Coherent control of two nuclear spins using the anisotropic hyperfine interaction

Design of pure heterodinuclear lanthanoid cryptate complexes

Heterolanthanide complexes are difficult to synthesize owing to the similar chemistry of the lanthanide ions. Consequently, very few purely heterolanthanide complexes have been synthesized. This is despite the fact that such complexes hold interesting optical and magnetic properties. To fine-tune these properties, it is important that one can choose complexes with any given combination of lanthanides. Herein we report a synthetic procedure which yields pure heterodinuclear lanthanide cryptates LnLn*LX3 (X = NO3 - or OTf-) based on the cryptand H3L = N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). In the synthesis the choice of counter ion and solvent proves crucial in controlling the Ln-Ln* composition. Choosing the optimal solvent and counter ion afford pure heterodinuclear complexes with any given combination of Gd(iii)-Lu(iii) including Y(iii). To demonstrate the versatility of the synthesis all dinuclear combinations of Y(iii), Gd(iii), Yb(iii) and Lu(iii) were synthesized resulting in 10 novel complexes of the form LnLn*L(OTf)3 with LnLn* = YbGd 1, YbY 2, YbLu 3, YbYb 4, LuGd 5, LuY 6, LuLu 7, YGd 8, YY 9 and GdGd 10. Through the use of 1H, 13C NMR and mass spectrometry the heterodinuclear nature of YbGd, YbY, YbLu, LuGd, LuY and YGd was confirmed. Crystal structures of LnLn*L(NO3)3 reveal short Ln-Ln distances of ∼3.5 Å. Using SQUID magnetometry the exchange coupling between the lanthanide ions was found to be anti-ferromagnetic for GdGd and YbYb while ferromagnetic for YbGd.

Efficient Implementation of a Quantum Algorithm in a Single Nitrogen-Vacancy Center of Diamond

Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover's quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.

Efficient Quantum Gates for Individual Nuclear Spin Qubits by Indirect Control

Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.

Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy

In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses.

Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit

We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio frequency pulses. Moreover, the multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.

A two-qubit molecular architecture for electron-mediated nuclear quantum simulation

A molecular architecture where two vanadyl-based qubits are linked together is herein described and investigated as a platform for quantum simulation.

A switchable interaction between pairs of highly coherent qubits is a crucial ingredient for the physical realization of quantum information processing. One promising route to enable quantum logic operations involves the use of nuclear spins as protected elementary units of information, qubits. Here we propose a simple way to use fast electronic spin excitations to switch the effective interaction between nuclear spin qubits and the realization of a two-qubit molecular architecture based on highly coherent vanadyl moieties to implement quantum logic operations. Controlled generation of entanglement between qubits is possible here through chemically tuned magnetic coupling between electronic spins, which is clearly evidenced by the splitting of the vanadium(iv) hyperfine lines in the continuous-wave electron paramagnetic resonance spectrum. The system has been further characterized by pulsed electron paramagnetic resonance spectroscopy, evidencing remarkably long coherence times. The experimentally derived spin Hamiltonian parameters have been used to simulate the system dynamics under the sequence of pulses required to implement quantum gates in a realistic description that includes also the harmful effect of decoherence. This demonstrates the possibility of using this molecular complex to implement a control-Z (CZ) gate and simple quantum simulations. Indeed, we also propose a proof-of-principle experiment based on the simulation of the quantum tunneling of the magnetization in a S = 1 spin system.

Ultra-broadband coplanar waveguide for optically detected magnetic resonance of nitrogen-vacancy centers in diamond

We report on coplanar waveguides (CPWs) designed for optically detected magnetic resonance of nitrogen-vacancy (NV) centers in diamonds. A broad band up to 15.8 GHz has been realized, which ensures that the electron spins can be manipulated under external magnetic fields up to 5000 G. The conversion factor of CPW has been measured by Rabi nutation experiments, which ranges from 6.64 G W^-1/2 to 10.60 G W^-1/2 in the frequency band from 0.76 GHz to 17.3 GHz. Broadband CPWs also provide high quality control pulses due to the minimization of the distortion. These characteristics will find potential applications in NV-based quantum information processing and single spin magnetometry.

Controlling Qubit Networks in Polynomial Time

Future quantum devices often rely on favorable scaling with respect to the number of system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in a time that scales at most polynomial in the number of qubits. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. Based on the developed upper bound, the set of gates is characterized that can be implemented polynomially in time. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally, a system is identified for which the gate set can be implemented with fewer controls.

NMRCloudQ: a quantum cloud experience on a nuclear magnetic resonance quantum computer

Cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms has followed up yet. Here, we report our new cloud quantum computing service - NMRCloudQ (http://nmrcloudq.com/zh-hans/), where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. In our current version, four qubits are already usable with in average 99.10% single-qubit gate fidelity and 97.15% two-qubit fidelity via randomized benchmaking tests. Improved control precisions as well as a new seven-qubit processor are also in preparation and will be available later.

