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

Limits of Noisy Quantum Metrology with Restricted Quantum Controls

The Heisenberg limit [(HL), with estimation error scales as 1/n] and the standard quantum limit (SQL, ∝1/sqrt[n]) are two fundamental limits in estimating an unknown parameter in n copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown though, whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this Letter, we discover various new limits for estimating qubit channels under restrictive controls. The HL is shown to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a single-qubit unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and for other cases a constant floor on the estimation error is proven. A practical example of the unitary protocol is provided.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9) Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Single-Shot Readout of a Nuclear Spin in Silicon Carbide

Solid-state qubits with a photonic interface is very promising for quantum networks. Color centers in silicon carbide have shown excellent optical and spin coherence, even when integrated with membranes and nanostructures. Additionally, nuclear spins coupled with electron spins can serve as long-lived quantum memories. Pioneering work previously has realized the initialization of a single nuclear spin and demonstrated its entanglement with an electron spin. In this Letter, we report the first realization of single-shot readout for a nuclear spin in SiC. We obtain a deterministic nuclear spin initialization and readout fidelity of 94.95% with a measurement duration of 1 ms. With a dual-step readout scheme, we obtain a readout fidelity as high as 99.03% within 0.28 ms by sacrificing the success efficiency. Our Letter complements the experimental toolbox of harnessing both electron and nuclear spins in SiC for future quantum networks.

Is Wave Function Collapse Necessary? Explaining Quantum Nondemolition Measurement of a Spin Qubit within Linear Evolution

The measurement problem dates back to the dawn of quantum mechanics. Here, we measure a quantum dot electron spin qubit through off-resonant coupling with a highly redundant ancilla, consisting of thousands of nuclear spins. Large redundancy allows for single-shot measurement with high fidelity ≈99.85%. Repeated measurements enable heralded initialization of the qubit and backaction-free detection of electron spin quantum jumps, attributed to burstlike fluctuations in a thermally populated phonon bath. Based on these results we argue that the measurement, linking quantum states to classical observables, can be made without any "wave function collapse" in agreement with the Quantum Darwinism concept.

Qudit-Based Spectroscopy for Measurement and Control of Nuclear-Spin Qubits in Silicon Carbide

Nuclear spins with hyperfine coupling to single electron spins are highly valuable quantum bits. Here we probe and characterize the particularly rich nuclear-spin environment around single silicon vacancy color centers (V2) in 4H-SiC. By using the electron spin-3/2 qudit as a four level sensor, we identify several sets of ^{29}Si and ^{13}C nuclear spins through their hyperfine interaction. We extract the major components of their hyperfine coupling via optical detected nuclear magnetic resonance, and assign them to shells in the crystal via the density function theory simulations. We utilize the ground-state level anticrossing of the electron spin for dynamic nuclear polarization and achieve a nuclear-spin polarization of up to 98±6%. We show that this scheme can be used to detect the nuclear magnetic resonance signal of individual spins and demonstrate their coherent control. Our work provides a detailed set of parameters and first steps for future use of SiC as a multiqubit memory and quantum computing platform.

Charge Stability and Charge-State-Based Spin Readout of Shallow Nitrogen-Vacancy Centers in Diamond

Spin-based applications of the negatively charged nitrogen-vacancy (NV) center in diamonds require an efficient spin readout. One approach is the spin-to-charge conversion (SCC), relying on mapping the spin states onto the neutral (NV0) and negative (NV-) charge states followed by a subsequent charge readout. With high charge-state stability, SCC enables extended measurement times, increasing precision and minimizing noise in the readout compared to the commonly used fluorescence detection. Nanoscale sensing applications, however, require shallow NV centers within a few nanometers distance from the surface where surface related effects might degrade the NV charge state. In this article, we investigate the charge state initialization and stability of single NV centers implanted ≈5 nm below the surface of a flat diamond plate. We demonstrate the SCC protocol on four shallow NV centers suitable for nanoscale sensing, obtaining a reduced readout noise of 5-6 times the spin-projection noise limit. We investigate the general applicability of the SCC for shallow NV centers and observe a correlation between the NV charge-state stability and readout noise. Coating the diamond with glycerol improves both the charge initialization and stability. Our results reveal the influence of the surface-related charge environment on the NV charge properties and motivate further investigations to functionalize the diamond surface with glycerol or other materials for charge-state stabilization and efficient spin-state readout of shallow NV centers suitable for nanoscale sensing.

