Concurrent sensing of vector magnetic field based on diamond nitrogen-vacancy ensemble using a time-divided hardware-synchronized protocol.

A diamond nitrogen-vacancy (NV) ensemble has been developed as a vector magnetometry platform for sensing external time-varying magnetic fields. However, due to the complexity of manipulating electron spins along different directions, a current vector NV magnetometer often needs a large amount of supporting equipment, preventing its applications in a compact circumstance. Here, we develop a hardware-level protocol to realize a multi-axis NV magnetometer using only a single channel of microwave generation and signal detection resources. This mechanism is to monitor each resonance serialized in a sequence and measure the electron-spin frequency shifts concurrently in real time. The functionality is realized by a home-made control system with an on-chip direct digital synthesis generator and signal processor. We finally achieve a vector sensitivity of around 14 nT/Hz on four different axes at the same time. We also analyze the phase delay of the sensing signal between different axes induced by the protocol. This protocol is compatible with other schemes to further improve the performance, such as hyperfine driving, balanced detection, and high-efficiency photon collection methods.

Suppressing Thermal Noise to Sub-Millikelvin Level in a Single-Spin Quantum System Using Realtime Frequency Tracking.

A single nitrogen-vacancy (NV) center in a diamond can be used as a nanoscale sensor for magnetic field, electric field or nuclear spins. Due to its low photon detection efficiency, such sensing processes often take a long time, suffering from an electron spin resonance (ESR) frequency fluctuation induced by the time-varying thermal perturbations noise. Thus, suppressing the thermal noise is the fundamental way to enhance single-sensor performance, which is typically achieved by utilizing a thermal control protocol with a complicated and highly costly apparatus if a millikelvin-level stabilization is required. Here, we analyze the real-time thermal drift and utilize an active way to alternately track the single-spin ESR frequency drift in the experiment. Using this method, we achieve a temperature stabilization effect equivalent to sub-millikelvin (0.8 mK) level with no extra environmental thermal control, and the spin-state readout contrast is significantly improved in long-lasting experiments. This method holds broad applicability for NV-based single-spin experiments and harbors the potential for prospective expansion into diverse nanoscale quantum sensing domains.

Four-Order Power Reduction in Nanoscale Electron-Nuclear Double Resonance with a Nitrogen-Vacancy Center in Diamonds.

Detecting nuclear spins using single nitrogen-vacancy (NV) centers is of particular importance in nanoscale science and engineering but often suffers from the heating effect of microwave fields for spin manipulation, especially under high magnetic fields. Here, we realize an energy-efficient nanoscale nuclear-spin detection using a phase-modulation electron-nuclear double resonance scheme. The microwave field can be reduced to 1/250 of the previous requirements, and the corresponding power is over four orders lower. Meanwhile, the microwave-induced broadening to the line-width of the spectroscopy is significantly canceled, and we achieve a nuclear-spin spectrum with a resolution down to 2.1 kHz under a magnetic field at 1840 Gs. The spectral resolution can be further improved by upgrading the experimental control precision. This scheme can also be used in sensing microwave fields and can be extended to a wide range of applications in the future.

Resource-Efficient Direct Characterization of General Density Matrix.

Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.

Noise Prediction and Reduction of Single Electron Spin by Deep-Learning-Enhanced Feedforward Control.

Noise-induced control imperfection is an important problem in applications of diamond-based nanoscale sensing, where measurement-based strategies are generally utilized to correct low-frequency noises in realtime. However, the spin-state readout requires a long time due to the low photon-detection efficiency. This inevitably introduces a delay in the noise-reduction process and limits its performance. Here we introduce the deep learning approach to relax this restriction by predicting the trend of noise and compensating for the delay. We experimentally implement feedforward quantum control of the nitrogen-vacancy center in diamond to protect its spin coherence and improve the sensing performance against noise. The new approach effectively enhances the decoherence time of the electron spin, which enables exploration of more physics from its resonant spectroscopy. A theoretical model is provided to explain the improvement. This scheme could be applied in general sensing schemes and extended to other quantum systems.

