High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit

www.nature.com/npjqi All rights reserved 2056-6387/15 ARTICLE OPEN High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit Dohun Kim1,2, Daniel R Ward1, Christie B Simmons1, Don E Savage3, Max G Lagally3, Mark Friesen1, Susan N Coppersmith1 and Mark A Eriksson1 We implement resonant single qubit operations on a semiconductor hybrid qubit hosted in a three-electron Si/SiGe double quantum dot structure. By resonantly modulating the double dot energy detuning and employing electron tunnelling-based readout, we achieve fast (4100 MHz) Rabi oscillations and purely electrical manipulations of the three-electron spin states. We demonstrate universal single qubit gates using a Ramsey pulse sequence as well as microwave phase control, the latter of which shows control of an arbitrary rotation axis on the X–Y plane of the Bloch sphere. Quantum process tomography yields π rotation gate fidelities higher than 93 (96)% around the X (Z) axis of the Bloch sphere. We further show that the implementation of dynamic decoupling sequences on the hybrid qubit enables coherence times longer than 150 ns. npj Quantum Information (2015) 1, 15004; doi:10.1038/npjqi.2015.4; published online 27 October 2015 INTRODUCTION Isolated spins in semiconductors provide a promising platform to explore quantum mechanical coherence and develop engineered quantum systems.1–13 Silicon has attracted great interest as a host material for developing spin qubits because of its weak spin-orbit coupling and hyperfine interaction, and several architectures based on gate defined quantum dots have been proposed and demonstrated experimentally.14,15 Recently, a quantum dot hybrid qubit formed by three electrons in a double quantum dot was proposed,16,17 and non-adiabatic pulsed-gate operation was implemented experimentally,18 demonstrating simple and fast electrical manipulations of spin states with a promising ratio of coherence time to manipulation time. However, the overall gate fidelity of the pulse-gated hybrid qubit is limited by relatively fast dephasing due to charge noise during one of the two required gate operations. Here we perform the first microwave-driven gate operations of a quantum dot hybrid qubit, avoiding entirely the regime in which it is most sensitive to charge noise. Resonant detuning modulation along with phase control of the microwaves enables a π rotation time of o 5 ns (50 ps) around X (Z) axis with high fidelities 493 (96)%. We also implement Hahn echo19–21 and Carr–Purcell (CP)22 dynamic decoupling sequences with which we demonstrate a coherence time of over 150 ns. We further discuss a pathway to improve gate fidelity to above 99%, exceeding the threshold for surface code based quantum error correction.23 The quantum dot hybrid qubit combines desirable features of charge (fast manipulation) and spin (long coherence time) qubits. The qubit states can be written as |0〉 = |↓〉|S〉, where Spffiffiffidenotes a psinglet state in the right dot, and ffiffiffiffiffiffiffiffi 91〉¼ 1= 39k〉9T 0 〉- 2=39m〉9T - 〉, where T0 and T_ are two of the triplet states in the right dot. The states |0〉 and |1〉 have the nearly same dependence on ε in the range of detuning at which the qubit is operated (Figures 1c and d), enabling quantum control that is largely insensitive to charge fluctuations. Moreover, 1 electric fields couple to the qubit states and enable high-speed manipulation.16,17,24–27 Previously, we experimentally demonstrated non-adiabatic quantum control (direct current (DC)-pulsed gating) of the hybrid qubit, where the manipulation and measurement scheme required the use of a detuning regime that is sensitive to charge noise (with ε near but not equal to zero —see Figure 1d).18 Moreover, DC gating requires abrupt changes in detuning. With a given bandwidth in the transmission line, pulse imperfections arising, e.g., from frequency dependent attenuation, lead to inaccurate control of rotation axes. In this work, we demonstrate resonant microwave-driven control and state-dependent tunnelling readout of the qubit, which together overcome this limitation of DC-pulsed gating and enable full manipulation on the Bloch sphere at a single operating point in detuning that is well-protected from charge noise. The experiments here are performed in a double dot with a gate design as shown in Figure 1a and with electron occupations as shown on the stability diagram of Figure 1b. The electron occupations and energy level alignments used for qubit initialisation, readout and microwave spectroscopy of the qubit states are shown schematically in Figure 1c. All the experiments reported here start with an initial dot occupation of (1,2) and with the system in state |0〉, prepared at a detuning ε ≈ 230 μeV; this detuning is also used for measurement and corresponds to point M in Figure 1b. After initialisation, we apply a microwave burst pattern at point O, which either coincides with point M or is reached through an adiabatic ramp in detuning (the latter case is illustrated in Figure 1b). The tunnel coupling between the two sides of the double quantum dot mediates an exchange interaction that enables transitions between the qubit states and can be driven by modulating the detuning.16 Qubit rotation occurs when the frequency of the applied microwave electric field is resonant with the qubit energy level difference. The measurement point M is chosen so that the Fermi level of the right Department of Physics, University of Wisconsin-Madison, Madison, WI, USA; 2Department of Materials Science and Engineering, Yonsei University, Seoul, South Korea and Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA. Correspondence: MA Eriksson () Received 17 February 2015; revised 13 May 2015; accepted 19 June 2015 3 © 2015 University of New South Wales/Macmillan Publishers Limited High-fidelity resonant gating D Kim et al 2 Figure 1. Microwave-driven coherent manipulation and readout of a hybrid qubit in a Si/SiGe double quantum dot device. (a) SEM image and schematic labelling of a device lithographically identical to the one used in the experiment. (b) Charge stability diagram near the (1,1)–(2,1)–(1,2) charge transition, showing the gate voltages used for microwave manipulation (O) and measurement (M). For clarity, a linear background slope was removed from the raw charge-sensing data. (c) Schematic description of the qubit initialisation, manipulation, readout and reset processes. (d) Energy E as a function of detuning ε for the qubit states, calculated with Hamiltonian parameters measured in ref. 18 (e) Inset: probability P1 of the state to be |1〉 at the end of the driving sequence shown as a function of ε and the excitation frequency f of the microwaves applied to gate R. In the main panel, the dashed green curve is the energy difference between the ground state and the lowest energy excited state, as determined in ref. 18. (f–j) Coherent Rabi oscillation measurements. (f) P1 as a function o (...truncated)