Sub-nanotesla sensitivity at the nanoscale with a single spin

High-sensitivity detection of the microscopic magnetic field is essential in many fields. Good sensitivity and high spatial resolution are mutually contradictory in measurement, which is quantified by the energy resolution limit. Here we report that a sensitivity of 0.5 nT/[Formula: see text] at the nanoscale is achieved experimentally by using nitrogen-vacancy defects in diamond with depths of tens of nanometers. The achieved sensitivity is substantially enhanced by integrating with multiple quantum techniques, including real-time-feedback initialization, dynamical decoupling with shaped pulses and repetitive readout via quantum logic. Our magnetic sensors will shed new light on searching new physics beyond the standard model, investigating microscopic magnetic phenomena in condensed matters, and detection of life activities at the sub-cellular scale.

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ∼10^{9} two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

Experimental Limit on Nonlinear State-Dependent Terms in Quantum Theory

Linear time evolution is one of the fundamental postulates of quantum theory. Past theoretical attempts to introduce nonlinearity into quantum evolution have violated causality. However, a recent theory has introduced nonlinear state-dependent terms in quantum field theory, preserving causality [D. E. Kaplan and S. Rajendran, Phys. Rev. D 105, 055002 (2022)PRVDAQ2470-001010.1103/PhysRevD.105.055002]. We report the results of an experiment that searches for such terms. Our approach, inspired by the Everett many-worlds interpretation of quantum theory, correlates a binary macroscopic classical voltage with the outcome of a projective measurement of a quantum bit, prepared in a coherent superposition state. Measurement results are recorded in a bit string, which is used to control a voltage switch. Presence of a nonzero voltage reading in cases of no applied voltage is the experimental signature of a nonlinear state-dependent shift of the electromagnetic field operator. We implement blinded measurement and data analysis with three control bit strings. Control of systematic effects is realized by producing one of the control bit strings with a classical random-bit generator. The other two bit strings are generated by measurements performed on a superconducting qubit in an IBM Quantum processor and on a ^{15}N nuclear spin in a nitrogen-vacancy center in diamond. Our measurements find no evidence for electromagnetic quantum state-dependent nonlinearity. We set a bound on the parameter that quantifies this nonlinearity |ε_{γ}|<4.7×10^{-11}, at 90% confidence level.

Quantum metrology with imperfect measurements

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections-with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

Quantum nonlinear spectroscopy of single nuclear spins

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Signals that look the same from their low-order correlations can often be distinguished by looking at higher-order ones. Here, the authors exploit the sensitivity of quantum nonlinear spectroscopy to fourth-order correlations to identify Gaussian noises, random-phased AC fields, and quantum spins.

Qubit teleportation between non-neighbouring nodes in a quantum network

Future quantum internet applications will derive their power from the ability to share quantum information across the network^1,2. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections³. Although many experimental demonstrations have been performed on different quantum network platforms^4-10, moving beyond directly connected nodes has, so far, been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighbouring nodes in a quantum network. The network uses three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that, once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications^2,11-13.

Tuning the adiabaticity of spin dynamics in diamond nitrogen vacancy centers

We study the spin dynamics of diamond nitrogen vacancy (NV) centers in an oscillating magnetic field along the symmetry axis of the NV in the presence of transverse magnetic fields. It is well-known that the coupling between the otherwise degenerate Zeeman levels |M_S= ±1⟩ due to strain and electric fields is responsible for a Landau-Zener process near the pseudo-crossing of the adiabatic energy levels when the axial component of the oscillating magnetic field changes sign. We derive an effective two-level Hamiltonian for the NV system that includes coupling between the two levels via virtual transitions into the third far-detuned level |M_S= 0⟩ induced by transverse magnetic fields. This coupling adds to the coupling due to strain and electric fields, with a phase that depends on the direction of the transverse field in the plane perpendicular to the NV axis. Hence, thetotal couplingof the Zeeman levels can be tuned to control the adiabaticity of spin dynamics by fully or partially compensating the effect of the strain and electric fields, or by enhancing it. Moreover, by varying the strength and direction of the transverse magnetic fields, one can determine the strength and direction of the local strain and electric fields at the position of the NV center, and even theexternalstress and electric field. The nuclear spin hyperfine interaction is shown to introduce a nuclear spin dependent offset of the axial magnetic field for which the pseudo-crossing occurs, while the adiabaticity remains unaffected by the nuclear spin. If the NV center is coupled to the environment, modeled by a bath with a Gaussian white noise spectrum, as appropriate for NVs near the diamond surface, then the spin dynamics is accompanied by relaxation of the Zeeman level populations and decoherence with a non-monotonic decrease of the purity of the system. The results presented here have important impact for metrology with NV centers, quantum control of spin systems in solids and coupled dynamics of spin and rotations in levitated nano-objects in the presence of magnetic fields.