An integrated and scalable experimental system for nitrogen-vacancy ensemble magnetometry.

Nitrogen-vacancy (NV) centers in diamond are extremely promising solid-state spin quantum sensors for magnetic field in recent years. The rapid development of NV-ensemble magnetometry has put forward higher requirements for high-speed data acquisition, real-time signal processing and analyzing, etc. However, the existing commercial instruments are bulky and expensive, which brings extra complexity to the weak magnetic field detection experiment and hinders the practicality and miniaturization of NV-ensemble magnetometry. Here, we report on an integrated and scalable experimental system based on a field-programmable-gate-array (FPGA) chip assisted with high-speed peripherals for NV-ensemble magnetometry, which presents a compact and compatible design containing high-speed data acquisition, oscilloscopes, signal generator, spectrum analyzer, lock-in amplifier, proportional-integral-derivative feedback controller, etc. To verify its applicability and reliability in experiments, various applications, such as optical magnetic resonance detection, optical cavity locking, and lock-in NV magnetometry, are conducted. We further realize the pump-enhanced magnetometry based on NV center ensembles using the optical cavity. Through the flexible FPGA design approach, this self-developed device can also be conveniently extended into atomic magnetometer and other quantum systems.

Multipoint Lock-in Detection for Diamond Nitrogen-Vacancy Magnetometry Using DDS-Based Frequency-Shift Keying.

In recent years, the nitrogen-vacancy (NV) center in diamonds has been demonstrated to be a high-performance multiphysics sensor, where a lock-in amplifier (LIA) is often adopted to monitor photoluminescence changes around the resonance. It is rather complex when multiple resonant points are utilized to realize a vector or temperature-magnetic joint sensing. In this article, we present a novel scheme to realize multipoint lock-in detection with only a single-channel device. This method is based on a direct digital synthesizer (DDS) and frequency-shift keying (FSK) technique, which is capable of freely hopping frequencies with a maximum of 1.4 GHz bandwidth and encoding an unlimited number of resonant points during the sensing process. We demonstrate this method in experiments and show it would be generally useful in quantum multi-frequency excitation applications, especially in the portable and highly mobile cases.

Sensitivity-enhanced magnetometry using nitrogen-vacancy ensembles via adaptively complete transitions overlapping.

Nitrogen-vacancy (NV) centers in diamond are suitable sensors of high-sensitivity magnetometry, which have attracted much interest in recent years. Here, we demonstrate sensitivity-enhanced ensemble magnetometry via adaptively complete transitions overlapping with a bias magnetic field equally projecting onto all existing NV orientations. Under such conditions, the spin transitions corresponding to different NV orientations are completely overlapped, which will bring about an obviously improved photoluminescence contrast. We, furthermore, introduce particle swarm optimization into the calibration process, to generate this bias magnetic field automatically and adaptively using computer-controlled Helmholtz coils. By applying this technique, we realize an ∼1.5 times enhancement and obtain a magnetic field sensitivity of 855pT/Hz by utilizing a group of completely overlapped transitions, compared to the 1.33nT/Hz obtained utilizing a single transition in continuous-wave magnetometry. Our approach can be conveniently applied in direction-fixed magnetic sensing and to obtain the potentially maximum sensitivity of ensemble-NV magnetometry.

Synchronized time tagger for single-photon detection in one- and two-dimension quantum experiments.

We report a synchronized time tagger based on a field-programmable-gate-array chip for one- or two-dimensional quantum experiments that require precise single-photon detections. The time tagger has a 9.2 ps single-shot root-mean-square precision and is equipped with a 1 GB dynamic memory for data storage. Because the relationship between the control parameter and acquired data is guaranteed by using hardware synchronization, the experiment can be performed much faster than conventional schemes that are based on software synchronization. With this technique, an improvement of up to 61.3% in efficiency is observed in a typical nitrogen-vacancy center quantum experiment. We further show advanced optical features of the center using the detected high-resolution photon-arrival information and provide detailed electrical benchmarking of the device. This technique could be easily extended to other quantum control systems.

