Coherence of an optically illuminated single nuclear spin qubit

Robust multi-qubit quantum network node with integrated error detection

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.

Restoring the Coherence of Quantum Emitters through Optically Driven Motional Narrowing Forces

Motional narrowing is a phenomenon by which a quantum state can be entangled with a noisy environment and still retain its intrinsic coherence. Using two optically induced motional forces driving the environmental electrical field amplitude and fluctuations, we present a compelling illustration of the effects of motional narrowing on the energy, line shape, and line width of a single quantum emitter, a Te₂ molecule embedded in ZnSe, subject to spectral diffusion. Motional narrowing is achieved in several regimes, irrespectively of the inhomogeneous disorder initially present and the charge reservoir state sourcing the field. The optimal coherence limit set by the radiative rate can be approached by accelerating spectral diffusion into the THz regime. Motional narrowing applies to any quantum systems for which environmental fluctuations can be deliberately accelerated and alleviates the need for perfected materials and devices.

Stability of superconducting resonators: Motional narrowing and the role of Landau-Zener driving of two-level defects

Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Ramsey Interferences and Spin Echoes from Electron Spins Inside a Levitating Macroscopic Particle

We report on observations of Ramsey interferences and spin echoes from electron spins inside a levitating macroscopic particle. The experiment is realized using nitrogen-vacancy (NV) centers hosted in a micron-sized diamond stored in a Paul trap both under atmospheric conditions and under vacuum. Spin echoes are used to show that the Paul trap preserves the coherence time of the embedded electron spins for more than microseconds. Conversely, the NV spin is employed to demonstrate high angular stability of the diamond even under vacuum. These results are significant steps towards strong coupling of NV spins to the rotational mode of levitating diamonds.

Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters

In nanoscale metrology, dissipation of the sensor limits its performance. Strong dissipation has a negative impact on sensitivity, and sensor–target interaction even causes relaxation or dephasing of the latter. The weak dissipation of nitrogen-vacancy (NV) sensors in room temperature diamond enables detection of individual target nuclear spins, yet limits the spectral resolution of nuclear magnetic resonance (NMR) spectroscopy to several hundred Hertz, which typically prevents molecular recognition. Here, we use the NV intrinsic nuclear spin as a nonvolatile classical memory to store NMR information, while suppressing sensor back-action on the target using controlled decoupling of sensor, memory, and target. We demonstrate memory lifetimes up to 4 min and apply measurement and decoupling protocols, which exploit such memories efficiently. Our universal NV-based sensor device records single-spin NMR spectra with 13 Hz resolution at room temperature.

Dissipation of the sensor is a limiting factor in metrology. Here, Pfender et al. suppress this effect employing the nuclear spin of an NV centre for robust intermediate storage of classical NMR information, allowing then to record single-spin NMR spectra with 13 Hz resolution at room temperature.

Entanglement distillation between solid-state quantum network nodes

The impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable imperfections necessitate a means to improve remote entanglement by local quantum operations. We realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. The heralded generation of two copies of a remote entangled state is demonstrated through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. The key combination of generating, storing, and processing entangled states should enable the exploration of multiparticle entanglement on an extended quantum network.

Quantum systems under frequency modulation

We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the appearance of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

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}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.

Delayed entanglement echo for individual control of a large number of nuclear spins

Methods to selectively detect and manipulate nuclear spins by single electrons of solid-state defects play a central role for quantum information processing and nanoscale nuclear magnetic resonance (NMR). However, with standard techniques, no more than eight nuclear spins have been resolved by a single defect centre. Here we develop a method that improves significantly the ability to detect, address and manipulate nuclear spins unambiguously and individually in a broad frequency band by using a nitrogen-vacancy (NV) centre as model system. On the basis of delayed entanglement control, a technique combining microwave and radio frequency fields, our method allows to selectively perform robust high-fidelity entangling gates between hardly resolved nuclear spins and the NV electron. Long-lived qubit memories can be naturally incorporated to our method for improved performance. The application of our ideas will increase the number of useful register qubits accessible to a defect centre and improve the signal of nanoscale NMR.

Single electrons of solid-state defects can be used to detect nearby nuclear spins, but so far only a few at a time have been resolved. Here the authors propose an approach based on delayed entanglement echo that demonstrates improved detection and manipulation capabilities of nuclear spins by an NV centre.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Long-term data storage in diamond

The negatively charged nitrogen vacancy (NV^-) center in diamond is the focus of widespread attention for applications ranging from quantum information processing to nanoscale metrology. Although most work so far has focused on the NV^- optical and spin properties, control of the charge state promises complementary opportunities. One intriguing possibility is the long-term storage of information, a notion we hereby introduce using NV-rich, type 1b diamond. As a proof of principle, we use multicolor optical microscopy to read, write, and reset arbitrary data sets with two-dimensional (2D) binary bit density comparable to present digital-video-disk (DVD) technology. Leveraging on the singular dynamics of NV^- ionization, we encode information on different planes of the diamond crystal with no cross-talk, hence extending the storage capacity to three dimensions. Furthermore, we correlate the center's charge state and the nuclear spin polarization of the nitrogen host and show that the latter is robust to a cycle of NV^- ionization and recharge. In combination with super-resolution microscopy techniques, these observations provide a route toward subdiffraction NV charge control, a regime where the storage capacity could exceed present technologies.

