Quantum computing, much like classical computing, relies on gates and memory to process and store quantum bits or qubits. Solid-state qubits are promising because of their potential for scaling into integrated quantum circuits consisting of thousands or millions of qubits. A single electron in a semiconductor nanostructure may act as a single qubit, with the electron's spin-up and spin-down states serving as logical 0 and 1. Unfortunately, the memory time of such a qubit is limited to a few microseconds.1,2 Therefore, we want quantum gates to be extremely fast in order to achieve many operations within the qubit's memory time.
Previously, researchers have used radio-frequency radiation to coherently manipulate the spin of a single electron in a semiconductor quantum dot (QD) nanostructure.3–6 Unfortunately, these radio-frequency pulses are slow, and typical operations using this technique take several nanoseconds. This would set a limit of about 1000 operations within the qubit's memory time, which is insufficient for many quantum computing protocols. We take a different approach: using ultrafast pulses of light, the single electron spin can be manipulated in a few tens of picoseconds,7 about one hundred times faster than previous approaches.
The state of the single spin can be represented as a vector on a sphere, called the Bloch sphere, as illustrated in Figure 1. A single-qubit operation is described as a rotation of the Bloch vector. We use a single mode-locked laser pulse to coherently rotate the electron spin about the x-axis (between the two spin states, up |↑〉 and down |↓〉) via a stimulated Raman transition. Rotations about the z-axis are accomplished by allowing the spin to precess in a static applied magnetic field.
We observe the spin state's projection along the z-axis by optical pumping with a tunable continuous-wave laser, a standard technique from atomic physics,8 and detecting the emitted photons using a photon-counting avalanche photodiode. An added benefit of optical pumping is that the process also initializes the spin state into the spin-up state |↑〉. Thus, in one experiment, we demonstrate a complete sequence of initialization, coherent control, and measurement of a single qubit. Our experiments begin by initializing the spin into a pure spin-up state |↑〉 with fidelity exceeding 90%. We then apply an optical pulse to rotate the spin vector about the x-axis into a coherent superposition of |↑〉 and |↓〉. By varying the intensity of the rotation pulse, we demonstrate over six complete Rabi oscillations between the two spin states as shown in Figure 2.
Figure 1. The electron spin state is represented by the bold arrow in the Bloch sphere. Pure spin-up and spin-down states are at the north and south poles of the Bloch sphere, respectively. The static magnetic field B causes rotation about the z-axis, while the ultrafast laser pulse causes rotation about the x-axis.
Figure 2. The signal is proportional to the projection of the spin vector on the z-axis after a rotation pulse is applied. The so-called Rabi oscillations occur as the spin is rotated about the x-axis by the laser pulse. a.u.: Arbitrary units.
In a second experiment, we demonstrate an effect called Ramsey interference. We rotate the initialized spin-up state by π/2 about the x-axis, then allow a variable rotation about the z-axis by Larmor precession. Finally, we apply a second π/2 rotation about the x-axis, and measure the spin's z-projection using optical pumping. As the time delay between pulses is varied, ‘Ramsey fringes’ (see Figure 3) are observed. In addition to demonstrating control of the qubit's phase, the Ramsey fringes allow us to deduce the fidelity of our π/2 rotations to be about 94%. A similar experiment performed with π rotation pulses showed our π-pulses to have 91% fidelity.
Figure 3. Ramsey interference is observed by applying a pair of π/2 rotations about the x-axis separated by a variable time delay.
The fast operations we have demonstrated will be important for scalable quantum computers based on semiconductor spin qubits. Next, we plan to use an optical cavity to convert between the stationary spin qubit and a ‘flying’ photonic qubit to transmit quantum information.
David Press received his MS degree in applied physics from Stanford University in 2006 as a fellow of Sony Corporation and the Natural Sciences and Engineering Research Council of Canada. He is currently a PhD candidate under the supervision of Yoshihisa Yamamoto.
National Institute of Informatics
Yoshihisa Yamamoto has been professor of applied physics and electrical engineering at Stanford University since 1992 and at the National Institute of Informatics since 2003. He is also a leader of the Japan Science and Technology Agency SORST and CREST projects on quantum information.