Room-temperature control and electrical readout of individual nitrogen-vacancy nuclear spins

Nuclear spins in semiconductors are leading candidates for future quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their long coherence time. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which, at cryogenic temperatures, enables probabilistic entanglement mediated optically by photonic links. Here, we demonstrate a concept of a microelectronic quantum device at ambient conditions using diamond as wide bandgap semiconductor. The basic quantum processor unit – a single ¹⁴N nuclear spin coupled to the NV electron – is read photoelectrically and thus operates in a manner compatible with nanoscale electronics. The underlying theory provides the key ingredients for photoelectric quantum gate operations and readout of nuclear qubit registers. This demonstration is, therefore, a step towards diamond quantum devices with a readout area limited by inter-electrode distance rather than by the diffraction limit. Such scalability could enable the development of electronic quantum processors based on the dipolar interaction of spin-qubits placed at nanoscopic proximity.

Nuclear spins in diamond are promising for applications in quantum technologies due to their long coherence times. Here, the authors demonstrate a scalable electrical readout of individual intrinsic ¹⁴N nuclear spins in diamond, mediated by hyperfine coupling to electron spin of the NV center, as a step towards room-temperature nanoscale diamond quantum devices.

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.

Realization of a multinode quantum network of remote solid-state qubits

The distribution of entangled states across the nodes of a future quantum internet will unlock fundamentally new technologies. Here, we report on the realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. In addition, we achieve real-time communication and feed-forward gate operations across the network. We demonstrate two quantum network protocols without postselection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Our work establishes a key platform for exploring, testing, and developing multinode quantum network protocols and a quantum network control stack.

High-fidelity single-shot readout of single electron spin in diamond with spin-to-charge conversion

High fidelity single-shot readout of qubits is a crucial component for fault-tolerant quantum computing and scalable quantum networks. In recent years, the nitrogen-vacancy (NV) center in diamond has risen as a leading platform for the above applications. The current single-shot readout of the NV electron spin relies on resonance fluorescence method at cryogenic temperature. However, the spin-flip process interrupts the optical cycling transition, therefore, limits the readout fidelity. Here, we introduce a spin-to-charge conversion method assisted by near-infrared (NIR) light to suppress the spin-flip error. This method leverages high spin-selectivity of cryogenic resonance excitation and flexibility of photoionization. We achieve an overall fidelity > 95% for the single-shot readout of an NV center electron spin in the presence of high strain and fast spin-flip process. With further improvements, this technique has the potential to achieve spin readout fidelity exceeding the fault-tolerant threshold, and may also find applications on integrated optoelectronic devices.

The NV centre in diamond has been used extensively in quantum information processing; however fault-tolerant readout of its spin remains challenging. Here, Zhang et al demonstrate a robust scheme that achieves high-fidelity readout via spin to charge conversion.

Cavity-enhanced microwave readout of a solid-state spin sensor

Overcoming poor readout is an increasingly urgent challenge for devices based on solid-state spin defects, particularly given their rapid adoption in quantum sensing, quantum information, and tests of fundamental physics. However, in spite of experimental progress in specific systems, solid-state spin sensors still lack a universal, high-fidelity readout technique. Here we demonstrate high-fidelity, room-temperature readout of an ensemble of nitrogen-vacancy centers via strong coupling to a dielectric microwave cavity, building on similar techniques commonly applied in cryogenic circuit cavity quantum electrodynamics. This strong collective interaction allows the spin ensemble’s microwave transition to be probed directly, thereby overcoming the optical photon shot noise limitations of conventional fluorescence readout. Applying this technique to magnetometry, we show magnetic sensitivity approaching the Johnson–Nyquist noise limit of the system. Our results pave a clear path to achieve unity readout fidelity of solid-state spin sensors through increased ensemble size, reduced spin-resonance linewidth, or improved cavity quality factor.

