Abstract Fault-tolerant quantum memory plays a key role in interfacing quantum computers with quantum networks to construct quantum computer networks. Manipulation of spin quantum memory generally requires a magnetic field, which hinders the integration with superconducting qubits. Completely zero-field operation is desirable for scaling up a quantum computer based on superconducting qubits. Here we demonstrate quantum error correction to protect the nuclear spin of the nitrogen as a quantum memory in a diamond nitrogen-vacancy center with two nuclear spins of the surrounding carbon isotopes under a zero magnetic field. The quantum error correction makes quantum memory resilient against operational or environmental errors without the need for magnetic fields and opens a way toward distributed quantum computation and a quantum internet with memory-based quantum interfaces or quantum repeaters.
Abstract Fault-tolerant quantum memory plays a key role in interfacing quantum computers with quantum networks to construct quantum computer networks. Manipulation of spin quantum memory generally requires a magnetic field, which hinders the integration with superconducting qubits. Completely zero-field operation is desirable for scaling up a quantum computer based on superconducting qubits. Here we demonstrate quantum error correction to protect the nuclear spin of the nitrogen as a quantum memory in a diamond nitrogen-vacancy center with two nuclear spins of the surrounding carbon isotopes under a zero magnetic field. The quantum error correction makes quantum memory resilient against operational or environmental errors without the need for magnetic fields and opens a way toward distributed quantum computation and a quantum internet with memory-based quantum interfaces or quantum repeaters.
Abstract Quantum networks can enable quantum communication and modular quantum computation. A powerful approach is to use multi-qubit nodes that provide quantum memory and computational power. Nuclear spins associated with defects in diamond are promising qubits for this role. However, dephasing during optical entanglement distribution hinders scaling to larger systems. Here, we show that a 13C-spin quantum memory in isotopically engineered diamond is robust to the optical link operation of a nitrogen-vacancy centre. The memory lifetime is improved by two orders-of-magnitude upon the state-of-the-art, surpassing reported times for entanglement distribution. Additionally, we demonstrate that the nuclear-spin state can survive ionisation and recapture of the nitrogen-vacancy electron. Finally, we use simulations to show that combining this memory with previously demonstrated entanglement links and gates can enable key network primitives, such as deterministic non-local two-qubit gates, paving the way for test-bed quantum networks capable of investigating complex algorithms and error correction.
Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.
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.
Abstract Quantum state readout is a key component of quantum technologies, including applications in sensing, computation, and secure communication. Readout fidelity can be enhanced by repeating readouts. However, the number of repeated readouts is limited by measurement backaction, which changes the quantum state that is measured. This detrimental effect can be overcome by storing the quantum state in an ancilla qubit, chosen to be robust against measurement backaction and to allow error correction. Here, we protect the electronic-spin state of a diamond nitrogen-vacancy center from measurement backaction using a robust multilevel 14N nuclear-spin memory and perform repetitive readout, as demonstrated in previous work on bulk diamond devices. We achieve additional protection using error correction based on the quantum logic of coherent feedback to reverse measurement backaction. The repetitive spin readout scheme provides a 13-fold enhancement of readout fidelity over conventional readout and the error correction a 2-fold improvement in the signal. These experiments demonstrate full quantum control of a nitrogen-vacancy center electronic-spin coupled to its host 14N nuclear spin inside a ~25 nm nanodiamond, creating a sensitive and biologically compatible platform for nanoscale quantum sensing. Our error-corrected repetitive readout scheme is particularly useful for quadrupolar nuclear magnetic resonance imaging in the low magnetic field regime where conventional repetitive readout suffers from strong measurement backaction. More broadly, methods for correcting longitudinal (bit-flip) errors described here could be used to improve quantum algorithms that require non-volatile local memory, such as correlation spectroscopy measurements for high resolution sensing.
The symmetry of the space where a spin qubit resides plays an essential role in the manipulation of quantum entanglement, which governs the performance of quantum information systems. Application of a magnetic field, which is usually necessary for spin manipulation and readout, inevitably breaks the spatial symmetry to induce competition among quantization axes between internal and external fields, thus limiting the purity of the entanglement. If we could manipulate and readout entanglement under a zero magnetic field, we would be able to avoid the competition among quantization axes to achieve ideally high fidelity. We here demonstrate the complete Bell state measurement, which is a core element of quantum processing, of two carbon nuclear spins in the vicinity of a diamond nitrogen-vacancy center. The demonstration was made possible by holonomic entanglement manipulations based on the geometric phase with a polarized microwave under a zero magnetic field, where the quantization axis is uniquely defined by the hyperfine field. The demonstrated scheme allows high-fidelity entanglement processing even when magnetic fields cannot be applied to the integration of superconducting and spin qubits, thereby paving the way for building fault-tolerant distributed quantum computers and quantum repeater networks.
Long-distance quantum communication and networking require quantum memory nodes with efficient optical interfaces and long memory times. We report the realization of an integrated two-qubit network node based on silicon-vacancy centers (SiVs) in diamond nanophotonic cavities. Our qubit register consists of the SiV electron spin acting as a communication qubit and the strongly coupled silicon-29 nuclear spin acting as a memory qubit with a quantum memory time exceeding 2 seconds. By using a highly strained SiV, we realize electron-photon entangling gates at temperatures up to 1.5 kelvin and nucleus-photon entangling gates up to 4.3 kelvin. We also demonstrate efficient error detection in nuclear spin-photon gates by using the electron spin as a flag qubit, making this platform a promising candidate for scalable quantum repeaters.