Manipulating solid-state spin concentration through charge transport.

Solid-state defects are attractive platforms for quantum sensing and simulation, e.g., in exploring many-body physics and quantum hydrodynamics. However, many interesting properties can be revealed only upon changes in the density of defects, which instead is usually fixed in material systems. Increasing the interaction strength by creating denser defect ensembles also brings more decoherence. Ideally one would like to control the spin concentration at will while keeping fixed decoherence effects. Here, we show that by exploiting charge transport, we can take some steps in this direction, while at the same time characterizing charge transport and its capture by defects. By exploiting the cycling process of ionization and recombination of NV centers in diamond, we pump electrons from the valence band to the conduction band. These charges are then transported to modulate the spin concentration by changing the charge state of material defects. By developing a wide-field imaging setup integrated with a fast single photon detector array, we achieve a direct and efficient characterization of the charge redistribution process by measuring the complete spectrum of the spin bath with micrometer-scale spatial resolution. We demonstrate a two-fold concentration increase of the dominant spin defects while keeping the T2 of the NV center relatively unchanged, which also provides a potential experimental demonstration of the suppression of spin flip-flops via hyperfine interactions. Our work paves the way to studying many-body dynamics with temporally and spatially tunable interaction strengths in hybrid charge-spin systems.

Exponentially Enhanced Non-Hermitian Cooling.

Certain non-Hermitian systems exhibit the skin effect, whereby the wave functions become exponentially localized at one edge of the system. Such exponential amplification of wavefunction has received significant attention due to its potential applications in, e.g., classical and quantum sensing. However, the opposite edge of the system, featured by exponentially suppressed wave functions, remains largely unexplored. Leveraging this phenomenon, we introduce a non-Hermitian cooling mechanism, which is fundamentally distinct from traditional refrigeration or laser cooling techniques. Notably, non-Hermiticity will not amplify thermal excitations, but rather redistribute them. Hence, thermal excitations can be cooled down at one edge of the system, and the cooling effect can be exponentially enhanced by the number of auxiliary modes, albeit with a lower bound that depends on the dissipative interaction with the environment. Non-Hermitian cooling does not rely on intricate properties such as exceptional points or nontrivial topology, and it can apply to a wide range of excitations.

Roadmap on nanoscale magnetic resonance imaging.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Laser Cooling of Nuclear Magnons.

The initialization of nuclear spin to its ground state is challenging due to its small energy scale compared with thermal energy, even at cryogenic temperature. In this Letter, we propose an optonuclear quadrupolar effect, whereby two-color optical photons can efficiently interact with nuclear spins. Leveraging such an optical interface, we demonstrate that nuclear magnons, the collective excitations of nuclear spin ensemble, can be cooled down optically. Under feasible experimental conditions, laser cooling can suppress the population and entropy of nuclear magnons by more than 2 orders of magnitude, which could facilitate the application of nuclear spins in quantum information science.

Communication-Efficient Quantum Algorithm for Distributed Machine Learning.

The growing demands of remote detection and an increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles two traditional machine learning problems, the least-square fitting and softmax regression problems, in the scenario where the dataset is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of O(log_{2}(N)/ε), where N is the number of data points and ε is the bound on parameter errors. Compared to classical and other quantum methods that achieve the same goal, our methods provide a communication advantage in the scaling with data volume. The core of our methods, the quantum bipartite correlator algorithm that estimates the correlation or the Hamming distance of two bit strings distributed across two parties, may be further applied to other information processing tasks.

Characterizing Temperature and Strain Variations with Qubit Ensembles for Their Robust Coherence Protection.

Solid-state spin defects, especially nuclear spins with potentially achievable long coherence times, are compelling candidates for quantum memories and sensors. However, their current performances are still limited by dephasing due to variations of their intrinsic quadrupole and hyperfine interactions. We propose an unbalanced echo to overcome this challenge by using a second spin to refocus variations of these interactions while preserving the quantum information stored in the nuclear spin free evolution. The unbalanced echo can be used to probe the temperature and strain distribution in materials. We develop first-principles methods to predict variations of these interactions and reveal their correlation over large temperature and strain ranges. Experiments performed in an ensemble of ∼10^{10} nuclear spins in diamond demonstrate a 20-fold dephasing time increase, limited by other noise sources. We further numerically show that our method can refocus even stronger noise variations than present in our experiments.

SARS-CoV-2 Quantum Sensor Based on Nitrogen-Vacancy Centers in Diamond.

The development of highly sensitive and rapid biosensing tools targeted to the highly contagious virus SARS-CoV-2 is critical to tackling the COVID-19 pandemic. Quantum sensors can play an important role because of their superior sensitivity and fast improvements in recent years. Here we propose a molecular transducer designed for nitrogen-vacancy (NV) centers in nanodiamonds, translating the presence of SARS-CoV-2 RNA into an unambiguous magnetic noise signal that can be optically read out. We evaluate the performance of the hybrid sensor, including its sensitivity and false negative rate, and compare it to widespread diagnostic methods. The proposed method is fast and promises to reach a sensitivity down to a few hundreds of RNA copies with false negative rate less than 1%. The proposed hybrid sensor can be further implemented with different solid-state defects and substrates, generalized to diagnose other RNA viruses, and integrated with CRISPR technology.

Bias in Error-Corrected Quantum Sensing.

The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.

Coherent feedback control of a single qubit in diamond.

Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach relies on open-loop quantum control techniques, including optimal-control algorithms based on analytical or numerical solutions, Lyapunov design and Hamiltonian engineering. An alternative strategy, inspired by the success of classical control, is feedback control. Because of the complications introduced by quantum measurement, closed-loop control is less pervasive in the quantum setting and, with exceptions, its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback-control algorithm using a solid-state spin qubit system associated with the nitrogen vacancy centre in diamond, using coherent feedback to overcome the limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the output state of the system (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling techniques, feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the coherence time of the ancilla), while allowing gate operations. It is thus more closely related to quantum error-correction schemes, although these require larger and increasing qubit overheads. Increasing the number of fresh ancillas enables protection beyond their coherence time. We further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring a trade-off between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.

Nanoscale Vector AC Magnetometry with a Single Nitrogen-Vacancy Center in Diamond.

Detection of AC magnetic fields at the nanoscale is critical in applications ranging from fundamental physics to materials science. Isolated quantum spin defects, such as the nitrogen-vacancy center in diamond, can achieve the desired spatial resolution with high sensitivity. Still, vector AC magnetometry currently relies on using different orientations of an ensemble of sensors, with degraded spatial resolution, and a protocol based on a single NV is lacking. Here we propose and experimentally demonstrate a protocol that exploits a single NV to reconstruct the vectorial components of an AC magnetic field by tuning a continuous driving to distinct resonance conditions. We map the spatial distribution of an AC field generated by a copper wire on the surface of the diamond. The proposed protocol combines high sensitivity, broad dynamic range, and sensitivity to both coherent and stochastic signals, with broad applications in condensed matter physics, such as probing spin fluctuations.

Observation of Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems.

Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Time-periodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particle-hole symmetries, by observing symmetry-induced Floquet selection rules. Notably, we exploit modulated driving to reach the strong light-matter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogen-vacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetry-protected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems.

Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme.

In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator.

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.

Identification and Control of Electron-Nuclear Spin Defects in Diamond.

We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. Finally, we create quantum coherence among the three electron spins, paving the way for the creation of genuine tripartite entanglement. This approach will be useful in assembling multispin quantum registers for applications in quantum sensing and quantum information processing.

Quantum interpolation for high-resolution sensing.

Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.

All-Optical Quantum Sensing of Rotational Brownian Motion of Magnetic Molecules.

Sensing the local environment through the motional response of small molecules lays the foundation of many fundamental technologies. The information on local viscosity, for example, is contained in the random rotational Brownian motions of molecules. However, detection of the motions is challenging for molecules with sub-nanometer scale or high motional rates. Here we propose and experimentally demonstrate a novel method of detecting fast rotational Brownian motions of small magnetic molecules. With electronic spins as sensors, we are able to detect changes in motional rates, which yield different noise spectra and therefore different relaxation signals of the sensors. As a proof-of-principle demonstration, we experimentally implemented this method to detect the motions of gadolinium (Gd) complex molecules with nitrogen-vacancy (NV) centers in nanodiamonds. With all-optical measurements of the NV centers' longitudinal relaxation, we distinguished binary solutions with varying viscosities. Our method paves a new way for detecting fast motions of sub-nanometer sized magnetic molecules with better spatial resolution than conventional optical methods. It also provides a new tool in designing better contrast agents in magnetic resonance imaging.

Nanoscale Vector dc Magnetometry via Ancilla-Assisted Frequency Up-Conversion.

Sensing static magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging, and materials science. Even more beneficial would be full vector magnetometry with nanoscale spatial resolution. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with nitrogen vacancy (NV) centers in diamond. Achieving vector magnetometry has, however, often required using an ensemble of sensors or degrading the sensitivity. Here we introduce a hybrid magnetometry platform, consisting of a sensor and an ancillary qubit, that allows vector magnetometry of static fields. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear spin qubit. In particular, sensing transverse fields relies on frequency up-conversion of the dc fields through the ancillary qubit, allowing quantum lock-in detection with low-frequency noise rejection. In combination with the Ramsey detection of longitudinal fields, our frequency up-conversion scheme delivers a sensitive technique for vector dc magnetometry at the nanoscale.

Ancilla-Free Quantum Error Correction Codes for Quantum Metrology.

Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Finally, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.

Emergent Prethermalization Signatures in Out-of-Time Ordered Correlations.

How a many-body quantum system thermalizes-or fails to do so-under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal out-of-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics.

Exploring Localization in Nuclear Spin Chains.

Characterizing out-of-equilibrium many-body dynamics is a complex but crucial task for quantum applications and understanding fundamental phenomena. A central question is the role of localization in quenching thermalization in many-body systems and whether such localization survives in the presence of interactions. Probing this question in real systems necessitates the development of an experimentally measurable metric that can distinguish between different types of localization. While it is known that the localized phase of interacting systems [many-body localization (MBL)] exhibits a long-time logarithmic growth in entanglement entropy that distinguishes it from the noninteracting case of Anderson localization (AL), entanglement entropy is difficult to measure experimentally. Here, we present a novel correlation metric, capable of distinguishing MBL from AL in high-temperature spin systems. We demonstrate the use of this metric to detect localization in a natural solid-state spin system using nuclear magnetic resonance (NMR). We engineer the natural Hamiltonian to controllably introduce disorder and interactions, and observe the emergence of localization. In particular, while our correlation metric saturates for AL, it slowly keeps increasing for MBL, demonstrating analogous features to entanglement entropy, as we show in simulations. Our results show that our NMR techniques, akin to measuring out-of-time correlations, are well suited for studying localization in spin systems.