Quantum computers promise to solve many difficult problems much faster than so-called classical computers, and they will be essential for certain calculations impossible by any other means.

While a quantum computer could conceivably look very different from its classical forebears, hardware that draws on the experience of the classical past — meaning silicon, in this case — would have significant technological and manufacturing advantages. 
 
That's why Thomas Schenkel of Lawrence Berkeley Laboratory's Accelerator and Fusion Research Division (AFRD) and his collaborators are working to demonstrate that a quantum logic system can work in silicon devices. 

“Essentially the goal is to find out if quantum computing is possible with donor electron-spin qubits in silicon,” says Schenkel, explaining that he and his group propose to use the spin states of donor atoms embedded in silicon as the fundamental components of a quantum computer: its quantum bits, or “qubits.” Unlike a classical bit that codes for one state or another — a 1 or a 0 — a qubit encodes these states simultaneously, holding them in superposition until measured.

An often used if overly simple illustration of the potential power of quantum computing is the tiny three-bit register. Whereas a three-bit register in a classical computer outputs just one of eight discrete states (000, 001, 010 … 111), three entangled qubits represent a mixture of all these states simultaneously. In general, the capacity of a quantum computer's register is 2 raised to the power of the number of qubits — in this case 23 — a value that expands rapidly. A few dozen entangled qubits could represent a difficult problem in a vast computational space.

In a classical computer bits are routinely encoded as distinguishable states of a physical system, for example, the orientation of magnetic domains on a hard drive or tape, or the number of electrons stored in transistors on a flash drive. Classical calculations are performed essentially one bit after another. What makes qubits distinctive is that they are subject to the peculiar laws of quantum mechanics, in particular entanglement.

Entangled systems with a limited number of permissible quantum states are spookily “connected.” Two electrons prepared together, one with spin up and one with spin down, remain entangled until a measurement is performed on one of them; when the state of one is measured (spin down, say), the state of the other is instantly determined (spin up), no matter how distant it may be. The same holds true for a dozen entangled particles, or a hundred, or more.

With quantum computing, says Schenkel, “The idea is to find the solution by first acting on all the entangled qubits in parallel through clever quantum gate operations, and then to extract the solution in measurements that simultaneously 'collapse' the superpositions of the entire system to a series of classical zeros and ones.”

One system for realizing a qubit is electron spin, an intrinsic property of electrons that, given an external magnetic field, forms an accessible two-level system. In conventional silicon transistors, group V elements like phosphorus, antimony, and bismuth are widely used as donors — atoms having one more valence electron than group IV silicon and thus useful for adjusting its electronic properties (commonly by causing the silicon to become n-type, or negatively conducting). At low temperature these donors, having one extra electron, represent natural quantum dots; the spin state of the extra electron defines the qubit. 

But the idea of donor electron-spin qubits in silicon is just one of many different proposals for realizing qubits, Schenkel says. Other approaches include schemes involving superconducting tunnel junctions, quantum dots, and neutral atoms in optical lattices. He says, “Ion-trap systems are currently in the lead, with amazing demonstrations of qubit control, with up to eight ions.”

Ion-trap systems electromagnetically suspend ionized atoms in free space and use laser beams to alter and measure their spin states, a tricky procedure. But in the long run, quantum computers based on silicon could be manufactured with familiar materials and methods — maybe even mass produced — and could prove easier to scale up.

One qubit at a time

Demonstrating a working single-qubit device is the first step to proving that quantum computing can work in silicon. Schenkel and his colleagues are developing a field-effect transistor made of isotopically enriched silicon, in which the flow of current through the device is sensitive to the spin state of a single donor atom — a “single-spin readout” device.

Demonstrating the readout of a single donor's electron spin is the biggest part of the challenge, one of three goals Schenkel and his collaborators are pursuing in parallel. Another is to develop a technique for placing the desired number of dopant atoms into the readout devices. They have already demonstrated significant progress toward this end with a scanning-probe alignment instrument that aims and positions an ion beam over a target.

“It will take many qubits to make a quantum computer,” Schenkel says, “and the qubits must remain entangled with one another for long periods of time — long with respect to the time it takes to execute basic quantum-gate operations. Here the coherence times should be at least ten thousand times longer then basic gate operation times. This ensures that error correction techniques can be applied efficiently.”

