Putting a new spin on quantum-dot qubits

Realizing the potential of quantum computing requires finding viable ways to store and manipulate representations of the binary bits, 0 and 1. The many two-level quantum systems being explored for such qubits include not only the up and down spins of trapped atoms or ions and the polarized states of photons, but also the quantum states of superconducting Josephson junctions and electron spins trapped in quantum dots. A quantum dot is a nanostructure that confines a conduction-band electron in three spatial dimensions.

Quantum-dot qubits take advantage of the extensive experience gained over decades of engineering and manufacturing semiconductor devices. They were proposed ¹ in 1998 by Daniel Loss (now at the University of Basel, Switzerland) and David DiVincenzo (RWTH Aachen University). A central challenge is to manipulate the electron spin in a time that’s short compared with the time for it to lose coherence, and to do it in a spatially selective way—so that each qubit can be addressed individually. Resonant magnetic fields can flip the spins, ² but the magnetic fields involved are not very selective spatially. Plus, the time to reverse the spin is too slow except at high field strengths. The experiments also require high frequencies and very low temperatures. “You put all of this together and it makes for a very hard experiment,” remarks Jason Petta of Princeton University.

A more desirable approach is to control the spins with just electric fields. ³ Although they can’t directly affect an electron’s magnetic moment, electric fields can impact it indirectly through the coupling between the electron’s orbital motion and its spin. Electrical control of single spins via such spin–orbit coupling was demonstrated three years ago in gallium arsenide quantum dots by Lieven Vandersypen and colleagues at the Delft University of Technology in the Netherlands, but the manipulation times were too slow (about 110 ns for a spin flip) to allow quick and precise control. ⁴

By turning to indium arsenide, whose spin–orbit coupling is known to be stronger than that in GaAs, ⁵ Leo Kouwenhoven and his collaborators at Delft and at the Eindhoven University of Technology have now demonstrated electrical control with spin-flip times of about 8 ns. ⁶ The experiment was done with quantum dots formed in a one-dimensional wire just 50 to 80 nm in diameter. Using a nanowire may enable experimenters to vary slightly the properties as a function of length. It should also facilitate the interfacing of the InAs with other materials. A more exotic possibility is that InAs nanowires might be used to create the Majorana particles that are of interest for topological quantum computing (see the box on page 20).

David Awschalom of the University of California, Santa Barbara (UCSB) describes the new experiment as “a beautiful demonstration of how coherent quantum states can be electrically manipulated via spin–orbit interactions.” He hopes that beyond its applicability to quantum computing, the work will lead to new fundamental studies of quantum spin transport.

A parallel approach to implementing quantum-dot qubits is to couple the spins on neighboring dots, thereby forming two-electron spin states. The qubit then consists of a double quantum dot, whose quantum state—singlet or triplet—can be rapidly controlled by voltage pulses ⁷ (see PHYSICS TODAY, March 2006, page 16 ). Last year Princeton’s Petta, along with Hong Lu and Art Gossard of UCSB, introduced a technique that enables control of a spin state as fast as 1.5 ns. ⁸ In addition, Amir Yacoby and his collaborators at Harvard University and at the Weizmann Institute of Science in Rehovot, Israel, have demonstrated techniques to extend the decoherence times for double quantum-dot qubits ⁹ to values as long as 200 µs. Charles Marcus and his colleagues at Harvard and at UCSB reported similar results. ¹⁰

Nanowire qubits

The device built by Kouwenhoven and his team is shown in figure 1a. The electrostatic potentials on five electric gates below the nanowire define two quantum dots, as shown in figures 1b and 1c. One dot is the qubit; the other is used for reading out the state of the qubit. The qubit operation scheme is depicted schematically in figure 1c. To initialize the information, the potentials are adjusted so that electrons can flow from one quantum dot to the next, but they do so one at a time and only if consecutive electrons have opposite spins. Thanks to the Pauli exclusion principle, current stops when the spins of electrons on the two dots are parallel. During manipulation of the quantum information, the potential of the qubit is reduced, and the charge blockade prevents electrons from escaping. To read out the final state of the qubit, electrons are again allowed to flow. The presence or absence of current signals tells experimenters whether the qubit spin ended up antiparallel or parallel to the readout spin.

