Single-gate, multipartite entanglement on a room-temperature quantum register

Abstract

Multipartite entanglement is an essential aspect of quantum systems, needed to execute quantum algorithms, implement error correction, and achieve quantum-enhanced sensing. In solid-state quantum registers such nitrogen-vacancy (NV) centers in diamond, entangled states are typically created using sequential, pairwise gates between the central electron and individual nuclear qubits. This sequential approach is slow and suffers from crosstalk errors. Here, we demonstrate a parallelized multi-qubit entangling gate to generate a four-qubit GHZ state using a room-temperature NV center in only 14.8 $μ$s $-$ 10 times faster than using sequences of two-qubit gates and close to the fundamental limit set by the hyperfine coupling frequencies. Parallel three-qubit gates are also realized with all nuclear-qubit subsets. The entangled states are verified by measuring multiple quantum coherences. The four-qubit parallel gate has a fidelity of 0.92(4), whereas the sequential four-qubit gate fidelity is only 0.69(3). The approach is generalizable to other solid-state platforms, and it lays the foundation for scalable generation and control of entanglement in practical devices.

Figures (5)

• Figure 1: Entanglement through dynamical decoupling in NV quantum registers(a) Schematic of the NV center including nearby $^{13}$C nuclear qubits $q_{\ell}$. Electron-nuclear entangling gates were implemented with XY8 DD, symbolically shown in the inset. Entangling gates rotate nuclear qubits about distinct axes $\hat{n}_{0}$ (dark blue) and $\hat{n}_{1}$ (red), conditioned on the two states of the electron. (b) DD spectroscopy measurements at $k=1,N=6$ and $k=2,N=12$; resonances associated with nuclear qubits $q_1$, $q_2$, and $q_3$ are marked with dashed lines. Error bars on points denote photon shot noise. Additional spectroscopy data can be found in SI Sec. IV. (c) Alignment of the electron-spin-dependent nuclear rotation axes, where $-1$ ($+1$) indicates perfectly (un)conditional rotations. Orange and purple shaded regions indicate the intersection of unit pulse times where $(\hat{n}_0 \cdot \hat{n}_1)^{(\ell)}<0$ for two and three nuclear qubits, respectively. (d)$M$-qubit entangling power metric $\varepsilon_{p,M}$ as a function of DD unit pulse parameters. At first-order, the maximum in $\varepsilon_{p,4}$ (green diamond) indicates an optimal DD sequence to create maximal four-way entanglement. At second-order, diamond markers indicate the optimum parameters for two-qubit entangling gates, as the maximum value of each nuclear qubit's bipartite entangling power, $\text{max}_{\ell}(\varepsilon_{p,2})$.
• Figure 2: Verifying entangled states using multiple quantum coherences(a) Quantum circuit to efficiently characterize entangled states using the MQC method wei2020verifying. (b) DD implementation of the MQC method used in this work (shown here for bipartite entanglement), in which only the nuclear qubits are subject to $Z_{\phi}$ gates. (c) Bloch-sphere visualization of the stages labeled in (b). First, both spins are initialized to $\ket{0}$ and rotated to equatorial superposition states (step 1). The conditional rotation that follows creates a Bell state, and a variable phase $\phi$ is added to the nuclear qubit (step 2). When the qubits are disentangled, $\phi$ is added to the electron phase (step 3) and the final electron rotation maps $\phi$ to an angle from $\hat{z}$, which is then measured through spin-dependent fluorescence (step 4). (d) Results of MQC experiments for bipartite entanglement ($M=2$ total qubits, $L=1$ nuclear qubit) with each nuclear qubit, $q_\ell$. Error bars on points denote photon shot noise, and uncertainties on $L$ are 68% confidence intervals from from fits to equation (\ref{['eq:MQC_prob_NV']}) with a variable amplitude, midpoint and phase.
• Figure 3: Generation and verification of multipartite GHZ states(a) Block-diagram quantum circuit for entanglement verification using multiple nuclear qubits. Qubits are initialized sequentially as shown in Fig. \ref{['fig:mqc_L1']}b. (b) Local gates used to prepare for GHZ state generation for $L=2$ or 3 nuclear qubits (green and blue shaded regions, respectively). Red shaded gates represent unwanted crosstalk effects, which manifest as $Z$-axis rotations on each nuclear qubit in the register that is not targeted with a white gate. The angles of the local gates (associated with the unit pulse repeats) were determined using numerical optimization, with the gate axes (associated with unit pulse times) remaining fixed as shown. (c,d) Results of three-qubit ($L=2$) MQC verification experiments using nuclear qubits $q_1$ and $q_2$ (data points in lower panels) corresponding to the parallel and sequential entangling gates shown in the upper panel. The corresponding disentangling gates in (a) are identical. Red (parallel) and blue (sequential) curves are sinusoidal fits to measure the number of entangled nuclear qubits $L$. See the SI, Sec. IX for results corresponding to all other combinations of qubits. (e,f) Results of four-qubit ($L=3$) MQC verification experiments. Error bars on points denote photon shot noise, and uncertainties on $L$ are 68% confidence intervals from from fits to equation (\ref{['eq:MQC_prob_NV']}).
• Figure 4: Entangling-gate fidelities(a) Quantum circuit to efficiently measure entangling-gate fidelity. After repeating the entangling gate $N_E$ times, the $Z$ projection of either the electron or an individual nuclear qubit is measured, and the combined results are used to approximate the $\ket{0}^{\otimes M}$ state fidelity. (b) Sub-circuit to measure nuclear-qubit $Z$ projections. (c) Experimental results (data points) for bipartite entangling gates associated with each nuclear qubit. Solid curves are fits using a noisy quantum channel model to extract the entangling-gate fidelity. (d,e) Experimental results (data points) for three-way and four-way entanglement generated either sequentially (top panel) or using a parallel gate (bottom panel). Repeating the parallel gate does not generally return exactly $\ket{0}^{\otimes M}$ due to its more complicated geometry; values of $N_E$ were chosen to maximize the overlap with $\ket{0}^{\otimes M}$. Fits to the data (solid curves) account for this effect along with gate errors and are used determine the fidelity of each gate. Error bars on points in (c-e) are propagated from each measurement's photon shot noise. (f) Entangling-gate fidelities determined from fits to the data in (c-e). Error bars denote 68% confidence intervals from fits to the noisy quantum channel model. (g) Entangling-gate durations. The number of electron pulses (equivalent to 2$N$) are printed above each bar.
• Figure 5: Generality of parallel entanglement in NV–nuclear registers(a) Likelihood of a register supporting parallel entanglement. In this analysis, we exclude registers that contain at least one strongly coupled nuclear qubit (red region, corresponding to 64% of configurations). Percentages listed above each bar correspond to the likelihood of weakly-coupled registers (green region) supporting parallel entanglement with at least one set of $L$ nuclear qubits. On average, the weakly-coupled registers contain 5.7 (2.5) individually-addressable nuclear qubits in total. (b) Number of unique subsets of $L$ nuclear qubits in registers hosting parallel entanglement. The middle black line represents the median, the box spans the interquartile range (IQR), the whiskers extend to $1.5 \times$ the IQR, and points indicate outliers. (c) Parallel and $k=2$ sequential entangling gate durations. (d) Parallel entanglement speedup factor.