Scalable Quantum Computing Using Solid-State Devices

The end limit of Moore’s Law scaling is the threshold of the quantum realm.

The field of solid-state quantum computing is in its infancy. Coherent operations on single qubits (the simplest type of quantum logical operation) have only recently been demonstrated (Nakamura et al., 1999; Vion et al., 2002). Nevertheless, there is a great deal of optimism that solid-state implementations of quantum computers will ultimately lead to scalable architectures in the same way that the invention of the transistor and integrated circuit presaged the development of large-scale and networked conventional computers. The optimism is based on the tremendous amount of research being done over a broad front that is heading steadily toward the development of devices for conventional computation built on nearly the atomic scale. This limit is the end of Moore’s Law scaling, but only the threshold of the quantum realm. Thus, the nascent field of solid-state quantum computing can capitalize on research intended for the development of smaller and faster conventional logical devices.

Many difficulties will have to be overcome before qubits can be integrated into solid-state systems. Because there are on the order of 1023 atoms in a solid-state device, it is very difficult to attain the decoupling from extraneous degrees of freedom that is necessary for large-scale quantum computing. Hence, much of the early research on solid-state quantum computing has been focused on identifying potential qubits inherently isolated from their surroundings. Most current research is focused either on superconducting qubits (quantum information is stored on flux states in a SQUID or on charge states of a small "Cooper pair box") or on electron-spin or nuclear-spin qubits in semiconductors. To have the necessary long decoherence times, these devices must invariably operate at low temperatures (< 1K). Even if research is successful, it is still not obvious that these technologies will be scalable (it is noteworthy that many conventional solid-state devices, such as bipolar transistors and tunnel diodes, proved to be unsuitable for very large-scale integrated circuits for reasons that only became apparent years after they were developed). Figure 1 shows the range of research being done on quantum computers.
A major surprise in the early days of quantum computing theory was that quantum error correction was possible at all; it has been shown that if a qubit of quantum information is redundantly coded into several qubits, errors in quantum computation can be reduced just as they can be corrected in classical communications channels (Neilson and Chuang, 2000). One certainty is that the operation of scalable quantum computers will rely heavily on error correction. There is a "threshold for error corrected continuous quantum computation." When errors at the single-qubit-level quantum operations are reduced below this threshold, quantum computation becomes possible.

The error threshold is still very stringent. At most, one error can occur in every ~104 operations. This level of accuracy is beyond the level of device variability of most, if not all, solid-state devices currently manufactured. Meeting the accuracy threshold will undoubtedly be one of the major challenges advocates for solid-state quantum computation will have to overcome. Even if the accuracy threshold can be reached, error correction will place a substantial overhead on the resources of a quantum computer because many physical qubits encode the same logical qubit. Also, most logical operations in the computer will simply be implementing error correction protocols (Steane, 2002).

Key Issues
Scaling of quantum computing will undoubtedly be a formidable task that justifies the skepticism expressed by many people (Keyes, 2001). Nevertheless, an outline of the leading issues can be helpful for a preliminary assessment of current approaches to large-scale quantum computing. Many of these issues relate to information flow rather than to individual quantum operations on which most current research is focused.

Efficient on-chip quantum communication will be essential for the development of large-scale solid-state quantum computing. Communication between devices is also important in conventional computers, but the need for quantum error correction necessitates the continuous transfer of redundant qubits throughout the computer. Rapid flow of quantum information will thus be essential for scalable quantum computing.

Cross talk must be minimized. As the number of qubits increases, the potential for errors due to unwanted coupling between qubits also increases. Spatially localized qubits could minimize this type of error.

Parallel logical and measurement operations must be possible. We usually distinguish between the coherent logical operations of a quantum computer and the measurements of 0’s and 1’s that must ultimately produce the results of an algorithm. Error correction, however, requires that both types of operations go on together; in large-scale quantum computers they should occur simultaneously.

Logic, measurement, and communication must be able to be performed at high speed. Because of the exponential acceleration of quantum algorithms, a quantum computer operating at any clock speed will outperform its classical counterpart. However, given a choice between two otherwise equivalent quantum computer architectures, the faster architecture will be the most desirable.

Individual quantum devices must be precisely engineered. The accuracy threshold for quantum computing suggests that the variability between quantum logical devices must differ by no more than 1 part in 104.

