High Fidelity Single-NV Qubit Quantum State Tomography by Photoelectric Readout

Abstract

Quantum computing is a rapidly developing field. However, the most commonly used qubits require cryogenic conditions to operate, which increases the costs and puts constraints on the up-scaling. Ambient solid-state qubits provide an alternative with potential for large-scale application. The nitrogen-vacancy (NV) center in diamond is one of the main candidates for solid-state computing architectures at room temperature and has proven to be competitive in terms of gate fidelity, quantum error correction, couplings, etc. Each NV center has an associated electronic spin that is conventionally read out by photoluminescence. However, regarding the creation of small, ambient NV-based quantum processors, the optical readout introduces limitations on the collection efficiency and resolution of the readout as well as the size of the final device and its integration into standard semiconductor architectures. In this work, we investigate the competitiveness of the photoelectric readout versus the traditional optical readout. In particular, we report on using photoelectrical detection to perform quantum state tomography measurements on a single NV center. We achieve the fidelity $0.995 \pm 0.0062$ for state reconstruction, comparable to optical measurements, demonstrating that the fidelity does not suffer from the adapted readout, highlighting the value of photoelectric detection for NV-based quantum processors.

Figures (6)

• Figure 1: Experimental setup with detail of printed circuit board containing diamond sample and connections to different devices. Electrodes can be seen on top of the diamond sample to collect the charge carriers for the photoelectric readout.
• Figure 2: Pulsed photocurrent detection protocol for Rabi measurements. The measurement is divided into envelopes (1, 2, ..., n) during which a certain part of the pulse protocol is being repeated. Each envelope contains the pulse sequence for one value of the Rabi period $\tau$. Both photocurrent and photoluminescence are recorded at the end of each envelope time. After envelope n has been performed, the loop starts again at envelope 1.
• Figure 3: Pulsed photocurrent detection protocol for PC-RPQST measurements. Like in PC-Rabi measurements, the pulse protocol is being repeated in envelopes (1, 2, ..., n) and at the end of each envelope, photoluminescence and photocurrent are recorded. The pulse sequence itself contains two distinct microwave pulses, of which the first one (duration $T_\theta$) determines the $\theta$-angle of the prepared state and the second one has a fixed phase difference compared to the former, which determines $\phi$, and a variable duration $\tau$ that will lead to Rabi oscillations.
• Figure 4: PC- (orange) and PL-RPQST (grey) for the state ($\theta$, $\phi$) = ($15^{\circ}$, $235^{\circ}$). The experimental data is fitted and phase angles of x- (a) and y-Rabi (b) are extracted. From these parameters, in this particular measurement, the electron spin state was reconstructed with a fidelity of 0.99991 (PL-RPQST) and 0.9998 (PC-RPQST).
• Figure 5: Electron spin states that were used in Rabi measurements. Each pink dot represents a state that was prepared and tomographed at least twice. The azimuthal angle $\theta$ is indicated next to the Bloch sphere quarter, while the polar angle $\phi$ is plotted on top of the sphere.