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An outstanding challenge in large-scale quantum platforms is to simultaneously achieve strong interactions, giving rise to the most interesting behaviors, and local addressing -that can probe them. In the context of correlated phases, local addressing enables one to directly probe the nature of the system's order. Meanwhile, for out-ofequilibrium dynamics, such addressing allows the study of quantum information spreading and operator growth. Here, we introduce a novel technique that enables the measurement of local correlation functions, down to single-site resolution, despite access to only global controls. Our approach leverages the intrinsic disorder present in a solid-state spin ensemble to dephase the nonlocal components of the correlation function. Utilizing this toolset, we measure both the spin and energy transport in nuclear spin chains. By tuning the interaction Hamiltonian via Floquet engineering, we investigate the cross-over between ballistic and diffusive hydrodynamics. Interestingly, when the system is both interacting and (nearly-)integrable, we observe the coexistence of diffusive spin transport with ballistic energy transport., main text 5 pages, 4 figures; SM 10 pages 5 figures

The growing demands of remote detection and 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 problem, in the scenario where the data set is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of $O(\frac{\log_2(N)}{\epsilon})$, where $N$ is the number of data points and $\epsilon$ is the bound on parameter errors. Compared to classical algorithms and other quantum algorithms that achieve the same output task, our algorithm provides a communication advantage in the scaling with the data volume. The building block of our algorithm, the quantum-accelerated estimation of distributed inner product and Hamming distance, could be further applied to various tasks in distributed machine learning to accelerate communication.

Photons and nuclear spins are two well-known building blocks in quantum information science and technology. Establishing an efficient interface between optical photons and nuclear spins, while highly desirable for hybridizing these two quantum systems, is challenging because the interactions between nuclear spins and the environment are usually weak in magnitude, and there is also a formidable gap between nuclear spin frequencies and optical frequencies. In this work, we propose an opto-nuclear quadrupolar (ONQ) effect, whereby optical photons can be efficiently coupled to nuclear spins, similar to Raman scattering. Compared to previous works, ancilla electron spins are not required for the ONQ effect. This leads to advantages such as applicability in defect-free nonmagnetic crystals and longer nuclear spin coherence time. In addition, the frequency of the optical photons can be arbitrary, so they can be fine-tuned to minimize the material heating and to match telecom wavelengths for long-distance communications. Using perturbation theory and first-principles calculations, we demonstrate that the ONQ effect is stronger by several orders of magnitude than other nonlinear optical effects that could couple to nuclear spins. Based on this rationale, we propose promising applications of the ONQ effect, including quantum memory, quantum transduction, and materials isotope spectroscopy. We also discuss issues relevant to the experimental demonstration of the ONQ effect., 40 pages, 6 figures

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 opto-nuclear 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 two orders of magnitude, which could facilitate the application of nuclear spins in quantum information science., Comment: 13 pages, 3 figures

Characterizing and understanding the environment affecting quantum systems is critical to elucidate its physical properties and engineer better quantum devices. We develop an approach to reduce the quantum environment causing single-qubit dephasing to a simple yet predictive noise model. Our approach, inspired by quantum noise spectroscopy, is to define a "self-consistent" classical noise spectrum, that is, compatible with all observed decoherence under various qubit dynamics. We demonstrate the power and limits of our approach by characterizing, with nanoscale spatial resolution, the noise experienced by two electronic spins in diamond that, despite their proximity, surprisingly reveal the presence of a complex quantum spin environment, both classically-reducible and not. Our results overcome the limitations of existing noise spectroscopy methods, and highlight the importance of finding predictive models to accurately characterize the underlying environment. Extending our work to multiqubit systems would enable spatially-resolved quantum sensing of complex environments and quantum device characterization, notably to identify correlated noise between qubits, which is crucial for practical realization of quantum error correction.

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.

Spin qubits associated with color centers are promising platforms for various quantum technologies. However, to be deployed in robust quantum devices, the variations of their intrinsic properties with the external conditions, and in particular temperature, should be known with high precision. Unfortunately, a predictive theory on the temperature dependence of the resonance frequency of electron and nuclear spin defects in solids remains lacking. In this work, we develop a first-principles method for the temperature dependence of zero phonon line, zero-field splitting, hyperfine interaction, and nuclear quadrupole interaction of color centers. As a testbed, we compare our ab-initio calculation results with experiments in the Nitrogen-Vacancy (NV) center finding good agreement. Interestingly, we identify the major origin of temperature dependence as a second-order effect of phonon vibration. The method is generally applicable to different color centers and provides a theoretical tool for designing high-precision quantum sensors.