Repeated quantum error correction on a continuously encoded qubit by real-time feedback

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

Large-scale quantum information processing requires the continuous protection of quantum states against errors. Here, the authors demonstrate active quantum error correction that improves the dephasing time of quantum states using a diamond quantum processor.

Quantum Zeno and Zeno-like effects in nitrogen vacancy centers

We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal (13)C nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a (13)C nuclear spin in the vicinity of an NV center.

Local and bulk (13)C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations

Polarizing nuclear spins is of fundamental importance in biology, chemistry and physics. Methods for hyperpolarizing ¹³C nuclei from free electrons in bulk usually demand operation at cryogenic temperatures. Room temperature approaches targeting diamonds with nitrogen-vacancy centres could alleviate this need; however, hitherto proposed strategies lack generality as they demand stringent conditions on the strength and/or alignment of the magnetic field. We report here an approach for achieving efficient electron-¹³C spin-alignment transfers, compatible with a broad range of magnetic field strengths and field orientations with respect to the diamond crystal. This versatility results from combining coherent microwave- and incoherent laser-induced transitions between selected energy states of the coupled electron–nuclear spin manifold. ¹³C-detected nuclear magnetic resonance experiments demonstrate that this hyperpolarization can be transferred via first-shell or via distant ¹³Cs throughout the nuclear bulk ensemble. This method opens new perspectives for applications of diamond nitrogen-vacancy centres in nuclear magnetic resonance, and in quantum information processing.

Hyperpolarization of nuclear spins for enhancing the sensitivity of magnetic resonance can typically be achieved at low temperatures. Here, the authors demonstrate room-temperature polarization of ¹³C derived from optically pumped electrons of nitrogen vacancies in diamonds with arbitrary orientations.

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.

Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae

Robust measurement of single quantum bits plays a key role in the realization of quantum computation and communication as well as in quantum metrology and sensing. We have implemented a method for the improved readout of single electronic spin qubits in solid-state systems. The method makes use of quantum logic operations on a system consisting of a single electronic spin and several proximal nuclear spin ancillae in order to repetitively readout the state of the electronic spin. Using coherent manipulation of a single nitrogen vacancy center in room-temperature diamond, full quantum control of an electronic-nuclear system consisting of up to three spins was achieved. We took advantage of a single nuclear-spin memory in order to obtain a 10-fold enhancement in the signal amplitude of the electronic spin readout. We also present a two-level, concatenated procedure to improve the readout by use of a pair of nuclear spin ancillae, an important step toward the realization of robust quantum information processors using electronic- and nuclear-spin qubits. Our technique can be used to improve the sensitivity and speed of spin-based nanoscale diamond magnetometers.

Could one make a diamond-based quantum computer?

We assess routes to a diamond-based quantum computer, where we specifically look towards scalable devices, with at least 10 linked quantum gates. Such a computer should satisfy the deVincenzo rules and might be used at convenient temperatures. The specific examples that we examine are based on the optical control of electron spins. For some such devices, nuclear spins give additional advantages. Since there have already been demonstrations of basic initialization and readout, our emphasis is on routes to two-qubit quantum gate operations and the linking of perhaps 10-20 such gates. We analyse the dopant properties necessary, especially centres containing N and P, and give results using simple scoping calculations for the key interactions determining gate performance. Our conclusions are cautiously optimistic: it may be possible to develop a useful quantum information processor that works above cryogenic temperatures.

Coherence and control of quantum registers based on electronic spin in a nuclear spin bath

We consider a protocol for the control of few-qubit registers comprising one electronic spin embedded in a nuclear spin bath. We show how to isolate a few proximal nuclear spins from the rest of the bath and use them as building blocks for a potentially scalable quantum information processor. We describe how coherent control techniques based on magnetic resonance methods can be adapted to these solid-state spin systems, to provide not only efficient, high fidelity manipulation but also decoupling from the spin bath. As an example, we analyze feasible performances and practical limitations in the realistic setting of nitrogen-vacancy centers in diamond.

Alkaline-earth-metal atoms as few-qubit quantum registers

We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth-metal atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with subwavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed.

Nanoscale magnetic sensing with an individual electronic spin in diamond

Detection of weak magnetic fields with nanoscale spatial resolution is an outstanding problem in the biological and physical sciences. For example, at a distance of 10 nm, the spin of a single electron produces a magnetic field of about 1 muT, and the corresponding field from a single proton is a few nanoteslas. A sensor able to detect such magnetic fields with nanometre spatial resolution would enable powerful applications, ranging from the detection of magnetic resonance signals from individual electron or nuclear spins in complex biological molecules to readout of classical or quantum bits of information encoded in an electron or nuclear spin memory. Here we experimentally demonstrate an approach to such nanoscale magnetic sensing, using coherent manipulation of an individual electronic spin qubit associated with a nitrogen-vacancy impurity in diamond at room temperature. Using an ultra-pure diamond sample, we achieve detection of 3 nT magnetic fields at kilohertz frequencies after 100 s of averaging. In addition, we demonstrate a sensitivity of 0.5 muT Hz(-1/2) for a diamond nanocrystal with a diameter of 30 nm.