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Fig. 1. Flip-flop <t>qubit</t> and device layout. (A) Energy level diagram of 31P donor electron (↑,↓) and nuclear (⇑,⇓) spin states, in the presence of a static magnetic field B0 ∼1 T along the z direction. Electron spin resonance (ESR) and nuclear mag- netic resonance (NMR) transitions are induced by oscillating magnetic fields. The flip-flop qubit is obtained by truncating the system to the ↓⇑, ↑⇓states, between which transitions are induced by EDSR. (B) Bloch sphere representation of the flip- flop qubit. (C) False-color scanning electron microscopy image of the device, com- prising a single-electron transistor (SET) (cyan) to read out the electron spin, local gate electrodes (red and purple) to control the donor potential, and MW antennas (brown) for electric (left, open-circuit) and magnetic (right, short-circuit) control of the donor spins. Here and elsewhere, we use the color orange to represent prop- erties related to the nuclear spin, blue for the electron spin, and green for the flip- flop qubit.
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Fig. 1. Flip-flop qubit and device layout. (A) Energy level diagram of 31P donor electron (↑,↓) and nuclear (⇑,⇓) spin states, in the presence of a static magnetic field B0 ∼1 T along the z direction. Electron spin resonance (ESR) and nuclear mag- netic resonance (NMR) transitions are induced by oscillating magnetic fields. The flip-flop qubit is obtained by truncating the system to the ↓⇑, ↑⇓states, between which transitions are induced by EDSR. (B) Bloch sphere representation of the flip- flop qubit. (C) False-color scanning electron microscopy image of the device, com- prising a single-electron transistor (SET) (cyan) to read out the electron spin, local gate electrodes (red and purple) to control the donor potential, and MW antennas (brown) for electric (left, open-circuit) and magnetic (right, short-circuit) control of the donor spins. Here and elsewhere, we use the color orange to represent prop- erties related to the nuclear spin, blue for the electron spin, and green for the flip- flop qubit.

Journal: Science advances

Article Title: An electrically driven single-atom "flip-flop" qubit.

doi: 10.1126/sciadv.add9408

Figure Lengend Snippet: Fig. 1. Flip-flop qubit and device layout. (A) Energy level diagram of 31P donor electron (↑,↓) and nuclear (⇑,⇓) spin states, in the presence of a static magnetic field B0 ∼1 T along the z direction. Electron spin resonance (ESR) and nuclear mag- netic resonance (NMR) transitions are induced by oscillating magnetic fields. The flip-flop qubit is obtained by truncating the system to the ↓⇑, ↑⇓states, between which transitions are induced by EDSR. (B) Bloch sphere representation of the flip- flop qubit. (C) False-color scanning electron microscopy image of the device, com- prising a single-electron transistor (SET) (cyan) to read out the electron spin, local gate electrodes (red and purple) to control the donor potential, and MW antennas (brown) for electric (left, open-circuit) and magnetic (right, short-circuit) control of the donor spins. Here and elsewhere, we use the color orange to represent prop- erties related to the nuclear spin, blue for the electron spin, and green for the flip- flop qubit.

Article Snippet: K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, S. Tarucha, Optimized electrical control of a Si/SiGe spin qubit in the presence of an induced frequency shift. npj Quantum Inf.

Techniques: Electron Paramagnetic Resonance, Electron Microscopy, Control

Fig. 3. Relaxation, coherence, and gate fidelity. (A) The flip-flop qubit relaxation time T1ff = 173(12) s is measured by initializing the donor in the a∣↑⇓〉+ b∣↓⇓〉state with ∣a∣2 ≈∣b∣2 ≈0.5 and replenishing the ∣↑⇓〉state population with adiabatic aESR1 inversion pulses applied every 5 s to counteract the electron relaxation channel ∣↑⇓〉→ ∣↓⇓〉. (B) Fitting the Ramsey and the Hahn echo decays using an exponential decay reveals T 2ff ¼ 4:09ð88Þ μs (with exponent 1.28) and TH 2ff ¼ 184ð24Þ μs (exponent 2), respectively. (C) Tabulated values of the relaxation and coherence times measured on the electron, nuclear, and flip-flop qubits. (D) Randomized benchmarking (RB) experiment for the flip-flop qubit, yielding an average one-qubit gate fidelity ℱ1Q = 98.4(2)%.

