, Si (and carbon-based) semiconductors have much smaller spin– orbit coupling strengths than GaAs and other III–V semiconductors, which generally translates into longer spin lifetimes. I proposed the first architecture for a quantum computer that takes advantage of the favorable properties of Si.11 Like the Loss–DiVincenzo approach, quantum operations are accomplished by controlling the exchange interactions between single electrons. The key difference is that the electrons are confined at isolated phosphorus donors in Si, instead of gate-defined quantum dots (Figure 2d). Donors are naturally defined single-electron quantum dots, confining precisely one electron in the 30 Å neighborhood of the P atom in the Si lattice. The electron wave function has a small amplitude extending a few hundred angstroms from the donor, so it is possible to control the exchange interaction between donors by applying a voltage to a gate located between the donor sites. An attribute of this proposal is that the quantum lifetimes of electrons and nuclear spins associated with P in Si have been thoroughly studied for almost 50 years and are known to be extraordinarily long.11,12 An obvious disadvantage is that building a donor-based quantum computer will require a new technology for placing single P donors into a Si crystal at prescribed sites. Doping of semiconductors is a ubiquitous and mature process in the semiconductor industry, but current processes involve

Figure 3. Schematic illustration of the potential (dashed lines) and the electron density (solid lines) for a quantum gate. A large potential barrier between the electron sites keeps the electrons isolated from one another, and the exchange interaction is small. Lowering the potential barrier turns on interactions, yielding a SWAP operation if the duration of the interaction is appropriate.

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Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials?

introducing many donors into a semiconductor either by diffusion or ion implantation—processes that inevitably introduce many donors into random locations in the silicon lattice. Nevertheless, the creation and study of single-dopant devices is currently an active area of research, and the results are very encouraging.25,26

Scaling Quantum Computation in Semiconductors It is arguably premature even to discuss scaling of quantum computer architectures: while research progress in the field is rapid, operations on one and two spins are currently the state of the art. Nonetheless, it is important to study scaling issues, since it is largely the exciting prospect of largescale semiconductor quantum computing that is driving progress in the field. Also, it is important to identify significant impediments to scaling so that research can be directed into areas that are not as likely to be scaling dead ends. It is noteworthy that many postmortems have been written about conventional computer technologies that failed to scale, in the hope that general properties could be identified that are favorable to scaling.27 Similar analyses may be applicable to assessing incipient quantum computer technologies. Intrinsic device variability is likely to be a major impediment to semiconductor quantum computer scaling. Such variability is the reason analog computers cannot be scaled, since small errors grow uncontrollably as complexity increases. It is also a severe problem facing many other novel approaches to computation.27 Classical digital circuits, with their binary outputs, can prevent small device variations from affecting a logic operation, allowing complexity to scale without limit. At first glance, it would appear that quantum logic will have the same problem as an analog computer: if the duration of the gate controlling coupling shown in Figure 1 is inappropriate, the result is a small error in the value of the resulting wave function. After many operations, the errors are sufficiently large that the wave function is completely randomized, and any quantum computer algorithm will fail. Shortly after the publication of Shor’s algorithm, theorists began applying the ideas of classical error correction to quantum information, and showed that quantum error correction is indeed possible.28 This development was surprising because quantum states are specified by continuous variables, and it was thought that arbitrarily small changes in these parameters would inevitably accumulate and lead ultimately to fatal errors. Quantum error correction entails redundant coding of quantum information and frequent measurement to

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keep the computation on track. Using these techniques, quantum algorithms can succeed as long as the error introduced by each gate operation is small.29 The maximum size of the error is dependent on the type of error and the error-correction protocol used, but is generally believed to be in the neighborhood of 0.01%. While the existence of errorcorrection protocols has spurred optimism that large-scale quantum computers will be possible, designing devices that have properties that are matched to 0.01% is still a very difficult prospect, especially in solidstate devices, where materials, fabrication, and processing all introduce substantial variations in the properties of the devices.

The Solution at a Small Scale: Hand Tuning The solution to the device variability problem that is being applied to current research devices and that may be applicable to small-scale quantum computers is to custom-tune each device so that a proper logic gate is applied to the qubits. In the context of the specific proposals discussed here, this process means applying different gate voltages to each device in an array to perform a given logic operation. While this is easy for a small number of devices (and may in fact be the method of choice for the foreseeable future), it will certainly become unwieldy if a future computer containing many thousands of devices is ever constructed. A particularly serious problem is that sending separate wires to every device in large two-dimensional arrays becomes unmanageable for even modestsized quantum processors.30 This “wire explosion” can only be prevented if many devices can be controlled with a single wire, and this will require all of the devices to have the same properties tuned to the precision necessary for quantum error correction (0.01%).

