As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable.
As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin hyperfine interaction with electron magnetic moment of basic atom and dipole-dipole interaction with nuclear moments of neighboring impurity atoms was considered, It was made estimations of allowed concentrations of magnetic impurities and of spin temperature whereby the required decoherence suppression is obtained. Semiclassical decoherence model of two qubit entangled states is also presented.
As another variant of the solid-state ensemble quantum computer, the gateless architecture of cellular-automaton with antiferromagnetically ordered electron spins is also discussed here.
A quantum information processing device, based on bulk solid state NMR of the quasi-one dimensional material hydroxyapatite, is proposed following the magnetic resonance force microscopy work of Yamamoto et al (quant-ph/0009122). In a macroscopic sample of hydroxyapatite, our solid state NMR model yields a limit of 10^8 qubits imposed by physics, while development of current technological considerations should allow an upper bound in the range of hundreds to thousands of qubits.
A dipolar recoupling technique is introduced as a new approach to quantum gate operation in solid-state NMR under magic angle spinning. The default-off property of inter-qubit interaction provides a simple way to controlled operation without requiring elaborate qubit-decoupling pulses.
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation …
Here we made an analysis of the principles of a semiconductor NMR quantum computer and its developments. The known variant of an individual-access computer (B. Kane) and alternative solid-state bulk-ensemble approach versions allowing to avoid some difficulties in implementing the first variant are considered.
A connection of the Wigner-Yanase skew information and multiple quantum (MQ) NMR coherences is considered at different temperatures and evolution times of nuclear spins with dipole-dipole interactions in MQ NMR experiments in solids. It is shown that the Wigner-Yanase skew information at temperature $T$ is equal to the double second moment of the MQ NMR spectrum at the double temperature for any evolution times. A comparison of the many-spin entanglement obtained with the Wigner-Yanase information and the Fisher information is conducted.
A scheme for decoupling and selectively recoupling large networks of dipolar-coupled spins is proposed. The scheme relies on a combination of broadband, decoupling pulse sequences applied to all the nuclear spins with a band-selective pulse sequence for single spin rotations or recoupling. The evolution-time overhead required for selective coupling is independent of the number of spins, subject to time-scale constraints, for which we discuss the feasibility. This scheme may improve the scalability of solid-state-NMR quantum computing architectures.
A three-qubit 13C solid-state nuclear magnetic resonance (NMR) system for quantum information processing, based on the malonic acid molecule, is used to demonstrate high-fidelity universal quantum control via strongly-modulating radio-frequency pulses. This control is achieved in the strong-coupling regime, in which the timescales of selective qubit addressing and of two-qubit interactions are comparable.
A phenomenological theory of spin-lattice relaxation of multiple-quantum coherences in systems of two dipolar coupled spins at low temperatures is developed. Intensities of multiple-quantum NMR coherences depending on the spin-lattice relaxation time are obtained. It is shown that the theory is also applicable to finite spin chains when the approximation of nearest neighbour interaction is used. An application of this theory to an estimation of the influence of decoherence processes on quantum entanglement and its fluctuations is briefly discussed.