Major Limitations
As yet, no proposed implementation for large-scale quantum computers has addressed all of these criteria. However, it is possible to outline the major limitations of the approaches currently receiving the most attention.

Trapped-ion quantum computers. Although ion traps are not traditionally thought of as solid-state devices, recent proposals include complex metallizations on substrates to control and move ions between sites and are similar in many important ways to solid-state implementations. Kielpinski et al. (2002) have addressed many scaling issues, but moving ions to move quantum information is an intrinsically slow process because ion masses are typically 105 that of electrons. Therefore, it would be desirable if quantum information could be carried on lighter particles (like electrons).

Superconducting-qubit quantum computers. The primary advantage of superconducting qubits is that they are macroscopic. Consequently, devices are being fabricated with relatively simple micron-scale lithography. A drawback is that quantum information must be moved in the computer by electromagnetic excitations on metal traces. Large-scale implementations of superconducting quantum computers may thus be vulnerable to cross talk, a problem also encountered in conventional computers that have complex metal interconnects.

Electron-spin and nuclear-spin quantum computers. Quantum computer architectures that use electron spins or nuclear spins as qubits in a solid-state quantum computer are perhaps the most technologically challenging (Kane, 2000). These architectures also have some compelling advantages: spin qubits are known to be extremely well isolated from their environments in some materials and have longer quantum lifetimes (measured using electron-spin and nuclear-spin resonance techniques) than any other qubit under investigation in solids. Interestingly, silicon - the material in which almost all conventional computers are implemented - is also characterized by extremely long-lived spin states that can potentially be used for quantum computing. Spin coupling is extremely local, so cross talk is minimal if spins can be well isolated. Spin can be conveniently transported rapidly on electrons driven by electric fields (Skinner et al., 2002). Finally, parallel, rapid quantum logic and measurement appear to be possible using spin qubits (Figure 2).

The major difficulty with spin-based implementations of quantum computers is that they require measurement and control of single electron spins or nuclear spins, a task that is only now on the threshold of realization. Scalable spin-based quantum computing will probably require the development of a new technology in which single atoms can be accurately positioned to create devices with the precision necessary for quantum computation. Fortunately, several promising approaches (Figure 3) for fabricating these single-atom devices are currently being explored (O’Brien et al., 2001).

Conclusion
The development of large-scale quantum computers will require an unprecedented combination of precision and complexity. Extremely complex conventional information processors are only possible because digital logic is tolerant to device variation. Quantum logic is much less forgiving. Thus, realizing the dream of a large-scale quantum computer will require that engineers overcome the daunting challenge of combining the precision of an atomic clock with the complexity of a modern microprocessor.

References
Kane, B.E. 2000. Silicon-based quantum computation. Fortschritte der Physik 48(9/11): 1023-1042.
Keyes, R.W. 2001. The cloudy crystal ball: electronic devices for logic. Philosophical Magazine B 81(9): 1315-1330.
Kielpinski, D., C. Monroe, and D.J. Wineland. 2002. Architecture for a large-scale ion-trap quantum computer. Nature 417(6890): 709-711.
Nakamura, Y., Y.A. Pashkin, and J.S. Tsai. 1999. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398(6730): 786.
Nielson, M.A., and I.L. Chuang. 2000. Quantum Computation and Quantum Information. Cambridge, U.K.: Cambridge University Press.
O’Brien, J.L., S.R. Schofield, M.Y. Simmons, R.G. Clark, A.S. Dzurak, N.J. Curson, B.E. Kane, N.S. McAlpine, M.E. Hawley, and G.W. Brown. 2001. Towards the fabrication of phosphorus qubits for a silicon quantum computer. Physical Review 64(16): 161401(R).
Skinner, A. J., M. E. Davenport, and B.E. Kane. 2000. Hydrogenic spin quantum computing in silicon: a digital approach. Available online at http://arxiv.org/abs/quant-ph/0206159.
Steane, A.M. 2002. Quantum computer architecture for fast entropy extraction. Quantum Information and Computation 2: 297-306.
Vion, D., A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, and M.H. Devoret. 2002. Manipulating the quantum state of an electrical circuit. Science 296(5569): 886-888.