Erika Kawakami

Gate fidelity and coherence of an electron spin in an Si/SiGe quantum dot with micromagnet

Significance A quantum computer is able to solve certain problems that cannot be solved by a classical computer within a reasonable time. The building block of a quantum computer is called a quantum bit (qubit), the counterpart of the conventional binary digit (bit). A qubit unavoidably interacts with its environment, leading to errors in the qubit state. This article reports on the qubit performance of an electron spin in a silicon/silicon-germanium (Si/SiGe) quantum dot, and examines the dominant error mechanisms. We demonstrate that this qubit can be electrically controlled with sufficient accuracy so that remaining errors could, in principle, be corrected using known protocols, even without isotopically purified silicon. This qubit also offers a quantum memory that lasts for almost 0.5 ms. The gate fidelity and the coherence time of a quantum bit (qubit) are important benchmarks for quantum computation. We construct a qubit using a single electron spin in an Si/SiGe quantum dot and control it electrically via an artificial spin-orbit field from a micromagnet. We measure an average single-qubit gate fidelity of ∼99% using randomized benchmarking, which is consistent with dephasing from the slowly evolving nuclear spins in the substrate. The coherence time measured using dynamical decoupling extends up to ∼400 μs for 128 decoupling pulses, with no sign of saturation. We find evidence that the coherence time is limited by noise in the 10-kHz to 1-MHz range, possibly because charge noise affects the spin via the micromagnet gradient. This work shows that an electron spin in an Si/SiGe quantum dot is a good candidate for quantum information processing as well as for a quantum memory, even without isotopic purification.

Second-Harmonic Coherent Driving of a Spin Qubit in a Si/SiGe Quantum Dot.

We demonstrate coherent driving of a single electron spin using second-harmonic excitation in a Si/SiGe quantum dot. Our estimates suggest that the anharmonic dot confining potential combined with a gradient in the transverse magnetic field dominates the second-harmonic response. As expected, the Rabi frequency depends quadratically on the driving amplitude, and the periodicity with respect to the phase of the drive is twice that of the fundamental harmonic. The maximum Rabi frequency observed for the second harmonic is just a factor of 2 lower than that achieved for the first harmonic when driving at the same power. Combined with the lower demands on microwave circuitry when operating at half the qubit frequency, these observations indicate that second-harmonic driving can be a useful technique for future quantum computation architectures.

Dressed photon-orbital states in a quantum dot: Intervalley spin resonance

The valley degree of freedom is intrinsic to spin qubits in Si/SiGe quantum dots. It has been viewed alternately as a hazard, especially when the lowest valley-orbit splitting is small compared to the thermal energy, or as an asset, most prominently in proposals to use the valley degree of freedom itself as a qubit. Here we present experiments in which microwave electric field driving induces transitions between both valley-orbit and spin states. We show that this system is highly nonlinear and can be understood through the use of dressed photon-orbital states, enabling a unified understanding of the six microwave resonance lines we observe. Some of these resonances are inter-valley spin transitions that arise from a non-adiabatic process in which both the valley and the spin degree of freedom are excited simultaneously. For these transitions, involving a change in valley-orbit state, we find a tenfold increase in sensitivity to electric fields and electrical noise compared to pure spin transitions, strongly reducing the phase coherence when changes in valley-orbit index are incurred. In contrast to this non-adiabatic transition, the pure spin transitions, whether arising from harmonic or subharmonic generation, are shown to be adiabatic in the orbital sector. The non-linearity of the system is most strikingly manifest in the observation of a dynamical anti-crossing between a spin-flip, inter-valley transition and a three-photon transition enabled by the strong nonlinearity we find in this seemly simple system.

Excitation of a Si/SiGe quantum dot using an on-chip microwave antenna

We report transport measurements on a Si/SiGe quantum dot subject to microwave excitation via an on-chip antenna. The response shows signatures of photon-assisted tunneling and only a small effect on charge stability. We also explore the use of a d.c. current applied to the antenna for generating tunable, local magnetic field gradients and put bounds on the achievable field gradients, limited by heating of the reservoirs.

Valley dependent anisotropic spin splitting in silicon quantum dots

Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to their exceptionally long coherence times and compatibility with the silicon transistor platform. To achieve electrical control of spins for qubit scalability, recent experiments have utilized gradient magnetic fields from integrated micro-magnets to produce an extrinsic coupling between spin and charge, thereby electrically driving electron spin resonance (ESR). However, spins in silicon QDs experience a complex interplay between spin, charge, and valley degrees of freedom, influenced by the atomic scale details of the confining interface. Here, we report experimental observation of a valley dependent anisotropic spin splitting in a Si QD with an integrated micro-magnet and an external magnetic field. We show by atomistic calculations that the spin-orbit interaction (SOI), which is often ignored in bulk silicon, plays a major role in the measured anisotropy. Moreover, inhomogeneities such as interface steps strongly affect the spin splittings and their valley dependence. This atomic-scale understanding of the intrinsic and extrinsic factors controlling the valley dependent spin properties is a key requirement for successful manipulation of quantum information in Si QDs.Silicon-based qubits: understanding coupling between spin and valleys in quantum dotsExperiments have now revealed the role of spin–orbit interaction in coupling electrons’ spin and valley degrees of freedom in silicon quantum dots. An international collaboration led by Rajib Rahman from Purdue University, United States, has measured the electron-spin resonance frequencies in a silicon quantum dot with an integrated micro-magnet as an external magnetic field was applied from different directions. The data revealed an anisotropic behavior of the spin resonance for different valley states—minima of the conduction band. Quantitative agreement with the experimental data could be obtained from spin-resolved atomistic tight-binding calculations by taking into account the spin–orbit interaction—normally neglected as too weak in bulk silicon. These new insights into the coupling between the spin and valley degree of freedom could be used to better protect or encode quantum information in quantum dots.