The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state NMR spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fi…
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum error correction is very well understood, experimental implementation has been lagging. We study the feasibility of implementing repeated rounds of quantum error correction with refreshed ancillas in solid state nuclear magnetic resonance (NMR). In particular we study the procedure proposed for extracting entropy that consists of two stages; an error correct…
In this work we experimentally study the efficiency of various dynamical decoupling sequences for suppressing decoherence of single as well as multiple quantum coherences on large spin-clusters. The system involves crystallites of a powdered sample containing a large number of molecular protons interacting via long-range dipole-dipole interaction. The multiple quantum coherences are prepared by progressively creating correlations in the spin lattice using standard pulse sequences implementing two-quantum average Hamiltonian. The spin system is then subjected to various dynamical decoupling seq…
We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid $^{129}Xe$ and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addressable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual…
Application of multiple rounds of Quantum Error Correction (QEC) is an essential milestone towards the construction of scalable quantum information processing devices. However, experimental realizations of it are still in their infancy. The requirements for multiple round QEC are high control fidelity and the ability to extract entropy from ancilla qubits. Nuclear Magnetic Resonance (NMR) based quantum devices have demonstrated high control fidelity with up to 12 qubits. On the other hand, the major challenge in the NMR QEC experiment is to efficiently supply ancilla qubits in highly pure stat…
We present a framework that uses a continuous frequency space to describe and design solid-state NMR experiments. The approach is similar to the well established Floquet treatment for NMR, but is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back…
We demonstrate a synchronized readout (SR) technique for spectrally selective detection of oscillating magnetic fields with sub-millihertz resolution, using coherent manipulation of solid state spins. The SR technique is implemented in a sensitive magnetometer (~50 picotesla/Hz^(1/2)) based on nitrogen vacancy (NV) centers in diamond, and used to detect nuclear magnetic resonance (NMR) signals from liquid-state samples. We obtain NMR spectral resolution ~3 Hz, which is nearly two orders of magnitude narrower than previously demonstrated with NV based techniques, using a sample volume of ~1 pic…
We report an observation of extremely long-lived spin states in systems of dipolar-coupled nuclear spins in solids. The 'suspended echo' experiment uses a simple stimulated echo pulse sequence and creates non-equilibrium states which live many orders of magnitude longer than the characteristic time of spin-spin dynamics T2. Large amounts of information can be encoded in such long-lived states, stored in a form of multi-spin correlations, and subsequently retrieved by an application of a single 'reading' pulse.
We theoretically investigate thermalization and spin diffusion driven by a quantum spin bath for a realistic solid-state NMR experiment. We consider polycrystalline L-alanine, and investigate how the spin polarization spreads among several $^{13}$C nuclear spins, which interact via dipole-dipole coupling with the bath of strongly dipolar-coupled $^1$H nuclear (proton) spins. We do this by using direct numerical simulation of the many-spin time-dependent Schrödinger equation. We find that, although the proton spins located near the carbon sites interact most strongly with the $^{13}$C spins, th…
This paper describes recent progress using nuclear magnetic resonance (NMR) as a platform for implementing quantum information processing (QIP) tasks. The basic ideas of NMR QIP are detailed, examining the successes and limitations of liquid and solid state experiments. Finally, a future direction for implementing quantum processors is suggested,utilizing both nuclear and electron spin degrees of freedom.
The free-induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spins ones coincide if there are many quite equivalent nearest neighbors V in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the…
The response of a quadrupolar nucleus (nuclear spin with I>1/2) to an oscillating radio-frequency (RF) pulse/field is delicately dependent on the ratio of the quadrupolar coupling constant to the amplitude of the pulse in addition to its duration and oscillating frequency. Consequently, analytic description of the excitation process in the density operator formalism has remained less transparent within existing theoretical frameworks. As an alternative, the utility of the "concept of effective Floquet Hamiltonians" is explored in the present study to explicate the nuances of the excitation pro…
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the techniques available for control are described along with the various implementations of quantum algorithms and quantum simulations that have been performed using NMR. The recent application of NMR control techniques to other quantum computing systems are reviewed before concluding with a description of the efforts currently underway to transition to solid st…
We demonstrate that Fokker-Planck equations in which spatial coordinates are treated on the same conceptual level as spin coordinates yield a convenient formalism for treating magic angle spinning NMR experiments. In particular, time dependence disappears from the background Hamiltonian (sample spinning is treated as an interaction), spherical quadrature grids are avoided completely (coordinate distributions are a part of the formalism) and relaxation theory with any linear diffusion operator is easily adopted from the Stochastic Liouville Equation theory. The proposed formalism contains Floqu…
We experimentally demonstrate quantum machine learning using NMR based on a framework of quantum reservoir computing. Reservoir computing is for exploiting natural nonlinear dynamics with large degrees of freedom, which is called a reservoir, for a machine learning purpose. Here we propose a concrete physical implementation of a quantum reservoir using controllable dynamics of a nuclear spin ensemble in a molecular solid. In this implementation, we demonstrate learning of nonlinear functions with binary or continuous variable inputs with low mean squared errors. Our implementation and demonstr…
Quantum computing exploits fundamentally new models of computation based on quantum mechanical properties instead of classical physics, and it is believed that quantum computers are able to dramatically improve computational power for particular tasks. At present, nuclear magnetic resonance (NMR) has been one of the most successful platforms amongst all current implementations. It has demonstrated universal controls on the largest number of qubits, and many advanced techniques developed in NMR have been adopted to other quantum systems successfully. In this review, we show how NMR quantum proc…
We propose a scheme for generating squeezed states in solid state circuits consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair box (CPB) and a superconducting transmission line resonator (STLR). The nonlinear interaction between the NMR and the STLR can be implemented by setting the external biased flux of the CPB at certain values. The interaction Hamiltonian between the NMR and the STLR is derived by performing Fr$\rm\ddot o$hlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the sta…
Nuclear magnetic resonance offers an appealing prospect for implementation of quantum computers, because of the long coherence times associated with nuclear spins, and extensive laboratory experience in manipulating the spins with radio frequency pulses. Existing proposals, however, suffer from a signal-to-noise ratio that decays exponentially in the number of qubits in the quantum computer. This places a severe limit on the size of the computations that can be performed by such a computer; estimates of that limit are well within the range in which a conventional computer taking exponentially …
We report here the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance (NMR) of a solid-state ensemble three-qubit system.