Structural Determination of a DNA Oligomer for a Molecular Spin Qubit Lloyd Model of Quantum Computers

The global molecular and local spin-site structures of a DNA duplex 22-oligomer with site-directed four spin-labeling were simulated by molecular mechanics (MM) calculations combined with Q-band pulsed electron-electron double resonance (PELDOR) spectroscopy. This molecular-spin bearing DNA oligomer is designed to give a complex testing ground for the structural determination of molecular spins incorporated in the DNA duplex, which serves as a platform for 1D periodic arrays of two or three non-equivalent electron spin qubit systems, (AB)n or (ABC)n, respectively, enabling to execute quantum computing or quantum information processing (Lloyd model of electron spin versions): A, B and C designate non-equivalent addressable spin qubits for quantum operations. The non-equivalence originates in difference in the electronic g-tensor. It is not feasible to determine the optimal structures for such DNA oligomers having molecular flexibility only by the MM calculations because there are many local minima in energy for their possible molecular structures. The spin-distance information derived from the PELDOR spectroscopy helps determine the optimal structures out of the possible ones acquired by the MM calculations. Based on the MM searched structures, we suggest the optimal structures for semi-macromolecules having site-directed multi-spin qubits. We emphasize that for our four molecular spins embedded in the DNA oligomer the Fajer’s error analysis in PELDOR-based distance measurements was of essential importance.

Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., T_{2}^{*} processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.

Randomized benchmarking of quantum gates implemented by electron spin resonance

Spin systems controlled and probed by magnetic resonance have been valuable for testing the ideas of quantum control and quantum error correction. This paper introduces an X-band pulsed electron spin resonance spectrometer designed for high-fidelity coherent control of electron spins, including a loop-gap resonator for sub-millimeter sized samples with a control bandwidth ∼40MHz. Universal control is achieved by a single-sideband upconversion technique with an I-Q modulator and a 1.2GS/s arbitrary waveform generator. A single qubit randomized benchmarking protocol quantifies the average errors of Clifford gates implemented by simple Gaussian pulses, using a sample of gamma-irradiated quartz. Improvements in unitary gate fidelity are achieved through phase transient correction and hardware optimization. A preparation pulse sequence that selects spin packets in a narrowed distribution of static fields confirms that inhomogeneous dephasing (1/T2(∗)) is the dominant source of gate error. The best average fidelity over the Clifford gates obtained here is 99.2%, which serves as a benchmark to compare with other technologies.

Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions

Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the spin-qubits in solids with the accuracy required by fault-tolerant quantum computation under ambient conditions remains elusive. Here, we quantitatively characterize the source of noise during quantum gate operation and demonstrate strategies to suppress the effect of these. A universal set of logic gates in a nitrogen-vacancy centre in diamond are reported with an average single-qubit gate fidelity of 0.999952 and two-qubit gate fidelity of 0.992. These high control fidelities have been achieved at room temperature in naturally abundant ¹³C diamond via composite pulses and an optimized control method.

High fidelity manipulation of diamond-based spin qubits is difficult at room temperature because of decoherence. Here, the authors show a universal set of logic gates in nitrogen-vacancy centres with average single-qubit and two-qubit gate fidelities of 0.999952 and 0.992, respectively.

Highly selective detection of individual nuclear spins with rotary echo on an electron spin probe

We consider an electronic spin, such as a nitrogen-vacancy center in diamond, weakly coupled to a large number of nuclear spins, and subjected to the Rabi driving with a periodically alternating phase. We show that by switching the driving phase synchronously with the precession of a given nuclear spin, the interaction to this spin is selectively enhanced, while the rest of the bath remains decoupled. The enhancement is of resonant character. The key feature of the suggested scheme is that the width of the resonance is adjustable, and can be greatly decreased by increasing the driving strength. Thus, the resonance can be significantly narrowed, by a factor of 10–100 in comparison with the existing detection methods. Significant improvement in selectivity is explained analytically and confirmed by direct numerical many-spin simulations. The method can be applied to a wide range of solid-state systems.