Mixed-signal data acquisition system for optically detected magnetic resonance of solid-state spins.

We report a mixed-signal data acquisition (DAQ) system for optically detected magnetic resonance (ODMR) of solid-state spins. This system is designed and implemented based on a field-programmable-gate-array chip assisted with high-speed peripherals. The ODMR experiments often require high-speed mixed-signal data acquisition and processing for general and specific tasks. To this end, we realized a mixed-signal DAQ system that can acquire both analog and digital signals with precise hardware synchronization. The system consisting of four analog channels (two inputs and two outputs) and 16 optional digital channels works at up to 125 MHz clock rate. With this system, we performed general-purpose ODMR and advanced lock-in detection experiments of nitrogen-vacancy (NV) centers, and the reported DAQ system shows excellent performance in both single and ensemble spin cases. This work provides a uniform DAQ solution for the NV center quantum control system and could be easily extended to other spin-based systems.

Calibration-Free Vector Magnetometry Using Nitrogen-Vacancy Center in Diamond Integrated with Optical Vortex Beam.

We report a new method to determine the orientation of individual nitrogen-vacancy (NV) centers in a bulk diamond and use them to realize a calibration-free vector magnetometer with nanoscale resolution. Optical vortex beam is used for optical excitation and scanning the NV center in a [111]-oriented diamond. The scanning fluorescence patterns of NV center with different orientations are completely different. Thus, the orientation information on each NV center in the lattice can be known directly without any calibration process. Further, we use three differently oriented NV centers to form a magnetometer and reconstruct the complete vector information on the magnetic field based on the optically detected magnetic resonance(ODMR) technique. Compared with previous schemes to realize vector magnetometry using an NV center, our method is much more efficient and is easily applied in other NV-based quantum sensing applications.

Experimental realization of a quantum support vector machine.

The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.

Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator.

Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.

Coherence-protected quantum gate by continuous dynamical decoupling in diamond.

In order to achieve reliable quantum-information processing results, we need to protect quantum gates along with the qubits from decoherence. Here we demonstrate experimentally on a nitrogen-vacancy system that by using a continuous-wave dynamical decoupling method, we might not only prolong the coherence time by about 20 times but also protect the quantum gates for the duration of the controlling time. This protocol shares the merits of retaining the superiority of prolonging the coherence time and at the same time easily combining with quantum logic tasks. This method can be useful in tasks where the duration of quantum controlling exceeds far beyond the dephasing time.

Quantum chemistry simulation on quantum computers: theories and experiments.

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system.

Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.

Simulation of chemical isomerization reaction dynamics on a NMR quantum simulator.

Quantum simulation can beat current classical computers with minimally a few tens of qubits. Here we report an experimental demonstration that a small nuclear-magnetic-resonance quantum simulator is already able to simulate the dynamics of a prototype laser-driven isomerization reaction using engineered quantum control pulses. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on current classical computers is feasible in the near future.

Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond.

The nitrogen-vacancy defect center (N-V center) is a promising candidate for quantum information processing due to the possibility of coherent manipulation of individual spins in the absence of the cryogenic requirement. We report a room-temperature implementation of the Deutsch-Jozsa algorithm by encoding both a qubit and an auxiliary state in the electron spin of a single N-V center. By thus exploiting the specific S=1 character of the spin system, we demonstrate how even scarce quantum resources can be used for test-bed experiments on the way towards a large-scale quantum computing architecture.

NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation.

It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (H2) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.

Quantum adiabatic algorithm for factorization and its experimental implementation.

We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in a NMR quantum information processor and experimentally factorize the number 21. In the range that our classical computer could simulate, the quantum adiabatic algorithm works well, providing evidence that the running time of this algorithm scales polynomially with the problem size.