Conventional optical readout limits the sensitivity of solid state spin sensors due to photon shot noise and poor contrast. Here, the authors demonstrate room-temperature microwave detection of an ensemble of NV centers embedded in a microwave cavity, which offers high-fidelity readout without time overhead.

Long-Term Spin State Storage Using Ancilla Charge Memories

We articulate confocal microscopy and electron spin resonance to implement spin-to-charge conversion in a small ensemble of nitrogen-vacancy (NV) centers in bulk diamond and demonstrate charge conversion of neighboring defects conditional on the NV spin state. We build on this observation to show time-resolved NV spin manipulation and ancilla-charge-aided NV spin state detection via integrated measurements. Our results hint at intriguing opportunities in the development of novel measurement strategies in fundamental science and quantum spintronics as well as in the search for enhanced forms of color-center-based metrology down to the limit of individual point defects.

Repetitive readout enhanced by machine learning

Single-shot readout is a key component for scalable quantum information processing. However, many solid-state qubits with favorable properties lack the single-shot readout capability. One solution is to use the repetitive quantum-non-demolition readout technique, where the qubit is correlated with an ancilla, which is subsequently read out. The readout fidelity is therefore limited by the back-action on the qubit from the measurement. Traditionally, a threshold method is taken, where only the total photon count is used to discriminate qubit state, discarding all the information of the back-action hidden in the time trace of repetitive readout measurement. Here we show by using machine learning (ML), one obtains higher readout fidelity by taking advantage of the time trace data. ML is able to identify when back-action happened, and correctly read out the original state. Since the information is already recorded (but usually discarded), this improvement in fidelity does not consume additional experimental time, and could be directly applied to preparation-by-measurement and quantum metrology applications involving repetitive readout.

Narrow Optical Line Widths in Erbium Implanted in TiO2

Atomic and atomlike defects in the solid state are widely explored for quantum computers, networks, and sensors. Rare earth ions are an attractive class of atomic defects that feature narrow spin and optical transitions that are isolated from the host crystal, allowing incorporation into a wide range of materials. However, the realization of long electronic spin coherence times is hampered by magnetic noise from abundant nuclear spins in the most widely studied host crystals. Here, we demonstrate that Er³⁺ ions can be introduced via ion implantation into TiO₂, a host crystal that has not been studied extensively for rare earth ions and has a low natural abundance of nuclear spins. We observe efficient incorporation of the implanted Er³⁺ into the Ti⁴⁺ site (>50% yield) and measure narrow inhomogeneous spin and optical line widths (20 and 460 MHz, respectively) that are comparable to bulk-doped crystalline hosts for Er³⁺. This work demonstrates that ion implantation is a viable path to studying rare earth ions in new hosts and is a significant step toward realizing individually addressed rare earth ions with long spin coherence times for quantum technologies.

Quantum non-demolition measurement of an electron spin qubit

Measurements of quantum systems inevitably involve disturbance in various forms. Within the limits imposed by quantum mechanics, there exists an ideal projective measurement that does not introduce a back action on the measured observable, known as a quantum non-demolition (QND) measurement^1,2. Here we demonstrate an all-electrical QND measurement of a single electron spin in a gate-defined quantum dot. We entangle the single spin with a two-electron, singlet-triplet ancilla qubit via the exchange interaction^3,4 and then read out the ancilla in a single shot. This procedure realizes a disturbance-free projective measurement of the single spin at a rate two orders of magnitude faster than its relaxation. The QND nature of the measurement protocol^5,6 enables enhancement of the overall measurement fidelity by repeating the protocol. We demonstrate a monotonic increase of the fidelity over 100 repetitions against arbitrary input states. Our analysis based on statistical inference is tolerant to the presence of the relaxation and dephasing. We further exemplify the QND character of the measurement by observing spontaneous flips (quantum jumps)⁷ of a single electron spin. Combined with the high-fidelity control of spin qubits^8-13, these results will allow for various measurement-based quantum state manipulations including quantum error correction protocols¹⁴.

