Mapping a 50-spin-qubit network through correlated sensing

Spins associated to optically accessible solid-state defects have emerged as a versatile platform for exploring quantum simulation, quantum sensing and quantum communication. Pioneering experiments have shown the sensing, imaging, and control of multiple nuclear spins surrounding a single electron spin defect. However, the accessible size of these spin networks has been constrained by the spectral resolution of current methods. Here, we map a network of 50 coupled spins through high-resolution correlated sensing schemes, using a single nitrogen-vacancy center in diamond. We develop concatenated double-resonance sequences that identify spin-chains through the network. These chains reveal the characteristic spin frequencies and their interconnections with high spectral resolution, and can be fused together to map out the network. Our results provide new opportunities for quantum simulations by increasing the number of available spin qubits. Additionally, our methods might find applications in nano-scale imaging of complex spin systems external to the host crystal.

Fault-tolerant operation of a logical qubit in a diamond quantum processor

Solid-state spin qubits is a promising platform for quantum computation and quantum networks^1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems^3–8, elementary quantum algorithms^8–11 and non-fault-tolerant error correction^12–14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations^15–18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science^15,19–27. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits^28–30. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins.

By using a five-qubit error-correcting code with a recently discovered flag protocol, a logical qubit that is operated fault-tolerantly is realized based on solid-state spin qubits in diamond.

Many-body-localized discrete time crystal with a programmable spin-based quantum simulator

[Figure: see text].

Orbital and Spin Dynamics of Single Neutrally-Charged Nitrogen-Vacancy Centers in Diamond

The neutral charge state plays an important role in quantum information and sensing applications based on nitrogen-vacancy centers. However, the orbital and spin dynamics remain unexplored. Here, we use resonant excitation of single centers to directly reveal the fine structure, enabling selective addressing of spin-orbit states. Through pump-probe experiments, we find the orbital relaxation time (430 ns at 4.7 K) and measure its temperature dependence up to 11.8 K. Finally, we reveal the spin relaxation time (1.5 s) and realize projective high-fidelity single-shot readout of the spin state (≥98%).

Algorithmic decomposition for efficient multiple nuclear spin detection in diamond

Efficiently detecting and characterizing individual spins in solid-state hosts is an essential step to expand the fields of quantum sensing and quantum information processing. While selective detection and control of a few ¹³C nuclear spins in diamond have been demonstrated using the electron spin of nitrogen-vacancy (NV) centers, a reliable, efficient, and automatic characterization method is desired. Here, we develop an automated algorithmic method for decomposing spectral data to identify and characterize multiple nuclear spins in diamond. We demonstrate efficient nuclear spin identification and accurate reproduction of hyperfine interaction components for both virtual and experimental nuclear spectroscopy data. We conduct a systematic analysis of this methodology and discuss the range of hyperfine interaction components of each nuclear spin that the method can efficiently detect. The result demonstrates a systematic approach that automatically detects nuclear spins with the aid of computational methods, facilitating the future scalability of devices.

Multipartite Entanglement Generation and Contextuality Tests Using Nondestructive Three-Qubit Parity Measurements

We report on the realization and application of nondestructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by a single-shot nondestructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the maximally mixed state. Furthermore, we implement a single-shot version of the Greenberger-Horne-Zeilinger experiment that can generate a quantum versus classical contradiction in each run. Finally, we test a state-independent noncontextuality inequality in eight dimensions. The techniques and insights developed are relevant for fundamental tests as well as for quantum information protocols such as quantum error correction.

One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment

Single electron spins coupled to multiple nuclear spins provide promising multi-qubit registers for quantum sensing and quantum networks. The obtainable level of control is determined by how well the electron spin can be selectively coupled to, and decoupled from, the surrounding nuclear spins. Here we realize a coherence time exceeding a second for a single nitrogen-vacancy electron spin through decoupling sequences tailored to its microscopic nuclear-spin environment. First, we use the electron spin to probe the environment, which is accurately described by seven individual and six pairs of coupled carbon-13 spins. We develop initialization, control and readout of the carbon-13 pairs in order to directly reveal their atomic structure. We then exploit this knowledge to store quantum states in the electron spin for over a second by carefully avoiding unwanted interactions. These results provide a proof-of-principle for quantum sensing of complex multi-spin systems and an opportunity for multi-qubit quantum registers with long coherence times.

Experimental creation of quantum Zeno subspaces by repeated multi-spin projections in diamond

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

Repeated observations of quantum states inhibit coherent evolution through the Zeno effect, providing opportunities for controlling multi-qubit systems. Here the authors demonstrate that projecting joint observables of three spins in diamond creates quantum Zeno subspaces that suppress dephasing.

Towards quantum networks of single spins: analysis of a quantum memory with an optical interface in diamond

Single defect centers in diamond have emerged as a powerful platform for quantum optics experiments and quantum information processing tasks. Connecting spatially separated nodes via optical photons into a quantum network will enable distributed quantum computing and long-range quantum communication. Initial experiments on trapped atoms and ions as well as defects in diamond have demonstrated entanglement between two nodes over several meters. To realize multi-node networks, additional quantum bit systems that store quantum states while new entanglement links are established are highly desirable. Such memories allow for entanglement distillation, purification and quantum repeater protocols that extend the size, speed and distance of the network. However, to be effective, the memory must be robust against the entanglement generation protocol, which typically must be repeated many times. Here we evaluate the prospects of using carbon nuclear spins in diamond as quantum memories that are compatible with quantum networks based on single nitrogen vacancy (NV) defects in diamond. We present a theoretical framework to describe the dephasing of the nuclear spins under repeated generation of NV spin-photon entanglement and show that quantum states can be stored during hundreds of repetitions using typical experimental coupling parameters. This result demonstrates that nuclear spins with weak hyperfine couplings are promising quantum memories for quantum networks.

Quantum information. Unconditional quantum teleportation between distant solid-state quantum bits

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward, quantum teleportation is achieved upon each attempt with an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing.

Universal control and error correction in multi-qubit spin registers in diamond

Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing. Pioneering experiments selected defects with favourably located nuclear spins with particularly strong hyperfine couplings. To progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here, we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single- and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes.

Detection and control of individual nuclear spins using a weakly coupled electron spin

We experimentally isolate, characterize, and coherently control up to six individual nuclear spins that are weakly coupled to an electron spin in diamond. Our method employs multipulse sequences on the electron spin that resonantly amplify the interaction with a selected nuclear spin and at the same time dynamically suppress decoherence caused by the rest of the spin bath. We are able to address nuclear spins with interaction strengths that are an order of magnitude smaller than the electron spin dephasing rate. Our results provide a route towards tomography with single-nuclear-spin sensitivity and greatly extend the number of available quantum bits for quantum information processing in diamond.