Highly confined guiding of low-loss plasmon waves in hybrid metal-dielectric slot waveguides

We report the observation of strongly confined plasmon modes in hybridized metal-dielectric slot waveguides, which consist of semiconductor-insulator-semiconductor nanostructures embedded inside the low-index gaps of conventional hybrid plasmonic configurations. Owing to the combined effects induced by the high-refractive-index-contrast dielectric slot and semiconductor-insulator-metal configurations, tight field localization (Aeff ~ λ(2)/1250-λ(2)/55) in conjunction with large propagation distances (L ~ 70-180 μm) can be realized simultaneously at telecommunication wavelength. Through comprehensive numerical simulations, the characteristics of the fundamental hybrid modes are revealed in detail by optimizing key structural parameters of the waveguides. The advantages over their traditional hybrid waveguiding counterparts are unraveled. In addition, the possibilities of extending our current design into other metal/dielectric composites are also discussed. Our studies regarding hybrid metal-dielectric slot structures and their alternatives in this paper are expected to provide effective approaches for the enhancement of traditional hybrid modes' properties and open up new opportunities for the constructions of high-performance plasmon waveguides and devices.

Universal control and error correction in multi-qubit spin registers in diamond

Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing. Pioneering experiments selected defects with favourably located nuclear spins with particularly strong hyperfine couplings. To progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here, we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single- and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes.

Protected quantum computing: interleaving gate operations with dynamical decoupling sequences

Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.

DAC-board based X-band EPR spectrometer with arbitrary waveform control

We present arbitrary control over a homogenous spin system, demonstrated on a simple, home-built, electron paramagnetic resonance (EPR) spectrometer operating at 8-10 GHz (X-band) and controlled by a 1 GHz arbitrary waveform generator (AWG) with 42 dB (i.e. 14-bit) of dynamic range. Such a spectrometer can be relatively easily built from a single DAC (digital to analog converter) board with a modest number of stock components and offers powerful capabilities for automated digital calibration and correction routines that allow it to generate shaped X-band pulses with precise amplitude and phase control. It can precisely tailor the excitation profiles "seen" by the spins in the microwave resonator, based on feedback calibration with experimental input. We demonstrate the capability to generate a variety of pulse shapes, including rectangular, triangular, Gaussian, sinc, and adiabatic rapid passage waveforms. We then show how one can precisely compensate for the distortion and broadening caused by transmission into the microwave cavity in order to optimize corrected waveforms that are distinctly different from the initial, uncorrected waveforms. Specifically, we exploit a narrow EPR signal whose width is finer than the features of any distortions in order to map out the response to a short pulse, which, in turn, yields the precise transfer function of the spectrometer system. This transfer function is found to be consistent for all pulse shapes in the linear response regime. In addition to allowing precise waveform shaping capabilities, the spectrometer presented here offers complete digital control and calibration of the spectrometer that allows one to phase cycle the pulse phase with 0.007° resolution and to specify the inter-pulse delays and pulse durations to ≤ 250 ps resolution. The implications and potential applications of these capabilities will be discussed.

Adiabatic and fast passage ultra-wideband inversion in pulsed EPR

We demonstrate that adiabatic and fast passage ultra-wideband (UWB) pulses can achieve inversion over several hundreds of MHz and thus enhance the measurement sensitivity, as shown by two selected experiments. Technically, frequency-swept pulses are generated by a 12 GS/s arbitrary waveform generator and upconverted to X-band frequencies. This pulsed UWB source is utilized as an incoherent channel in an ordinary pulsed EPR spectrometer. We discuss experimental methodologies and modeling techniques to account for the response of the resonator, which can strongly limit the excitation bandwidth of the entire non-linear excitation chain. Aided by these procedures, pulses compensated for bandwidth or variations in group delay reveal enhanced inversion efficiency. The degree of bandwidth compensation is shown to depend critically on the time available for excitation. As a result, we demonstrate optimized inversion recovery and double electron electron resonance (DEER) experiments. First, virtually complete inversion of the nitroxide spectrum with an adiabatic pulse of 128ns length is achieved. Consequently, spectral diffusion between inverted and non-inverted spins is largely suppressed and the observation bandwidth can be increased to increase measurement sensitivity. Second, DEER is performed on a terpyridine-based copper (II) complex with a nitroxide-copper distance of 2.5nm. As previously demonstrated on this complex, when pumping copper spins and observing nitroxide spins, the modulation depth is severely limited by the excitation bandwidth of the pump pulse. By using fast passage UWB pulses with a maximum length of 64ns, we achieve up to threefold enhancement of the modulation depth. Associated artifacts in distance distributions when increasing the bandwidth of the pump pulse are shown to be small.

Bandwidth-limited control and ringdown suppression in high-Q resonators

We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.

Controlling and exploiting phases in multi-spin systems using electron spin resonance and nuclear magnetic resonance

The phase of a superposition state is a quintessential characteristic that differentiates a quantum bit of information from a classical one. This phase can be manipulated dynamically or geometrically, and can be exploited to sensitively estimate Hamiltonian parameters, perform faithful quantum state tomography and encode quantum information into multiple modes of an ensemble. Here we discuss the methods that we have employed to manipulate and exploit the phase information of single-, two-, multi-qubit and multi-mode spin systems.