Amplitude noise, which inflicts a random two-qubit term, is one of the main obstacles preventing the implementation of a high-fidelity two-body gate below the fault-tolerance threshold. This noise is difficult to refocus as any refocusing technique could only tackle noise with frequency below the operation rate. Since the two-qubit-gate speed is normally the slowest rate in the system, it constitutes the last bottleneck toward an implementation of a gate below the fault-tolerant threshold. Here we propose to use composite pulses as a dynamical decoupling approach in order to reduce two-qubit-gate noise for trapped-ion systems. This is done by refocusing the building blocks of ultrafast entangling gates, where the amplitude noise is reduced to shot-to-shot noise. We present detailed simulations showing that the fault-tolerance threshold could be achieved using the proposed approach.

Dynamic nuclear polarization (DNP) of molecules in a solution at room temperature has the potential to revolutionize nuclear magnetic resonance spectroscopy and imaging. The prevalent methods for achieving DNP in solutions are typically most effective in the regime of small interaction correlation times between the electron and nuclear spins, limiting the size of accessible molecules. To solve this limitation, we design a mechanism for DNP in the liquid phase that is applicable for large interaction correlation times. Importantly, while this mechanism makes use of a resonance condition similar to solid-state DNP, the polarization transfer is robust to a relatively large detuning from the resonance due to molecular motion. We combine this scheme with optically polarized nitrogen-vacancy (NV) center spins in nanodiamonds to design a setup that employs optical pumping and is therefore not limited by room temperature electron thermal polarization. We illustrate numerically the effectiveness of the model in a flow cell containing nanodiamonds immobilized in a hydrogel, polarizing flowing water molecules 4700-fold above thermal polarization in a magnetic field of 0.35 T, in volumes detectable by current NMR scanners

We study the nonequilibrium dynamics of the linear-to-zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap, and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.

The sensitivity of magnetic resonance imaging (MRI) depends strongly on nuclear spin polarisation and, motivated by this observation, dynamical nuclear spin polarisation has recently been applied to enhance MRI protocols (Kurhanewicz et al 2011 Neoplasia 13 81). Nuclear spins associated with the ¹³C carbon isotope (nuclear spin I = 1/2) in diamond possess uniquely long spin lattice relaxation times (Reynhardt and High 2011 Prog. Nucl. Magn. Reson. Spectrosc. 38 37). If they are present in diamond nanocrystals, especially when strongly polarised, they form a promising contrast agent for MRI. Current schemes for achieving nuclear polarisation, however, require cryogenic temperatures. Here we demonstrate an efficient scheme that realises optically induced ¹³C nuclear spin hyperpolarisation in diamond at room temperature and low ambient magnetic field. Optical pumping of a nitrogen-vacancy centre creates a continuously renewable electron spin polarisation which can be transferred to surrounding ¹³C nuclear spins. Importantly for future applications we also realise polarisation protocols that are robust against an unknown misalignment between magnetic field and crystal axis.

Dynamical nuclear polarization holds the key for orders of magnitude enhancements of nuclear magnetic resonance signals which, in turn, would enable a wide range of novel applications in biomedical sciences. However, current implementations of DNP require cryogenic temperatures and long times for achieving high polarization. Here we propose and analyze in detail protocols that can achieve rapid hyperpolarization of 13C nuclear spins in randomly oriented ensembles of nanodiamonds at room temperature. Our protocols exploit a combination of optical polarization of electron spins in nitrogen-vacancy centers and the transfer of this polarization to 13C nuclei by means of microwave control to overcome the severe challenges that are posed by the random orientation of the nanodiamonds and their nitrogen-vacancy centers. Specifically, these random orientations result in exceedingly large energy variations of the electron spin levels that render the polarization and coherent control of the nitrogen-vacancy center electron spins as well as the control of their coherent interaction with the surrounding 13C nuclear spins highly inefficient. We address these challenges by a combination of an off-resonant microwave double resonance scheme in conjunction with a realization of the integrated solid effect which, together with adiabatic rotations of external magnetic fields or rotations of nanodiamonds, leads to a protocol that achieves high levels of hyperpolarization of the entire nuclear-spin bath in a randomly oriented ensemble of nanodiamonds even at room temperature. This hyperpolarization together with the long nuclear-spin polarization lifetimes in nanodiamonds and the relatively high density of 13C nuclei has the potential to result in a major signal enhancement in 13C nuclear magnetic resonance imaging and suggests functionalized and hyperpolarized nanodiamonds as a unique probe for molecular imaging both in vitro and in vivo.

When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error correction, in which the signal is generated by a two qubit Hamiltonian term. This two-qubit term is provided by the dynamics of a tunable coupler between two transmon qubits. For fast enough correction, it is possible to lengthen the coherence time of the device beyond the relaxation limit.

A fundamental goal of quantum technologies concerns the exploitation of quantum coherent dynamics for the realization of novel quantum applications such as quantum computing, quantum simulation, and quantum metrology. A key challenge on the way towards these goals remains the protection of quantum coherent dynamics from environmental noise. Here, we propose a concept of a hybrid dressed state from a pair of continuously driven systems. It allows sufficiently strong driving fields to suppress the effect of environmental noise while at the same time being insusceptible to both the amplitude and phase noise in the continuous driving fields. This combination of robust features significantly enhances coherence times under realistic conditions and at the same time provides new flexibility in Hamiltonian engineering that otherwise is not achievable. We demonstrate theoretically applications of our scheme for a noise-resistant analog quantum simulation in the well-studied physical systems of nitrogen-vacancy centers in diamond and of trapped ions. The scheme may also be exploited for quantum computation and quantum metrology.

