Application of nuclear magnetic resonance (NMR) spectroscopy to nanoscale samples has remained an elusive goal, achieved only with great experimental effort at subkelvin temperatures. We demonstrated detection of NMR signals from a (5-nanometer)(3) voxel of various fluid and solid organic samples under ambient conditions. We used an atomic-size magnetic field sensor, a single nitrogen-vacancy defect center, embedded ~7 nanometers under the surface of a bulk diamond to record NMR spectra of various samples placed on the diamond surface. Its detection volume consisted of only 10(4) nuclear spins with a net magnetization of only 10(2) statistically polarized spins.

Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation. Although algorithms for error correction have been known for some time, experimental realizations are scarce. Here we show quantum error correction in a heterogeneous, solid-state spin system. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen-vacancy defect. Implementation of a novel non-local gate generic to our electron-nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon, quantum dots, silicon carbide or rare-earth ions in solids.

To exploit the quantum coherence of electron spins in solids in future technologies such as quantum computing, it is first vital to overcome the problem of spin decoherence due to their coupling to the noisy environment. Dynamical decoupling, which uses stroboscopic spin flips to give an average coupling to the environment that is effectively zero, is a particularly promising strategy for combating decoherence because it can be naturally integrated with other desired functionalities, such as quantum gates. Errors are inevitably introduced in each spin flip, so it is desirable to minimize the number of control pulses used to realize dynamical decoupling having a given level of precision. Such optimal dynamical decoupling sequences have recently been explored. The experimental realization of optimal dynamical decoupling in solid-state systems, however, remains elusive. Here we use pulsed electron paramagnetic resonance to demonstrate experimentally optimal dynamical decoupling for preserving electron spin coherence in irradiated malonic acid crystals at temperatures from 50 K to room temperature. Using a seven-pulse optimal dynamical decoupling sequence, we prolonged the spin coherence time to about 30 mus; it would otherwise be about 0.04 mus without control or 6.2 mus under one-pulse control. By comparing experiments with microscopic theories, we have identified the relevant electron spin decoherence mechanisms in the solid. Optimal dynamical decoupling may be applied to other solid-state systems, such as diamonds with nitrogen-vacancy centres, and so lay the foundation for quantum coherence control of spins in solids at room temperature.

Nuclear magnetic resonance spectroscopy and magnetic resonance imaging at the ultimate sensitivity limit of single molecules or single nuclear spins requires fundamentally new detection strategies. The strong coupling regime, when interaction between sensor and sample spins dominates all other interactions, is one such strategy. In this regime, classically forbidden detection of completely unpolarized nuclei is allowed, going beyond statistical fluctuations in magnetization. Here we realize strong coupling between an atomic (nitrogen–vacancy) sensor and sample nuclei to perform nuclear magnetic resonance on four 29Si spins. We exploit the field gradient created by the diamond atomic sensor, in concert with compressed sensing, to realize imaging protocols, enabling individual nuclei to be located with Angstrom precision. The achieved signal-to-noise ratio under ambient conditions allows single nuclear spin sensitivity to be achieved within seconds.

Magnetic resonance is essential in revealing the structure and dynamics of biomolecules. However, measuring the magnetic resonance spectrum of single biomolecules has remained an elusive goal. We demonstrate the detection of the electron spin resonance signal from a single spin-labeled protein under ambient conditions. As a sensor, we use a single nitrogen vacancy center in bulk diamond in close proximity to the protein. We measure the orientation of the spin label at the protein and detect the impact of protein motion on the spin label dynamics. In addition, we coherently drive the spin at the protein, which is a prerequisite for studies involving polarization of nuclear spins of the protein or detailed structure analysis of the protein itself.

A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time (PT ) symmetry can still display entirely real spectra [1]. The Hermiticity requirement may be replaced by PT symmetry to develop an alternative formulation of quantum mechanics [2, 3]. A series of experiments have been carried out with classical systems including optics [4], electronics [5][6][7], microwaves[8], mechanics [9] and acoustics [10][11][12]. However, there are few experiments to investigate PT symmetric physics in quantum systems. Here we report the first observation of the PT symmetry breaking in a single spin system. We have developed a novel method to dilate a general PT symmetric Hamiltonian into a Hermitian one, which can be realized in a practical quantum system. Then the state evolutions under PT symmetric Hamiltonians, which range from PT symmetric unbroken to broken regions, have been experimentally observed with a single nitrogen-vacancy (NV) center in diamond. Due to the universality of the dilation method, our result opens a door for further exploiting and understanding the physical properties of PT symmetric Hamiltonian in quantum systems. arXiv:1812.05226v1 [quant-ph]

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.

After the pioneering works by van der Waals [15,16], Mayer [17,18], and von Hove [19], it had been known that different phases (e.g., liquid and gas phases) of a thermodynamic system have the same microscopic interactions but the free energy of the system encounters a singularity (non-analytic) point in the physical parameter space where the phase transition occurs. A rigorous relation between the analytic properties of free energies and thermodynamics (in particular, phase transitions) was established by Lee Here we report on experimental observation of Lee-Yang zeros via central spin decoherence measurement, using liquid-state nuclear magnetic resonance (NMR) of trimethylphosphite (TMP) molecules (Fig. 1a) nuclear spins under a magnetic field 9.4 Tesla, respectively. The coupling to the 1 H nuclear spins splits the NMR resonance of the 31 P nuclear spin into 10 peaks corresponding to the 10 quantized polarizations of the 9 1 H spins (Fig. 1b). Note that the microscopic Hamiltonian above is of the anti-ferromagnetic Heisenberg type instead of the ferromagnetic Ising type and the magnetic field was strong. To facilitate observation of the Lee-Yang zeros on the unit circle, we used the quantum simulation method to prepare ensembles of the bath that are described by the effective density matrix (see The probe spin coherence, except for the normalization factor   Thus we not only directly observed the Lee-Yang zeros in experiments for the first time, which conceptually completes the analytic description of statistical physicsand thermodynamics, but also demonstrated the feasibility of using probe spin coherence to determine the thermodynamic properties of the baths and more generally, to access thermodynamics on the complex plane of physical parameters [14]. METHODS SUMMARYThe sample was a 1:1 by volume solution of trimethylphosphite (TMP) and acetone-d 6 in a 5-mm NMR tube. All NMR experiments were performed on a Bruker Avance III 400 MHz (9.4 T) spectrometer at room temperature. The 2  hard pulse length was approximately 13 μsec on the hydrogen channel and 17 μsec on the phosphor channel.The measured longitudinal and transverse relaxation times were respectively 1 5.6 T  sec and