Journal: Science advances

Article Title: An electrically driven single-atom "flip-flop" qubit.

doi: 10.1126/sciadv.add9408

Figure Lengend Snippet: Fig. 3. Relaxation, coherence, and gate fidelity. (A) The flip-flop qubit relaxation time T1ff = 173(12) s is measured by initializing the donor in the a∣↑⇓〉+ b∣↓⇓〉state with ∣a∣2 ≈∣b∣2 ≈0.5 and replenishing the ∣↑⇓〉state population with adiabatic aESR1 inversion pulses applied every 5 s to counteract the electron relaxation channel ∣↑⇓〉→ ∣↓⇓〉. (B) Fitting the Ramsey and the Hahn echo decays using an exponential decay reveals T 2ff ¼ 4:09ð88Þ μs (with exponent 1.28) and TH 2ff ¼ 184ð24Þ μs (exponent 2), respectively. (C) Tabulated values of the relaxation and coherence times measured on the electron, nuclear, and flip-flop qubits. (D) Randomized benchmarking (RB) experiment for the flip-flop qubit, yielding an average one-qubit gate fidelity ℱ1Q = 98.4(2)%.

Article Snippet: K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, S. Tarucha, Optimized electrical control of a Si/SiGe spin qubit in the presence of an induced frequency shift. npj Quantum Inf.

Techniques:

Fig. 4. Electrical drive via hyperfine modulation. (A) Linear dependence of the flip-flop Rabi frequencies on the voltage at the output of the MW source. (B) Stark shift of the hyperfine coupling produced by a dc voltage applied to the FD gate, as extracted from the shift of the NMR1 resonance frequency. An independent calibration of the line attenuation at MW confirms that the flip-flop qubit is driven by dynamic modulation of the hyperfine coupling. (C) Triangulation of the most probable location of the donor under study, obtained through COMSOL finite-element models informed by the capacitive coupling between the donor and each electrostatic gate (see section S5). The contours indicate the 1σ and 2σ confidence regions. (D) Amplitude of the MW electric field Eac around the donor location, estimated using the same COMSOL model as above, assuming a voltage on the FD gate VFD = 1 Vpp. We find Eac ≈3.5 MV/m at the most likely donor location.

Journal: Science advances

Article Title: An electrically driven single-atom "flip-flop" qubit.

doi: 10.1126/sciadv.add9408

Figure Lengend Snippet: Fig. 4. Electrical drive via hyperfine modulation. (A) Linear dependence of the flip-flop Rabi frequencies on the voltage at the output of the MW source. (B) Stark shift of the hyperfine coupling produced by a dc voltage applied to the FD gate, as extracted from the shift of the NMR1 resonance frequency. An independent calibration of the line attenuation at MW confirms that the flip-flop qubit is driven by dynamic modulation of the hyperfine coupling. (C) Triangulation of the most probable location of the donor under study, obtained through COMSOL finite-element models informed by the capacitive coupling between the donor and each electrostatic gate (see section S5). The contours indicate the 1σ and 2σ confidence regions. (D) Amplitude of the MW electric field Eac around the donor location, estimated using the same COMSOL model as above, assuming a voltage on the FD gate VFD = 1 Vpp. We find Eac ≈3.5 MV/m at the most likely donor location.

Article Snippet: K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, S. Tarucha, Optimized electrical control of a Si/SiGe spin qubit in the presence of an induced frequency shift. npj Quantum Inf.

Techniques: Produced

Fig. 5. Experimental setup. Wiring and instrumentation used to control and read out the donor spin qubit. The red dashed square defines the implantation region for this qubit device.

Journal: Science advances

Article Title: An electrically driven single-atom "flip-flop" qubit.

doi: 10.1126/sciadv.add9408

Figure Lengend Snippet: Fig. 5. Experimental setup. Wiring and instrumentation used to control and read out the donor spin qubit. The red dashed square defines the implantation region for this qubit device.

Article Snippet: K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, S. Tarucha, Optimized electrical control of a Si/SiGe spin qubit in the presence of an induced frequency shift. npj Quantum Inf.

Techniques: Control