We propose to experimentally explore the Haldane phase in spin-one XXZ antiferromagnetic chains using trapped ions. We show how to adiabatically prepare the ground states of the Haldane phase, demonstrate their robustness against sources of experimental noise, and propose ways to detect the Haldane ground states based on their excitation gap and exponentially decaying correlations, nonvanishing nonlocal string order, and doubly degenerate entanglement spectrum.

The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (“qutrits”) with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.

We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.

We construct Lindbladians associated with controlled stochastic Hamiltonians in the weak coupling regime. This construction allows us to determine the power spectrum of the noise from measurements of dephasing rates. Moreover, by studying the derived equation it is possible to optimize the control as well as to test numerical algorithms that solve controlled stochastic Schrödinger equations. A few examples are worked out in detail.

A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.

We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed nonadiabatically. For a second order phase transition, the Kibble–Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.

Interferometry with massive particles may have the potential to explore the limitations of standard quantum mechanics, in particular where it concerns its boundary with general relativity and the yet to be developed theory of quantum gravity. This development is hindered considerably by the lack of experimental evidence and testable predictions. Analyzing effects that appear to be common to many of such theories, such as a modification of the energy dispersion and of the canonical commutation relation within the standard framework of quantum mechanics, has been proposed as a possible way forward. Here we analyze in some detail the impact of a modified energy-momentum dispersion in a Ramsey-Bordé setup and provide achievable bounds of these correcting terms when operating such an interferometer with nanodiamonds. Thus, taking thermal and gravitational disturbances into account will show that without specific prerequisites, quantum gravity modifications may in general be suppressed requiring a revision of previously estimated bounds. As a possible solution we propose a stable setup which is rather insensitive to these effects. Finally, we address the problems of decoherence and pulse errors in such setups and discuss the scalings and advantages with increasing particle mass.

The realization of scalable arrangements of nitrogen vacancy (NV) centers in diamond remains a key challenge on the way towards efficient quantum information processing, quantum simulation and quantum sensing applications. Although technologies based on implanting NV-centers in bulk diamond crystals or hybrid device approaches have been developed, they are limited by the achievable spatial resolution and by the intricate technological complexities involved in achieving scalability. We propose and demonstrate a novel approach for creating an arrangement of NV-centers, based on the self-assembling capabilities of biological systems and their beneficial nanometer spatial resolution. Here, a self-assembled protein structure serves as a structural scaffold for surface functionalized nanodiamonds, in this way allowing for the controlled creation of NV-structures on the nanoscale and providing a new avenue towards bridging the bio–nano interface. One-, two- as well as three-dimensional structures are within the scope of biological structural assembling techniques. We realized experimentally the formation of regular structures by interconnecting nanodiamonds using biological protein scaffolds. Based on the achievable NV-center distances of 11 nm, we evaluate the expected dipolar coupling interaction with neighboring NV-centers as well as the expected decoherence time. Moreover, by exploiting these couplings, we provide a detailed theoretical analysis on the viability of multiqubit quantum operations, suggest the possibility of individual addressing based on the random distribution of the NV intrinsic symmetry axes and address the challenges posed by decoherence and imperfect couplings. We then demonstrate in the last part that our scheme allows for the high-fidelity creation of entanglement, cluster states and quantum simulation applications.

We propose an all-optical scheme to prolong the quantum coherence of a negatively charged nitrogen-vacancy (NV) center in diamond at cryogenic temperatures. Optical control of the NV spin suppresses energy fluctuations of the  ground states and forms an energy gap protected subspace. By optical control, the spectral linewidth of magnetic resonance is much narrower and the measurement of the frequencies of magnetic field sources has higher resolution. The optical control also improves the sensitivity of the magnetic field detection and can provide measurement of the directions of signal sources.

Laser-cooled and trapped ions can crystallize and feature discrete solitons that are nonlinear, topologically protected configurations of the Coulomb crystal. Such solitons, as their continuum counterparts, can move within the crystal, while their discreteness leads to the existence of a gap-separated, spatially localized motional mode of oscillation above the spectrum. Suggesting that these unique properties of discrete solitons can be used for generating entanglement between different sites of the crystal, we study a detailed proposal in the context of state-of-the-art experimental techniques. We analyze the interaction of periodically driven planar ion crystals with optical forces, revealing the effects of micromotion in radio-frequency traps inherent to such structures, as opposed to linear ion chains. The proposed method requires Doppler cooling of the crystal and sideband cooling of the soliton’s localized modes alone. Since the gap separation of the latter is nearly independent of the crystal size, this approach could be particularly useful for producing entanglement and studying system-environment interactions in large, two- and possibly three-dimensional systems.

The signal to noise ratio of quantum sensing protocols scales with the square root of the coherence time. Thus, increasing this time is a key goal in the field. By utilizing quantum error correction, we present a novel way of prolonging such coherence times beyond the fundamental limits of current techniques. We develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. We examine the use of entangled versue untangled states, and error correction’s reach of the Heisenberg limit. The effects of error correction on coherence times are calculated and we show that measurement precision can be enhanced for both one-directional and general noise.

A proposal to use trapped ions to implement spin-one XXZ antiferromagnetic chains as an experimental tool to explore the Haldane phase is presented. We explain how to reach the Haldane phase adiabatically, demonstrate the robustness of the ground states to noise in the magnetic field and Rabi frequencies, and propose a way to detect them using their characteristics: an excitation gap and exponentially decaying correlations, a nonvanishing nonlocal string order, and a double degenerate entanglement spectrum. Scaling up to higher dimensions and more frustrated lattices, we obtain richer phase diagrams, and we can reach spin liquid phase, which can be detected by its entanglement entropy which obeys the boundary law.