Quantum Control and Sensing of Nuclear Spins by Electron Spins under Power Limitations

State of the art quantum sensing experiments targeting frequency measurements or frequency addressing of nuclear spins require one to drive the probe system at the targeted frequency. In addition, there is a substantial advantage to performing these experiments in the regime of high magnetic fields, in which the Larmor frequency of the measured spins is large. In this scenario we are confronted with a natural challenge of controlling a target system with a very high frequency when the probe system cannot be set to resonance with the target frequency. In this contribution we present a set of protocols that are capable of confronting this challenge, even at large frequency mismatches between the probe system and the target system, both for polarization and for quantum sensing.

High-resolution spectroscopy of single nuclear spins via sequential weak measurements

Nuclear magnetic resonance (NMR) of single spins have recently been detected by quantum sensors. However, the spectral resolution has been limited by the sensor’s relaxation to a few kHz at room temperature. This can be improved by using quantum memories, at the expense of sensitivity. In contrast, classical signals can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. When applied to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurement. Here we report sequential weak measurements on a single ¹³C nuclear spin. The back-action causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.

Quantum sensors can have exceptional properties but the limits on their performance involve nonclassical effects such as quantum backaction. Here the authors show how to mitigate the effects of backaction on the spectral resolution of an NV centre nuclear spin sensor by controlling the measurement strength.

Robust universal photonic quantum gates operable with imperfect processes involved in diamond nitrogen-vacancy centers inside low-Q single-sided cavities

Robust universal quantum gates with an extremely high fidelity hold an important position in large-scale quantum computing. Here, we propose a scheme for several robust universal photonic quantum gates on a two-or three-photon system, including the controlled-NOT gate, the Toffoli gate, and the Fredkin gate, assisted by low-Q single-sided cavities. In our scheme, the quantum gates are robust against imperfect process occurring with the photons and the electron spins in diamond nitrogen-vacancy (NV) centers inside low-Q cavities. Errors due to the imperfect process are transferred to some heralding responses, which may lead to a direct recycling procedure to remedy the success probability of the quantum gates. As a result, the adverse impact of the imperfect process on fidelity is eliminated, greatly relaxing the restrictions on implementation of various quantum gates in experiments. Furthermore, the scheme is designed in a compact and heralded style, which can increase the robustness against environmental noise and local fluctuation, thus decreasing the operation time, the error probability, and the quantum resource consumption in a large-scale integrated quantum circuit. The near-unity fidelity and not-too-low efficiency with current achievable experimental techniques guarantees the feasibility of the scheme.

Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond

The diamond nitrogen-vacancy (NV) center is a leading platform for quantum information science due to its optical addressability and room-temperature spin coherence. However, measurements of the NV center’s spin state typically require averaging over many cycles to overcome noise. Here, we review several approaches to improve the readout performance and highlight future avenues of research that could enable single-shot electron-spin readout at room temperature.

Sensing Coherent Dynamics of Electronic Spin Clusters in Solids

We observe coherent spin exchange between identical electronic spins in the solid state, a key step towards full quantum control of electronic spin registers in room temperature solids. In a diamond substrate, a single nitrogen vacancy (NV) center coherently couples to two adjacent S=1/2 dark electron spins via the magnetic dipolar interaction. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of the NV. Finally, as a demonstration of coherent control, we selectively couple and transfer polarization between the NV and the pair of electron spins. Our observations enable the realization of fast quantum gate operations and quantum state transfer in a scalable, room temperature, quantum processor.

Broadband multiresonator quantum memory-interface

In this paper we experimentally demonstrated a broadband scheme of the multiresonator quantum memory-interface. The microwave photonic scheme consists of the system of mini-resonators strongly interacting with a common broadband resonator coupled with the external waveguide. We have implemented the impedance matched quantum storage in this scheme via controllable tuning of the mini-resonator frequencies and coupling of the common resonator with the external waveguide. Proof-of-principal experiment has been demonstrated for broadband microwave pulses when the quantum efficiency of 16.3% was achieved at room temperature. By using the obtained experimental spectroscopic data, the dynamics of the signal retrieval has been simulated and promising results were found for high-Q mini-resonators in microwave and optical frequency ranges. The results pave the way for the experimental implementation of broadband quantum memory-interface with quite high efficiency η > 0.99 on the basis of modern technologies, including optical quantum memory at room temperature.