Intrinsic Limits on Device Variability in Semiconductor Quantum Computers: QuantumDot Approaches Will it ever be possible to fabricate semiconductor devices with a small enough device variability that hand-tuning is not necessary? If the devices discussed here are made with perfect precision, will they have the 0.01% precision required? I first consider the quantum-dot proposal, with the electrons confined in GaAs/AlGaAs quantum wells, which I assume are flawlessly fabricated, as are the surface gates that create the single-electron quantum dots and modulate the exchange interaction coupling. Unfortunately, there is a source of variability that can still affect the devices: the modulation doping necessary to ensure that

electrons are in the quantum well before the gate voltages are applied. Because the doping layer is spatially separated from the electrons in the quantum well, the scattering of electrons in the well is dramatically reduced, enabling the creation of extremely highmobility-electron systems in modulationdoped structures.31 However, the dopants, randomly located some distance away from the electrons, do still contribute a disorder potential that will affect the performance of gated devices.32 The effect of the dopants will be particularly pronounced on the magnitudes of the exchange interaction between two quantum dots, since small variations in the potential at the barrier can have a large effect on the tunneling amplitude between the dots and, hence, on the value of the exchange interaction (Figure 4). For the well-studied system of a double quantum well in GaAs/ AlGaAs heterostructures, a 3 meV variation in the potential energy in the barrier has approximately a 100% effect on the strength of the exchange coupling.19 It is straightforward to calculate the RMS value of potential energy fluctuations coming from modulation doping in typical double-dot systems. For a two-dimensional doping density n, a separation a between the doping layer and the electron layer, and a distance w from the electrons to the top gate, the result is: URMS 

e2n  



2 ln

w2 , 2w   (1)

where e is the electron charge and  is the dielectric constant of the semiconductor. For typical device values,8,22 (n  3  1011/cm2, a  200 Å, w  1000 Å, and   12), I obtain URMS  15 meV. Thus, the natural variability in devices that is purely attributable to modulation doping is already enough to have a 100% effect on the properties, far greater than the 0.01% thought to be required for quantum logic devices that are not hand-tuned. It may be possible to mitigate this problem by controlling the placement of dopants (assumed for donor devices in Si) or by using alternative gating techniques that eliminate modulation doping.33,15 The severity of the problem, however, illustrates that inherent small fluctuations that have no effect on the performance of individual devices can nonetheless be lethal to large-scale architectures.

Intrinsic Limits on Device Variability in Semiconductor Quantum Computers: Donors in Silicon Since the prospect of donor-based quantum computing is predicated on develop-

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Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials?

Figure 4. (a) Contour diagram of the potential in the neighborhood of two quantum dots, with arrows showing the paths the electrons must traverse to create transitions between states. The amplitude for these transitions to occur is extremely sensitive to the potential at the saddle point separating the two dots. (b) Side view of the dots, showing the randomly distributed donors in the modulation-doping layer. These dopants have a large effect on device variation, as described in the text.

ing a technology for the precise placement of single donors, it may seem that intrinsic device variation will be less of a problem in this system, and indeed, that was the hope when the proposal was first put forward. Given, however, that precise placement of donors is a severe challenge, the correct question to ask for this architecture is, what is the magnitude of the device variations induced by small misplacement of the donors from their target sites? Unfortunately, a subtle effect arising from the band structure of silicon means that even if donors are misplaced by a single lattice site, the effect on the exchange interaction can be on the order of 100%. As stated earlier, the exchange interaction is related to the amplitude for the electrons to tunnel between quantum dots or donors. In Si, the electron conduction-band minimum is sixfold degenerate. Thus, there are six different terms that contribute to the tunneling amplitude. These terms, however, can interfere with one another, leading to rapid oscillations in the tunneling amplitude as the relative positions of the donors are varied 34 (Figure 5). The large size of this effect means that unless there is essentially perfect placement of the donors, variations in the parameters of the logic gates will require hand-tuning, and scaling of the architecture will be difficult.35 The large variability discussed here is certainly not proof that semiconductor quantum computers cannot be scaled; in

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fact, several proposals have been developed that significantly reduce the problems with the quantum dots and donor proposals. For example, the rapid oscillations in the donor exchange interaction can be reduced in strained silicon, where the number of degenerate conduction bands is reduced from six to two.36 The oscillations are also not expected to be present in silicon-based architectures in which gates confine single electrons into quantum dots.15 It is also possible to use dipole–dipole interactions between spins rather than the exchange interaction, resulting in coupling strengths between spins that do not oscillate 37 (although the long-ranged dipole–dipole interaction is not as easily gated as the exchange interaction). Finally, it may be possible to design systems with essentially digital exchange interactions (either ON or OFF), with strengths given by properties of the device that are not very sensitive to device variation.38 While all of these approaches are worthy of exploration, it is likely that intrinsic device variability will be an important factor to evaluate in virtually any solid-state quantum computer design.

