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

MainQuantum registers in solid-state materials are the basis for quantum networking1,2,3,4,5,6,7, quantum information processing8,9,10,11,12,13,14,15,16,17,18,19 and quantum sensing20,21,22,23,24,25,26,27. The nitrogen-vacancy (NV) centre in a diamond is the most well-established solid-state quantum register, and it is especially notable for featuring room-temperature spin coherence. The central electron spin, initialized and measured optically, serves as an interface for detecting and controlling surrounding spins, including 13C nuclei28,29,30. Owing to their small gyromagnetic ratios, nuclear spins interact weakly with their environment and have long coherence times, making them attractive memory qubits. Generating high-fidelity entanglement between the electron and multiple nuclei is essential for error correction11,29 and enhanced sensing beyond the standard quantum limit25,26,27.To extend the electron-spin coherence time to be comparable with that of nuclear qubits, it must be decoupled from its environment; this is achieved using dynamical decoupling (DD) control sequences. Crucially, DD sequences can be designed to initialize, control and read-out individual nuclear qubits, all while decoupling the electron from other noise sources8,29. At cryogenic temperatures, where coherent optical transitions facilitate high-fidelity read-out and spin lifetimes extend beyond 1 min (refs. 10,31), DD sequences have facilitated the realization of quantum networking nodes1,2,3,4 and preliminary fault tolerance using nuclear quantum registers11. At room temperature, where read-out is less efficient32 and coherence times are shorter, DD extends coherence times and enables entanglement-assisted enhanced sensing protocols suitable for practical use cases27,33. The performance of such networking, computing and sensing schemes remains limited by the speed and fidelity of generating multipartite entangled states.Using DD sequences to control multipartite entanglement presents two critical challenges. First, each DD sequence is calibrated to generate bipartite entanglement with a single nucleus, thereby requiring long, sequential gates to entangle multiple nuclear qubits. Second, due to the always-on spin–spin interactions within the quantum register, executing sequences of nuclear gates leads to unwanted rotations of all other qubits (that is, crosstalk). Parallelized entangling gates address both these issues. Recent approaches in trapped-ion and neutral-atom platforms include specialized multi-qubit gates34,35,36 and the simultaneous implementation of multiple two-qubit gates37,38,39. For solid-state registers operating in the strong-coupling regime (that is, with hyperfine coupling frequencies larger than the inhomogeneous linewidth of electron spin), multi-qubit entangling gates can be achieved using frequency-selective conditional electron pulses16,17,18,19. However, strongly coupled registers are rare in nature; therefore, they either need to be engineered17,18,19 or identified through screening16. Their scalability is limited by the need for strong, widely spaced couplings for individual addressability. Weakly coupled registers typically offer larger register sizes that enable more robust error correction and networking capabilities4,10,11, but the sequential application of DD sequences leads to impractical gate times and errors for multi-qubit control.In this work, we design, implement and benchmark a multi-qubit gate using a single DD sequence that facilitates the efficient generation of multipartite entanglement, even at room temperature. We use the entanglement metric framework developed in refs. 40,41 to design DD sequences that address multiple weakly coupled 13C nuclear qubits surrounding an NV centre (Fig. 1a). Essentially, this approach leverages the crosstalk inherent in DD sequences to simultaneously create conditional rotations of multiple nuclear qubits in which each rotation is locally equivalent to a CNOT gate. We experimentally generate four-qubit GHZ entangled states that include the electron and three weakly coupled 13C nuclear qubits, and we verify them by measuring multiple quantum coherences (MQCs). The largest parallel gates are an order of magnitude faster and have substantially higher fidelity than their sequential counterparts.Fig. 1: Entanglement through DD in NV quantum registers.Full size imagea, Schematic of the NV centre including nearby 13C nuclear qubits qℓ. Electron–nuclear entangling gates were implemented with XY8 DD, symbolically shown in the inset. Entangling gates rotate nuclear qubits about distinct axes \({\hat{\mathbf{n}}}_{0}\) (dark blue) and \({\hat{\mathbf{n}}}_{1}\) (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 q1, q2 and q3 are marked with dashed lines. Data points denote mean values over 106 shots and error bars denote the photon shot noise. Additional spectroscopy data are provided in Supplementary Section IV. c, Alignment of the electron-spin-dependent nuclear rotation axes, where −1 (+1) indicates perfectly (un)conditional rotations. The orange- and purple-shaded regions indicate the intersection of unit-pulse times, where \({({\hat{\mathbf{n}}}_{0}\cdot {\hat{\mathbf{n}}}_{1})}^{(\ell )} 15 kHz (based on the location of the spin-bath resonance) and A⊥ > 10 kHz (so that a sufficiently small N can address the qubit). With these cut-offs, the average number of weakly coupled, addressable nuclear qubits per register is 5.7, with a standard deviation of 2.5 at natural 13C concentration.For each of these registers, we searched for parallel entangling gates following the algorithm in ref. 41. Additional details are provided in Supplementary Sections V and VI. Because a large number of registers were generated to improve statistical significance, a conservative parallel entangling gate search was used. Specifically, a maximum of N ≤ 50 and a minimum non-unitary entangling power of \({\varepsilon }_{{\rm{p}},M}({\mathcal{E}})\ge 0.8\) were imposed. Hence, these results represent a lower bound on the available gates. Supplementary Section VI provides additional simulations of gate durations, comparisons with k = 2 and k = 3 sequential two-qubit gates, and the infidelity arising from residual entanglement.