Metal-dielectric antennas for efficient photon collection from diamond color centers

A central challenge in quantum technologies based on atom-like defects is the efficient collection of the emitter's fluorescence. Optical antennas are appealing as they offer directional emission together with spontaneous emission rate enhancement across a broad emitter spectrum. In this work, we introduce and optimize metal-dielectric nanoantenna designs recessed into a diamond substrate and aligned with quantum emitters. We analyze tradeoffs between external quantum efficiency, collection efficiency, radiative Purcell factor, and overall collected photon rate. This analysis shows that an optimized metal-dielectric hybrid structure can increase the collected photon rate from a nitrogen vacancy center by over two orders of magnitude compared to a bare emitter.

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.

Implementation of single-photon quantum routing and decoupling using a nitrogen-vacancy center and a whispering-gallery-mode resonator-waveguide system

Quantum router is a key element needed for the construction of future complex quantum networks. However, quantum routing with photons, and its inverse, quantum decoupling, are difficult to implement as photons do not interact, or interact very weakly in nonlinear media. In this paper, we investigate the possibility of implementing photonic quantum routing based on effects in cavity quantum electrodynamics, and present a scheme for single-photon quantum routing controlled by the other photon using a hybrid system consisting of a single nitrogen-vacancy (NV) center coupled with a whispering-gallery-mode resonator-waveguide structure. Different from the cases in which classical information is used to control the path of quantum signals, both the control and signal photons are quantum in our implementation. Compared with the probabilistic quantum routing protocols based on linear optics, our scheme is deterministic and also scalable to multiple photons. We also present a scheme for single-photon quantum decoupling from an initial state with polarization and spatial-mode encoding, which can implement an inverse operation to the quantum routing. We discuss the feasibility of our schemes by considering current or near-future techniques, and show that both the schemes can operate effectively in the bad-cavity regime. We believe that the schemes could be key building blocks for future complex quantum networks and large-scale quantum information processing.

Dissipatively Stabilized Quantum Sensor Based on Indirect Nuclear-Nuclear Interactions

We propose to use a dissipatively stabilized nitrogen vacancy (NV) center as a mediator of interaction between two nuclear spins that are protected from decoherence and relaxation of the NV due to the periodical resets of the NV center. Under ambient conditions this scheme achieves highly selective high-fidelity quantum gates between nuclear spins in a quantum register even at large NV-nuclear distances. Importantly, this method allows for the use of nuclear spins as a sensor rather than a memory, while the NV spin acts as an ancillary system for the initialization and readout of the sensor. The immunity to the decoherence and relaxation of the NV center leads to a tunable sharp frequency filter while allowing at the same time the continuous collection of the signal to achieve simultaneously high spectral selectivity and high signal-to-noise ratio.

Demonstration of diamond microlens structures by a three-dimensional (3D) dual-mask method

Diamond is a promising platform for quantum information technologies (QITs) mainly due to the properties of color centers including spin read-out, magnetic field sensing, and entanglement between different nitrogen-vacancy (NV) centers. High photon collection efficiency is essential for a high fidelity optical single-shot readout of electronic spin in the color center. To avoid total internal reflection, sculpting solid immersion lenses in the diamond surface is an ideal natural choice. Three-dimensional (3D) microstructures can be made in a photoresist material by a special lithography method. These structures can be subsequently transferred into silicon, diamond or other semiconductors by plasma etching with appropriate selectivity. However, this method cannot be directly implemented into making large height diamond microlenses where the selectivity between diamond and the photoresist is very low. In this work, we propose and demonstrate a dual mask method to achieve an overall high selectivity between diamond and photoresist via the interlayer of single crystalline silicon. By tuning the process parameters of the two etching steps, diamond micro-lenses with large variable height are successfully demonstrated..

Scheme for Detection of Single-Molecule Radical Pair Reaction Using Spin in Diamond

The radical pair reaction underlies the magnetic field sensitivity of chemical reactions and is suggested to play an important role in both chemistry and biology. Current experimental evidence is based on ensemble measurements; however, the ability to probe the radical pair reaction at the single-molecule level would provide valuable information concerning its role in important biological processes. Here, we propose a scheme to detect the charge recombination rate in a radical pair reaction under ambient conditions by using single nitrogen-vacancy center spin in diamond. We demonstrate theoretically that it is possible to detect the effect of the geomagnetic field on the radical pair reaction and propose the present scheme as a possible hybrid model chemical compass.