The Future of Quantum Computing: Devices Fabricated with Atomic Precision The extreme sensitivity to device variability of the quantum computer architectures discussed here is obviously a major roadblock to scalable quantum computing. It is certainly possible that alternative designs can be developed that are intrinsi-

Figure 5. Diagram of the exchange interaction in a system of two donors in Si as a function of donor separation. If only a single conduction-band valley were occupied (as is the case in GaAs), the exchange interaction would rapidly but smoothly diminish with donor separation (dashed curve).The sixfold degeneracy of the conduction band leads to rapid oscillations of the exchange interaction (solid line). Solid circles are possible sites on the silicon lattice.

cally less sensitive to fluctuations, and it may be possible that schemes will be developed that will make it possible to efficiently tune every device in a large quantum computer. Finally, algorithms can be developed that minimize the contribution of device variability to quantum computer operation. Nevertheless, it is probable that the development of materials and fabrication techniques yielding extremely small device variations will be absolutely necessary to the eventual construction of a largescale quantum computer in solid-state materials. To some degree, this goal is also important for scaling conventional electronics, but the constraints will inevitably be much more stringent for quantum computing: for example, the development of materials with high isotopic purity may be necessary for spin-based quantum computers, but are unlikely to be relevant for any foreseeable conventional electronic devices. One example of a success story in the development of new materials that allowed new classes of quantum devices to be created was the development and perfection of high-mobility GaAs/AlGaAs heterostructures, made possible by the invention of modulation doping. Improvement of these devices over a period of 25 years led to improvements in mobility of over four orders of magnitude27,39 and enabled the discovery of novel correlated states of the electrons at low temperatures, such as the fractional quantum Hall effect, and the eventual development of new classes of electronic devices with an unprecedented degree of perfection. While this process began with a new insight, much of the continuing progress has been the result of painstaking gradual improvements in the technology of molecular-beam epitaxy of these materials. Ultimately, the only way to prevent device variation from being an obstacle to large-scale quantum computing is to be able to fabricate devices at the atomic scale: devices constructed with the exact same atomic configuration will inherently have identical properties. While such a technological achievement will be extraordinarily difficult, it is almost the certain endpoint of the technological progress made over the last 50 years focused on creating ever-smaller semiconductor devices with increasingly well-controlled properties. The work done at IBM over the past decade, where atomic structures40 and even atomscale devices41 have been fabricated one atom at a time with a scanning tunneling microscope (STM), has established that engineering at this scale is possible. These results have spurred efforts to use similar STM techniques to precisely place phosphorus donors into a silicon host to produce the

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Can We Build a Large-Scale Quantum Computer Using Semiconductor Materials?

building blocks for a silicon quantum computer.21 While early results are very encouraging, it remains to be proven that the placement of donors can be done with the perfect precision necessary to prevent large device variability. Atom-scale fabrication techniques— certainly those involving STM manipulation—are intrinsically unable to efficiently produce devices in the volumes typically required for the large-scale integration of conventional electronics. This failing may not be a fatal deficiency for quantum logic devices, where relatively small numbers of devices, by the standards of conventional computing (hundreds or thousands of devices), would still be a tremendous advance in the state of the art for quantum computing. It is possible that methods for highly parallel fabrication of atom-scale devices may be developed in the future or that chemical methods of self-assembly will be relevant. The prospect of large-scale quantum computing in semiconductors is far from certain: the early sense that solid-state approaches to quantum logic will have significant technological advantages over alternative approaches needs to be tempered with the fact that device variability is ubiquitous in semiconductor materials and that most of the proposed technologies for semiconductor quantum computing are extremely sensitive to these variations. It is likely that these failings will hardly matter in the next few years, when experiments will be focused on a very small number of devices. Ultimately, however, these issues may prove to be decisive and highlight the need to begin exploring materials and fabrication techniques that are at the ultimate limit of atomic perfection.

Acknowledgments The author benefited from helpful discussions with Xuedong Hu during the preparation of this manuscript. Research is supported by the U.S. National Security Agency and the Advanced Research and Development Activity (ARDA).

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Bruce E. Kane has worked in semiconductor physics for 20 years, starting at Princeton University and then at Bell Laboratories on studies of the quantum Hall effect in GaAs/AlGaAs heterostructures. Intrigued by the prospect of quantum computing, he set out in the late 1990s to develop viable approaches for performing quantum logic in semiconductor devices. He has subsequently presented dozens of talks to a wide variety of audiences on quantum computing and its implementation in semiconductors. Kane has been a member of the quantum computing research team at the University of Maryland’s Laboratory for Physical Sciences since 1999. He holds a BA degree in physics from the University of California, Berkeley, and a PhD degree in physics from Princeton. Kane can be reached by e-mail at kane@ lps.umd.edu. ■

MRS BULLETIN • VOLUME 30 • FEBRUARY 2005