So the group's third goal is to show that donor atoms can be placed into silicon transistors by ion implantation techniques and still retain their essential spin coherence properties. In a recent article in Applied Physics Letters, Schenkel's team demonstrated that the electrons of donor atoms can indeed maintain their spin states and phase coherence for the length of time needed to perform elemental quantum computing. 

“Spin resonance measurements performed by our collaborator Steve Lyon and members of his group at Princeton University showed phase coherence times several milliseconds long for electron spin states in atoms of antimony, which had been implanted into isotopically enriched silicon,” says Schenkel. The silicon was annealed after ion implantation in a standard heating process that repairs damage to the silicon crystal lattice caused by the implantation itself.

“A donor atom's ability to function as a qubit depends on its being placed on a lattice position,” Schenkel explains. “Implantation is not a gentle process; it's like sending a bowling ball into a bunch of pins. During the rapid annealing step, the scattered pins arrange themselves back into their proper lattice positions. Only now, on one position the pin is replaced by the bowling ball.”

After low doses of antimony were implanted in the silicon, annealing coaxed the antimony donors onto lattice positions where they were electrically active. Their spin states showed remarkably long coherence times, about one millisecond at the slightly chilly temperature of liquid helium. Nor had the antimony atoms diffused much during the annealing, thus fulfilling two of the major requirements needed to demonstrate the team's concept of quantum computation.

These promising results motivate the next, all-important (and much more difficult) step: the development of a readout transistor for single spins.

“Progress in understanding spin coherence properties in silicon, device development, and our work in ion placement are converging, allowing us to shoot for qubit demonstrations in well-tempered transistors”, Schenkel says, although he cautions that there is still “a huge gap between demonstrating a single qubit and a quantum computer with hundreds or thousands of qubits that can outperform current classical computers.”

Yet, says Schenkel, “the appeal of quantum computing in silicon has always been allegedly long spin-coherence times and scalability. We have now shown that coherence times really do remain quite long in realistic predevice structures. Once we can show a reliable single spin readout, we hope that the scalability advantages inherent in mature silicon technology will push the door to multiqubit logic demonstrations wide open.”

Some of the most intriguing possible applications of quantum computers are in methods of encryption and decryption, key to business communications and national security. This is one reason the National Security Agency recently made a $2.8 million “quantum-computing concept maturation” (QCCM) grant to Schenkel's group. While no classified research of any kind is done at Berkeley Lab, the NSA supports basic research on high-performance computing programs, including the quantum computer architectures of the future.  

Of his group's project to demonstrate donor-electron-spin qubits in silicon, Schenkel says, “We have now set up a well defined archery target to shoot at. The QCCM grant represents the bunch of arrows that is handed to us.”

Investigating the theory, fabrication, and measurement of quantum computing devices in silicon with Schenkel are co-investigators Jeffrey Bokor of MSD and the University of California at Berkeley's Department of Electrical Engineering and Computer Sciences; nanofabrication wizard J. A. Liddle of Berkeley Lab's Materials Sciences Division (MSD); Birgitta Whaley and Rogerio de Sousa of UC Berkeley's Department of Chemistry and Pitzer Center for Theoretical Chemistry; and Stephen Lyon and Alexei Tyryshkin of Princeton University's Department of Electrical Engineering.

Additional information

“Electrical activation and electron spin coherence of ultralow dose of antimony implants in silicon,” by T. Schenkel, J. A. Liddle, and A. Persaud of Berkeley Lab; A. M. Tyryshkin and S. A. Lyon of Princeton; R. de Sousa and K. B. Whaley of UC Berkeley; J. Bokor and J. Shangkuan of Berkeley Lab and UC Berkeley; and I. Chakarov of Silvaco International, appeared in the 13 March 2006 issue of Applied Physics Letters (http://www.lbl.gov/Science-Articles/Archive/assets/images/2006/May/17-Wed/Schenkel-Coherence.pdf).

More about theoretical and experimental advances in quantum computing at Berkeley Lab at http://www.lbl.gov/Science-Articles/Archive/sabl/2005/June/02-quantum-comp.html.

More about algorithms for quantum computers at http://www.lbl.gov/Science-Articles/Archive/CSD-quantum-chemistry.html.

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This article first appeared in Science@Berkeley Lab (http://enews.lbl.gov/)