In a lattice ${\cal L}$ of nuclear spins with ABCABCABC... type periodic structure embedded in a single-crystal solid, each ABC-unit can be used to store quantum information and the information can be moved around via some cellular shifting mechanism. Impurity doping marks a special site D$\not\in{\cal L}$ which together with the local spin lattice constitute a quantum automaton where the D site serves as the input/output port and universal quantum logic is done through two-body interactions between two spins at D and a nearby site. The novel NMR quantum computer can be easily scaled up and ma…
Nuclear spins are promising candidates for quantum information processing because their good isolation from the environment precludes the rapid loss of quantum coherence. Many strategies have been developed to further extend their decoherence times. Some of them make use of decoupling techniques based on the Carr-Purcell and Carr-Purcell-Meiboom-Gill pulse sequences. In many cases, when applied to inhomogeneous samples, they yield a magnetization decay much slower than the Hahn echo. However, we have proved that these decays cannot be associated with longer decoherence times as coherences rema…
First-principles calculations of high-temperature spin dynamics in solids in the context of nuclear magnetic resonance (NMR) is a long-standing problem, whose conclusive solution can significantly advance the applications of NMR as a diagnostic tool for material properties. In this work, we propose a new hybrid quantum-classical method for computing NMR free induction decay(FID) for spin $1/2$ lattices. The method is based on the simulations of a finite cluster of spins $1/2$ coupled to an environment of interacting classical spins via a correlation-preserving scheme. Such simulations are show…
Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for…
After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this hi…
We propose a method of controlling a quantum logic gate in a solid-state NMR quantum computer. A switchable inter-qubit coupling can be generated by using the longitudinal component of the Suhl-Nakamura interaction induced by a local singlet-triplet excitation in a 1-D antiferromagnet with a spin gap.
As a complementary analysis tool to conventional high-field NMR, zero- to ultralow-field (ZULF) NMR detects nuclear magnetization signals in the sub-microtesla regime. Spin-exchange relaxation-free (SERF) atomic magnetometers provide a new generation of sensitive detector for ZULF NMR. Due to the features such as low-cost, high-resolution and potability, ZULF NMR has recently attracted considerable attention in chemistry, biology, medicine, and tests of fundamental physics. This review describes the basic principles, methodology and recent experimental and theoretical development of ZULF NMR, …
Refocalization sequences in Nuclear Magnetic Resonance (NMR) can in principle reverse the coherent evolution under the secular dipolar Hamiltonian of a closed system. We use this experimental strategy to study the effect of irreversible decoherence on the signal amplitude attenuation in a single crystal hydrated salt where the nuclear spin system consists in the set of hydration water proton spins having a strong coupling within each pair and a much weaker coupling with other pairs. We study the experimental response of attenuation times with temperature, crystal orientation with respect to th…
Solids and rigid tissues such as bone, ligaments, and tendons, typically appear dark in magnetic resonance imaging (MRI), which is due to the extremely short-lived proton nuclear magnetic resonance (NMR) signals. This short lifetime is due to strong dipolar interactions between immobilized proton spins, which render it challenging to detect these signals with sufficient resolution and sensitivity. Here we show the possibility of exciting long-lived signals in cortical bone tissue with a signature consistent with that of bound water signals. Contrary to long-standing belief, it is further shown…
Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: $ i) $ the free evolution of the NMR quadrupolar system and, by analogy with the e…
We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at a low temperatures. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)_{y}-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. The both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensit…