To understand the spin–orbit coupling used to manipulate the qubit spin, consider an electron moving in the electric field of the positively charged nuclei in the semiconductor. In its rest frame, the electron experiences not only an electric field from those charges but also a magnetic field, which interacts with the electron’s magnetic moment, or spin. The experimenters exploit that coupling by applying a 13-GHz microwave field to electrode 4 to move the electron slightly back and forth with a frequency on resonance with the spin-precession frequency.

To demonstrate that spin–orbit coupling allows coherent spin control, Kouwenhoven and his collaborators measured the current through the coupled quantum dots as a function of the burst time for the oscillating field. The current varies cyclically as the spin changes its orientation, resulting in the so-called Rabi oscillations seen in figure 2. The experimenters could resolve at least five cycles before decoherence excessively damped the signal. Each half cycle represents a spin flip. The shortest cycle, corresponding to a frequency of 60 MHz, was obtained at the highest microwave power.

One disappointment of the InAs nanowire qubit is the short spin decoherence time. Decoherence most likely results from the interaction of the electron spins with the magnetic field of the randomly oriented nuclear spins. Fluctuating nuclear spins produce a shift in the precession frequency and in the resonance condition of the electron spin. Because measurements of Rabi oscillations are averaged in time over a million single-spin measurements, the qubit rotates by a slightly different angle each measurement, thereby causing the apparent decoherence—that is, the washing out of the Rabi oscillations.

To partially reverse its effect, researchers have borrowed the spin-echo technique from nuclear magnetic resonance: First they allow the spins to evolve freely for a period of time T. They then apply a pulse of just the right duration to flip the spins and wait another time period of T before reading out the qubit. The effect of the field on the flipped spins in the second period acts to cancel the decoherence that occurred during the first.

By repeated application of the spin-echo technique to the InAs nanowire qubits, the Delft–Eindhoven collaborators were able to extend the decoherence time to nearly 200 ns. That is still orders of magnitude below the 270 µs times measured in GaAs singlet–triplet qubits using multiple-pulse spin echo techniques.⁹ The long time measured in GaAs has been shown to result from the slow dynamics of the nuclear bath and is in quantitative agreement with theoretical predictions. ¹¹ It’s not known if the same effect exists in InAs. Kouwenhoven suspects that InAs’s shorter decoherence time is related to the larger nuclear spin of indium compared with gallium or arsenic.

Flexibility of nanowires

One reason for interest in the recent Delft–Eindhoven work is the possibility of combining different semiconductor materials in the same nanowire. Kouwenhoven points out this should be much easier in nanowires because you don’t have the same strain due to lattice mismatch that arises on a 2D surface. For example, one might mate InAs with nuclear-spin-free silicon so that qubits can still be manipulated using the strong spin–orbit coupling of InAs while being stored in silicon, where they survive far longer. Another possibility is to create an optoelectronic device to convert the spin state to a photon for long-distance transportation of quantum information.

Experimenters might also be able to tailor the composition of the nanowire as a function of its length: By causing each qubit to experience a slightly different Zeeman splitting (via a difference in gyromagnetic ratios between adjacent dots), they could address each one more precisely.

Sankar Das Sarma of the University of Maryland is especially excited about InAs nanowires as a possible new approach to topological computation (see the box). The basic element of a topological computer is a non-abelian quasiparticle that does not obey the same symmetry rules as fermions or bosons under exchange of identical particles (see the article by Das Sarma, Michael Freedman, and Chetan Nayak in PHYSICS TODAY, July 2006, page 32 ). Das Sarma is among those who have proposed that a non-abelian particle known as a Majorana fermion might arise from spin–orbit coupling in a semiconductor, if that semiconductor is placed in a magnetic field in the proximity of a conventional superconductor.

It’s certainly too early to pick a winner in the competition for the elements of a quantum computer. Perhaps a combination of approaches will be the best answer to the challenges of quantum computation.