Robust hyperparallel photonic quantum entangling gate with cavity QED

Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlled-phase-flip gate for a two-photon system in both the polarization and spatial-mode degrees of freedom (DOFs), in which the noise caused by the inequality of two reflection coefficients can be depressed efficiently. This gate doubles the quantum entangling operation synchronously on a photon system and can reduce the quantum resources consumed largely and depress the photonic dissipation efficiently, compared with the two cascade quantum entangling gates in one DOF. It has a near unit fidelity. Moreover, we show that the balance condition can be obtained in both the weak coupling regime and the strong coupling regime, and the high-fidelity quantum gate operation is easier to be realized in the balance condition than the ones in the ideal condition in experiment.

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.

Nanoscale Imaging of Current Density with a Single-Spin Magnetometer

Charge transport in nanostructures and thin films is fundamental to many phenomena and processes in science and technology, ranging from quantum effects and electronic correlations in mesoscopic physics, to integrated charge- or spin-based electronic circuits, to photoactive layers in energy research. Direct visualization of the charge flow in such structures is challenging due to their nanometer size and the itinerant nature of currents. In this work, we demonstrate noninvasive magnetic imaging of current density in two-dimensional conductor networks including metallic nanowires and carbon nanotubes. Our sensor is the electronic spin of a diamond nitrogen-vacancy center attached to a scanning tip and operated under ambient conditions. Using a differential measurement technique, we detect DC currents down to a few μA with a current density noise floor of ∼2 × 10⁴ A/cm². Reconstructed images have a spatial resolution of typically 50 nm, with a best-effort value of 22 nm. Current density imaging offers a new route for studying electronic transport and conductance variations in two-dimensional materials and devices, with many exciting applications in condensed matter physics and materials science.

Nuclear quantum-assisted magnetometer

Magnetic sensing and imaging instruments are important tools in biological and material sciences. There is an increasing demand for attaining higher sensitivity and spatial resolution, with implementations using a single qubit offering potential improvements in both directions. In this article we describe a scanning magnetometer based on the nitrogen-vacancy center in diamond as the sensor. By means of a quantum-assisted readout scheme together with advances in photon collection efficiency, our device exhibits an enhancement in signal to noise ratio of close to an order of magnitude compared to the standard fluorescence readout of the nitrogen-vacancy center. This is demonstrated by comparing non-assisted and assisted methods in a T₁ relaxation time measurement.

Optical magnetic detection of single-neuron action potentials using quantum defects in diamond

Magnetic fields from neuronal action potentials (APs) pass largely unperturbed through biological tissue, allowing magnetic measurements of AP dynamics to be performed extracellularly or even outside intact organisms. To date, however, magnetic techniques for sensing neuronal activity have either operated at the macroscale with coarse spatial and/or temporal resolution-e.g., magnetic resonance imaging methods and magnetoencephalography-or been restricted to biophysics studies of excised neurons probed with cryogenic or bulky detectors that do not provide single-neuron spatial resolution and are not scalable to functional networks or intact organisms. Here, we show that AP magnetic sensing can be realized with both single-neuron sensitivity and intact organism applicability using optically probed nitrogen-vacancy (NV) quantum defects in diamond, operated under ambient conditions and with the NV diamond sensor in close proximity (∼10 µm) to the biological sample. We demonstrate this method for excised single neurons from marine worm and squid, and then exterior to intact, optically opaque marine worms for extended periods and with no observed adverse effect on the animal. NV diamond magnetometry is noninvasive and label-free and does not cause photodamage. The method provides precise measurement of AP waveforms from individual neurons, as well as magnetic field correlates of the AP conduction velocity, and directly determines the AP propagation direction through the inherent sensitivity of NVs to the associated AP magnetic field vector.

