Single-Shot Readout of a Nuclear Spin Weakly Coupled to a Nitrogen-Vacancy Center at Room Temperature

Single-shot readout of qubits is required for scalable quantum computing. Nuclear spins are superb quantum memories due to their long coherence time, but are difficult to be read out in a single shot due to their weak interaction with probes. Here we demonstrate single-shot readout of a weakly coupled ${}^{13}\mathrm{C}$ nuclear spin at room temperature, which is unresolvable in traditional protocols. States of the weakly coupled nuclear spin are trapped and read out projectively by sequential weak measurements, which are implemented by dynamical decoupling pulses. A nuclear spin coupled to the nitrogen-vacancy (NV) center with strength 330 kHz is read out in 200 ms with a fidelity of 95.5%. This work provides a general protocol for single-shot readout of weakly coupled qubits at room temperature and therefore largely extends the range of physical systems for scalable quantum computing.

Figure 1

System and experimental scheme for dynamical decoupling enabled quantum measurement. (a) An NV electron spin (red) and its ${}^{13}\mathrm{C}$ nuclear spin bath (purple). The spin state of a strongly coupled ${}^{13}\mathrm{C}$ nuclear spin can be mapped to the electron spin through selective MW pulses. For weakly coupled nuclear spins, DD is employed to address the target one while decoupling the other nuclear spins. (b) Coherence of the center electron spin under CPMG-12 (red line) and CPMG-1 (gray line), as a function of the pulse interval $\tau$. (c) The accumulated phase of the center electron spin (and thus the measurement strength of the weakly coupled target nuclear spin) is controlled by the pulse number of the applied CPMG sequence.

Figure 2

Controlling the strength of measurement on a weakly coupled nuclear spin by dynamical decoupling. (a) 2D CPMG signal as a function of the pulse number and the interval duration, under an external magnetic field of 305 G. Individual nuclear spins are selected by tuning the intervals between two CPMG pulses. The number of total applied pulses determines the measurement strength of the selected nuclear spin. (b) Typical CPMG signal as a function of the interval duration. (c) Typical CPMG signal as a function of the pulse number. When no nuclear spin is resonant ($\tau =200\mathrm{ns}$, black line), the coherence of the center spin is well protected. When a nuclear spin is resonantly selected ($\tau =456\mathrm{ns}$, red line with blue point), the coherence of the electron spin is modulated by the entanglement with the nuclear spin.

Figure 3

Single-shot readout of a weakly coupled nuclear spin. (a) Pulse sequence. The weakly coupled nuclear spin is selectively addressed by CPMG pulses with resonant $\tau$, and a subsequent optical readout reveals the state of the target nuclear spin. (b) Typical quantum jump signal of the weakly coupled nuclear spin under an external magnetic field of 691 G. Each data point is a sum of 40 000 cycles of measurement of the center electron spin. (c) Photon count distributions after the target nuclear spin state selected by the photon count thresholds of $<2300$ for $|\downarrow ⟩$ and $>2520$ for $|\uparrow ⟩$. (d) Single-shot readout fidelity as a function of the readout threshold. With a threshold of 2400, the readout fidelity is 95.5% for both $|\downarrow ⟩$ and $|\uparrow ⟩$.

Figure 4

Trajectory of nuclear spin state under repetitive weak measurements. (a) Samples of trajectory, calculated with realistic hyperfine tensor. Red circles are for relative weak measurements ($P_1$), about 40 steps are needed to reach the stable state $\{|\uparrow ⟩,|\downarrow ⟩\}$; Navy square are for relative strong measurement ($P_2$). Inset, dependence of the target nuclear spin precession frequency on magnetic field strength (solid line). $P_1$ and $P_2$ are experimental optimized conditions to observe jump signal. (b) The positions of $P_1$ and $P_2$ in CPMG parameter space.