The power of quantum sensing rests on its ultimate precision limit, quantified by the quantum Cram\'er-Rao bound (QCRB), which can surpass classical bounds. In multi-parameter estimation, the QCRB is not always saturated as the quantum nature of associated observables may lead to their incompatibility. Here we explore the precision limits of multi-parameter estimation through the lens of quantum geometry, enabling us to experimentally evaluate the QCRB via quantum geometry measurements. Focusing on two- and three-parameter estimation, we elucidate how fundamental quantum uncertainty principles prevent the saturation of the bound. By linking a metric of "quantumness" to the system geometric properties, we investigate and experimentally extract the attainable QCRB for three-parameter estimations., Comment: 13 pages, 4 figures

Periodically driven Floquet quantum systems could provide a promising platform to investigate novel physics out of equilibrium1, but the drive generically heats the system to a featureless infinite-temperature state2–4. Fortunately, for high driving frequency, the heat absorption rate has been theoretically predicted to be exponentially small, giving rise to a long-lived prethermal regime that exhibits all the intriguing properties of Floquet systems5–8. Here we experimentally observe Floquet prethermalization using NMR techniques and probe the heating rate. We first show the relaxation of a far-from-equilibrium initial state to a long-lived prethermal state, well described by a time-independent ‘prethermal’ Hamiltonian. By measuring the autocorrelation of this prethermal Hamiltonian we can further experimentally confirm the predicted exponentially slow heating rate. More strikingly, we find that, on the timescale at which the prethermal Hamiltonian picture breaks down, the Floquet system still possesses other quasiconservation laws. Our results demonstrate that it is possible to realize robust Floquet engineering, thus enabling the experimental observation of non-trivial Floquet phases of matter. A periodically driven Floquet quantum many-body system initially prepared in a far-from-equilibrium state may exhibit prethermalization: that is, before reaching its thermal equilibrium the system first relaxes to a long-lived quasistationary state.

The identifiability of a system is concerned with whether the unknown parameters in the system can be uniquely determined with all the possible data generated by a certain experimental setting. A test of quantum Hamiltonian identifiability is an important tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this paper, we generalize the identifiability test based on the Similarity Transformation Approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a Structure Preserving Transformation (SPT) method for non-minimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness., 14 pages, 2 figures

Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the optimal pulsed control field can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a \emph{lower bound} for the sensor sensitivity, and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond., Main text: 16 pages, 5 figures. Supplemental Material: 5 pages, 2 figures

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, thanks to 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., 14 pages, 4 figures

Periodically driven quantum systems, known as Floquet systems, have been a focus of non-equilibrium physics in recent years, thanks to their rich dynamics. Not only time-periodic systems exhibit symmetries similar to those in spatially periodic systems, but they also display novel behavior due to symmetry breaking. Characterizing such dynamical symmetries is crucial, but the task is often challenging, due to limited driving strength and the lack of an experimentally accessible characterization protocol. Here, we show how to characterize dynamical symmetries including parity, rotation, and particle-hole symmetry by observing the symmetry-induced selection rules between Floquet states. Specifically, we exploit modulated quantum driving to reach the strong light-matter coupling regime and we introduce a protocol to experimentally extract the transition elements between Floquet states from the coherent evolution of the system. Using the nitrogen-vacancy center in diamond as an experimental testbed, we apply our methods to observe symmetry-protected dark states and dark bands, and the coherent destruction of tunneling effect. Our work shows how to exploit the quantum control toolkit to study dynamical symmetries that can arise in topological phases of strongly-driven Floquet systems.