Nanoscale nuclear magnetic resonance (NMR) signals can be measured through hyperfine interaction to paramagnetic electron sensor spins. A heterodyne approach is widely used to overcome the electron spin lifetime limit in spectral resolution. It uses a series of modified Hahn echo pulse sequences applied coherently with precession signal resulting in a subsampled NMR signal. Due to challenges with applying high electron Rabi frequencies its application is limited to low fields, thus the full potential of the method is not yet exploited at high magnetic fields, beneficial for NMR. Here we presen…
Nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy of bulk quantum materials have provided insight into phenomena such as quantum phase criticality, magnetism, and superconductivity. With the emergence of nanoscale 2-D materials with magnetic phenomena, inductively-detected NMR and NQR spectroscopy are not sensitive enough to detect the smaller number of spins in nanomaterials. The nitrogen-vacancy (NV) center in diamond has shown promise in bringing the analytic power of NMR and NQR spectroscopy to the nanoscale. However, due to depth-dependent formation effi…
We have characterized spin-squeezed states produced at a temperature of $26^\circ{\mathrm C}$ on a Nuclear Magnetic Resonance (NMR) quadrupolar system. The implementation is carried out in an ensemble of $^{133}$Cs nuclei with spin $I=7/2$ of a lyotropic liquid crystal sample. We identify the source of spin squeezing due to the interaction between the quadrupole moment of the nuclei and the electric field gradients internally present in the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing. The quantitative a…
Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately "rewind" the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analys…
This article aims to review the developments, both theoretical and experimental, that have in the past decade laid the ground for a new approach to solid state quantum computing. Measurement-based quantum computing (MBQC) requires neither direct interaction between qubits nor even what would be considered controlled generation of entanglement. Rather it can be achieved using entanglement that is generated probabilistically by the collapse of quantum states upon measurement. Single electronic spins in solids make suitable qubits for such an approach, offering long coherence times and well defin…
We present a new concept for homonuclear dipolar recoupling in magic-angle-spinning (MAS) solid-state NMR experiments which avoids the problem of dipolar truncation. This is accomplished through the introduction of a new NMR pulse sequence design principle: the triple oscillating field technique. We demonstrate this technique as an efficient means to accomplish broadband dipolar recoupling of homonuclear spins, while decoupling heteronuclear dipolar couplings and anisotropic chemicals shifts and retaining influence from isotropic chemical shifts. In this manner, it possible to synthesize Ising…
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\fracπ{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomize…
Nanomagnetometry using the nitrogen-vacancy (NV) centre in diamond has attracted a great deal of interest because of the combined features of room temperature operation, nanoscale resolution and high sensitivity. One of the important goals for nano-magnetometry is to be able to detect nanoscale nuclear magnetic resonance (NMR) in individual molecules. Our theoretical analysis shows how a single molecule at the surface of diamond, with characteristic NMR frequencies, can be detected using a proximate NV centre on a time scale of order seconds with nanometer precision. We perform spatio-temporal…
Detecting and controlling nuclear spin nano-ensembles is crucial for the further development of nuclear magnetic resonance (NMR) spectroscopy and for the emerging solid state quantum technology. Here we present the fabrication of a $\approx$ 1 nanometre thick diamond layer consisting of $^{13}$C nuclear spins doped with Nitrogen-Vacancy centres (NV) embedded in a spin-free $^{12}$C crystal matrix. A single NV in the vicinity of the layer is used for polarization of the $^{13}$C spins and the readout of their magnetization. We demonstrate a method for coherent control of few tens of nuclear spi…
We review recent progress made in quantum information processing (QIP) which can be applied in the simulation of quantum systems and chemical phenomena. The review is focused on quantum algorithms which are useful for quantum simulation of chemistry and advances in nuclear magnetic resonance (NMR) and electron spin resonance (ESR) QIP. Discussions also include a number of recent experiments demonstrating the current capabilities of the NMR QIP for quantum simulation and prospects for spin-based implementations of QIP.