General hyperconcentration of photonic polarization-time-bin hyperentanglement assisted by nitrogen-vacancy centers coupled to resonators

Entanglement concentration protocol (ECP) is used to extract the maximally entangled states from less entangled pure states. Here we present a general hyperconcentration protocol for two-photon systems in partially hyperentangled Bell states that decay with the interrelation between the time-bin and the polarization degrees of freedom (DOFs), resorting to an input-output process with respect to diamond nitrogen-vacancy centers coupled to resonators. We show that the resource can be utilized sufficiently and the success probability is largely improved by iteration of the hyper-ECP process. Besides, our hyper-ECP can be directly extended to concentrate nonlocal partially hyperentangled N-photon Greenberger-Horne-Zeilinger states, and the success probability remains unchanged with the growth of the number of photons. Moreover, the time-bin entanglement is a useful DOF and it only requires one path for transmission, which means it not only economizes on a large amount of quantum resources but also relaxes from the path-length dispersion in long-distance quantum communication.

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.

Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators

We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.

Single spin magnetic resonance

Different approaches have improved the sensitivity of either electron or nuclear magnetic resonance to the single spin level. For optical detection it has essentially become routine to observe a single electron spin or nuclear spin. Typically, the systems in use are carefully designed to allow for single spin detection and manipulation, and of those systems, diamond spin defects rank very high, being so robust that they can be addressed, read out and coherently controlled even under ambient conditions and in a versatile set of nanostructures. This renders them as a new type of sensor, which has been shown to detect single electron and nuclear spins among other quantities like force, pressure and temperature. Adapting pulse sequences from classic NMR and EPR, and combined with high resolution optical microscopy, proximity to the target sample and nanoscale size, the diamond sensors have the potential to constitute a new class of magnetic resonance detectors with single spin sensitivity. As diamond sensors can be operated under ambient conditions, they offer potential application across a multitude of disciplines. Here we review the different existing techniques for magnetic resonance, with a focus on diamond defect spin sensors, showing their potential as versatile sensors for ultra-sensitive magnetic resonance with nanoscale spatial resolution.

Photonic Quantum Networks formed from NV(-) centers

In this article we present a simple repeater scheme based on the negatively-charged nitrogen vacancy centre in diamond. Each repeater node is built from modules comprising an optical cavity containing a single NV⁻, with one nuclear spin from ¹⁵N as quantum memory. The module uses only deterministic processes and interactions to achieve high fidelity operations (>99%), and modules are connected by optical fiber. In the repeater node architecture, the processes between modules by photons can be in principle deterministic, however current limitations on optical components lead the processes to be probabilistic but heralded. Our resource-modest repeater architecture contains two modules at each node, and the repeater nodes are then connected by entangled photon pairs. We discuss the performance of such a quantum repeater network with modest resources and then incorporate more resource-intense strategies step by step. Our architecture should allow large-scale quantum information networks with existing or near future technology.

Entanglement dynamics of Nitrogen-vacancy centers spin ensembles coupled to a superconducting resonator

Exploration of macroscopic quantum entanglement is of great interest in both fundamental science and practical application. We investigate a hybrid quantum system that consists of two nitrogen-vacancy centers ensembles (NVE) coupled to a superconducting coplanar waveguide resonator (CPWR). The collective magnetic coupling between the NVE and the CPWR is employed to generate macroscopic entanglement between the NVEs, where the CPWR acts as the quantum bus. We find that, this NVE-CPWR hybrid system behaves as a system of three coupled harmonic oscillators, and the excitation prepared initially in the CPWR can be distributed into these two NVEs. In the nondissipative case, the entanglement of NVEs oscillates periodically and the maximal entanglement always keeps unity if the CPWR is initially prepared in the odd coherent state. Considering the dissipative effect from the CPWR and NVEs, the amount of entanglement between these two NVEs strongly depends on the initial state of the CPWR, and the maximal entanglement can be tuned by adjusting the initial states of the total system. The experimental feasibility and challenge with currently available technology are discussed.

Strongly polarizing weakly coupled (13)C nuclear spins with optically pumped nitrogen-vacancy center

Enhancing the polarization of nuclear spins surrounding the nitrogen-vacancy (NV) center in diamond has recently attracted widespread attention due to its various applications. Here we present an analytical formula that not only provides a clear physical picture for the recently observed polarization reversal of strongly coupled(13)C nuclei over a narrow range of magnetic field [H. J. Wang et al., Nat. Commun. 4, 1940 (2013)], but also demonstrates the possibility to strongly polarize weakly coupled (13)C nuclei. This allows sensitive magnetic field control of the (13)C nuclear spin polarization for NMR applications and significant suppression of the (13)C nuclear spin noise to prolong the NV spin coherence time.