Engineering desired Hamiltonian in quantum many-body systems is essential for applications such as quantum simulation, computation and sensing. Conventional quantum Hamiltonian engineering sequences are designed using human intuition based on perturbation theory, which may not describe the optimal solution and is unable to accommodate complex experimental imperfections. Here we numerically search for Hamiltonian engineering sequences using deep reinforcement learning (DRL) techniques and experimentally demonstrate that they outperform celebrated sequences on a solid-state nuclear magnetic resonance quantum simulator. As an example, we aim at decoupling strongly-interacting spin-1/2 systems. We train DRL agents in the presence of different experimental imperfections and verify robustness of the output sequences both in simulations and experiments. Surprisingly, many of the learned sequences exhibit a common pattern that had not been discovered before, to our knowledge, but has an meaningful analytical description. We can thus restrict the searching space based on this control pattern, allowing to search for longer sequences, ultimately leading to sequences that are robust against dominant imperfections in our experiments. Our results not only demonstrate a general method for quantum Hamiltonian engineering, but also highlight the importance of combining black-box artificial intelligence with understanding of physical system in order to realize experimentally feasible applications., Comment: 20 pages, 10+6 figures, 1+2 tables

The Mollow triplet is a fundamental signature of quantum optics, and has been observed in numerous quantum systems. Although it arises in the 'strong driving' regime of the quantized field, where the atoms undergo coherent oscillations, it can be typically analyzed within the rotating wave approximation. Here we report the first observation of high-order effects in the Mollow triplet structure due to strong driving. In experiments, we explore the regime beyond the rotating wave approximation using concatenated continuous driving that has less stringent requirements on the driving field power. We are then able to reveal additional transition frequencies, shifts in energy levels, and corrections to the transition amplitudes. In particular, we find that these amplitudes are more sensitive to high-order effects than the frequency shifts, and that they still require an accurate determination in order to achieve high-fidelity quantum control. The experimental results are validated by the Floquet theory, which enables the precise numerical simulation of the evolution and further provides an analytical form for an effective Hamiltonian that approximately predicts the spin dynamics beyond the rotating wave approximation.

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., Comment: 6 + 13 pages, 2 + 8 figures. Comments welcome

1. Introduction Alkali metal ions such as sodium and potassium ions play fundamental roles in biology. Therefore, developing highly sensitive and selective methods to both detect and quantify these ions for biological applications including medical diagnostics and imaging is of considerable importance. In recent years, quantum sensors have emerged as powerful tools to detect chemical and biological signals. In particular, nitrogen-vacancy (NV) centers in diamond act as stable fluorescence markers and magnetic field sensors, and have been investigated as quantum sensors for applications ranging from material science to chem-istry and biology. A promising avenue to detect biological signals is to transduce them into the signals that can be readout by NV centers. For instance, the NV's charge state is closely related to its surrounding electrostatic environment [1, 2]. Meanwhile, NV centers in nanodiamonds (NDs) have already demonstrated their ability to detect biological processes with high spatial resolution [3, 4], and are the object of mant intense study due to their favorable properties, ranging from very high photo- and thermal-stability to biocompatibility, in contrast to many florescent biomarkers that are used to detect ions. In this work, with surface engineering of ND, we study a quantum sensor that is capable of detecting specific ions such as sodium ions. We will show that the presence of metal ions will change the charge state of NV centers inside ND, which can be read out by measuring the photoluminescence (PL) spectrum.

Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good digital quantum simulators is the fidelity of the engineered dynamics given a finite set of elementary operations. Here we present a framework for optimizing the order of operations based on a geometric picture, thus abstracting from the operation details and achieving computational efficiency. Based on this geometric framework, we provide two alternative second-order Trotter expansions: one with optimal fidelity at a short timescale, and the second robust at a long timescale. Thanks to the improved fidelity at different timescales, the two expansions we introduce can form the basis for experimental-constrained digital quantum simulation.

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T2, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 102 spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T3≈(0.15±0.02)/T2, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments. Fil: Sánchez, Claudia Marina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Chattah, Ana Karina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Wei, K. X.. Massachusetts Institute of Technology; Estados Unidos Fil: Buljubasich Gentiletti, Lisandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Cappellaro, P.. Massachusetts Institute of Technology; Estados Unidos Fil: Pastawski, Horacio Miguel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina

Quantum network is a promising platform for many ground-breaking applications that lie beyond the capability of its classical counterparts. Efficient entanglement generation on quantum networks with relatively limited resources such as quantum memories is essential to fully realize the network's capabilities, the solution to which calls for delicate network design and is currently at the primitive stage. In this study we propose an effective routing scheme to enable automatic responses for multiple requests of entanglement generation between source-terminal stations on a quantum lattice network with finite edge capacities. Multiple connection paths are exploited for each connection request while entanglement fidelity is ensured for each path by performing entanglement purification. The routing scheme is highly modularized with a flexible nature, embedding quantum operations within the algorithmic workflow, whose performance is evaluated from multiple perspectives. In particular, three algorithms are proposed and compared for the scheduling of capacity allocation on the edges of quantum network. Embodying the ideas of proportional share and progressive filling that have been well-studied in classical routing problems, we design a new scheduling algorithm, the propagatory update method, which in certain aspects overrides the two algorithms based on classical heuristics in scheduling performances. The general solution scheme paves the road for effective design of efficient routing and flow control protocols on applicational quantum networks., Comment: 25 pages, 18 figures

Quantum metrology is a powerful tool for explorations of fundamental physical phenomena and applications in material science and biochemical analysis. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by interactions between them. Here, using a dense ensemble of interacting electronic spins in diamond, we demonstrate a novel approach to quantum metrology to surpass such limitations. It is based on a new method of robust quantum control, which allows us to simultaneously suppress the undesired effects associated with spin-spin interactions, disorder, and control imperfections, enabling a fivefold enhancement in coherence time compared to state-of-the-art control sequences. Combined with optimal spin state initialization and readout directions, this allows us to achieve an ac magnetic field sensitivity well beyond the previous limit imposed by interactions, opening a new regime of high-sensitivity solid-state ensemble magnetometers., publishedVersion

Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting Floquet many-body phases over exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from non-conserved ones, allowing to single out a set of linearly-independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanism underlying the quasi-conservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid state nuclear magnetic resonance systems., Comment: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1912.05799

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., Comment: v3: 5+8 pages, close to published version

Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum information. A phenomenological model, which describes the system using a complete set of local integrals of motion (LIOMs), provides a powerful tool to understand MBL, but can be usually only computed approximately. Here we explicitly compute a complete set of LIOMs with a non-perturbative approach, by maximizing the overlap between LIOMs and physical spin operators in real space. The set of LIOMs satisfies the desired exponential decay of weight of LIOMs in real-space. This LIOM construction enables a direct mapping from the real space Hamiltonian to the phenomenological model and thus enables studying the localized Hamiltonian and the system dynamics. We can thus study and compare the localization lengths extracted from the LIOM weights, their interactions, and dephasing dynamics, revealing interesting aspects of many-body localization. Our scheme is immune to accidental resonances and can be applied even at phase transition point, providing a novel tool to study the microscopic features of the phenomenological model of MBL., Comment: 8+3 pages, 8+6 figures

The performance of solid-state quantum sensors based on electronic spin defects is often limited by the presence of environmental spin impurities that cause decoherence. A promising approach to improve these quantum sensors is to convert environment spins into useful resources for sensing. Here we demonstrate the efficient use of an unknown electronic spin defect in the proximity of a nitrogen-vacancy center in diamond as both a quantum sensor and a quantum memory. We first experimentally evaluate the improvement in magnetic field sensing provided by mixed entangled states of the two electronic spins. Our results critically highlight the tradeoff between the advantages expected from increasing the number of spin sensors and the typical challenges associated with increasing control errors, decoherence rates, and time overheads. Still, by taking advantage of the spin defect as both a quantum sensor and a quantum memory whose state can be repetitively measured to improve the readout fidelity, we can achieve a gain in performance over the use of a single-spin sensor. These results show that the efficient use of available quantum resources can enhance quantum devices, pointing to a practical strategy towards quantum-enhanced sensing and information processing by exploiting environment spin defects., Comment: 7 pages, 4 figures

Nitrogen-vacancy centers in diamond are promising as sensitive vector magnetometers, quantum repeaters, and qubits, but realizing this potential has been limited by the diamond material itself. Here a comprehensive study addresses creation of nitrogen-vacancy centers, balancing the impact of irradiation and annealing on the quantum coherence properties of commercial material. Photoluminescence decomposition analysis is used to quantitatively determine the neutral-to-negative charge-state ratio, and for insight into the impact of electron irradiation on material quantum coherence properties.