A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi 1d structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, I_{i,+}I_{j,+} + I_{i,-}I_{j,-}. We contrast the decoherence of adamantane, a standard 3d system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on 13-C labelled Alanine by creating the non-physical Hamiltonian ZZZ corresponding to a three body interaction.
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.
Multiple quantum (MQ) NMR with a dipolar ordered initial state opens new possibilities for the exploration of many-spin entanglement. In this paper, we investigate many-spin entanglement in a gas of spin-carrying molecules (atoms) in nanocavities in the conditions of MQ NMR with a dipolar ordered initial state. The second moment of the distribution of the intensities of MQ NMR coherences, which provides a lower bound on the quantum Fisher information, is used for an estimate of the number of the entangled spins. Many-spin entanglement is investigated at different temperatures and different num…
Quantum correlations in multiple quantum (MQ) NMR experiments are investigated in two-spin systems (dimers). In the initial moment of time one spin is in a pure quantum polarized state and the other spin is in the thermodynamic equilibrium state defined by the temperature of the sample. MQ NMR dynamics of dimers is investigated. It is shown that MQ NMR coherences of only the zeroth and second orders emerge in such a system. The intensities of those coherences are calculated. Entangled states appear in the course of the system evolution in the MQ NMR experiment. The quantum discord is obtained …
The effect of Gaussian fluctuations of nanopores filled with a gas of spin-carrying molecules ($s=1/2$) on the multiple quantum (MQ) NMR dynamics is investigated at different variances and correlation times of the fluctuations. We show that the fluctuations smooth out the evolution of MQ NMR coherence intensities which rapidly oscillate as functions of time in the absence of fluctuations. The growth and decay of the MQ coherence clusters in the fluctuating nanopore are also investigated.
We use multiple quantum (MQ) NMR dynamics of a gas of spin-carrying molecules in nanocavities at high and low temperatures for an investigation of many-particle entanglement. A distribution of MQ NMR intensities is obtained at high and low temperatures in a system of 201 spins 1/2. The second moment of the distribution, which provides a lower bound on the quantum Fisher information, sheds light on the many-particle entanglement in the system. The dependence of the many-particle entanglement on the temperature is investigated. Almost all spins are entangled at low temperatures.
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.
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a small-size system already displays singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
Dymanics of spin dimers in multiple quantum NMR experiment is studied on the 5-qubit superconducting quantum processor of IBM {Quantum Experience} for the both {pure} ground and thermodynamic equilibrium (mixed) initial states. The work can be considered as a first step towards an application of quantum computers to solving problems of magnetic resonance. This article is dedicated to Prof. Klaus Möbius and Prof. Kev Salikhov on the occasion of their 85th birthdays.
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. Relaxation of the …
We discuss the commonly encountered problem when optimizing NMR pulses using optimal control that the otherwise very precise NMR theory does not provide as excellent agreement with experiments. We hypothesize that this disagreement is due to phase transients in the pulse due to abrupt phase- and amplitude changes resulting in a large bandwidth. We apply the GROUP algorithm that gives high fidelity pulses with a low bandwidth compared to the typical GRAPE pulses. Our results obtain a better agreement between experiment and simulations supporting our hypothesis and solution to the problem.
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle …
Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. T…
We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of 1/2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with nearest-neighbor dipole -dipole interactions; (2) a more realistic model with interactions between all spins. It is shown that the entangled states appear between remote particles which do not interact directly (model 1), while the interaction between all spins (model 2) not always results in entanglement between remote spins.
We propose a scalable method on the basis of nth-order coupling operators to construct f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa (D-J) quantum algorithm. The novel n-qubit entangling transformations are easily implemented via J-couplings between neighboring spins. The seven-qubit modified D-J quantum algorithm and seventh-order coupling transformations are then experimentally demonstrated with liquid state nuclear magnetic resonance (NMR) techniques. The method may offer the possibility of creating generally entangled states of n qubits and simulating n-body inter…
Quantum correlations are investigated theoretically in a two-spin system with the dipole-dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of $π/2$-pulses only and the delays between the pulses can differ. The second scheme contains $φ$-pulses ($0<φ<π$) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between $π/2$-pulses at arbitraty temperatures. Entangl…
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…
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…
The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution …
Feynman, in 1982, proposed the idea of using a quantum simulator to perform quantum simulations. A quantum simulator is basically a controllable quantum system that can mimic the dynamics of other quantum systems we wish to study. In this thesis we investigate some aspects of quantum simulation using both unitary and nonunitary controls. In the unitary part, we experimentally simulated the phenomenon of quantum many-body freezing, and also developed a general protocol to decompose an arbitrary unitary operator. In the nonunitary part, we studied phase decoherence by artificially inducing it. W…
The 19F spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multi-pulse control, the nuclear spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analy…
We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear spins-1/2. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the non-secular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin pair entanglement, concurrence, coincides qualitatively with the intensity of MQ coherences of the plus/minus second order an…
We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged non-secular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum $\hat I^2$. We use the basis of common eigenstates of $\hat I^2$ and the projection of $I$ on the external magnetic field for investigation of MQ NMR dynamics…
As opposed to traditional methods of multiple-quantum NMR spectroscopy authors of the article [G.A. Alvarez, D. Suter, Phys. Rev. A 84, 012320 (2011)] generated the effective double-quantum Hamiltonian, with the slight adding usual secular dipole-dipole Hamiltonian to the first one at the stage of the correlations preparing (so the perturbation appeared). At this framework the width of MQ spectra reveals tending to any constant amount with the growing up of the time. Also there were shown that the spectral width decreases with increasing perturbation strength. The growing up of the cluster siz…
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…
Using an NMR quantum computer, we experimentally simulate the quantum phase transition of a Heisenberg spin chain. The Hamiltonian is generated by a multiple pulse sequence, the nuclear spin system is prepared in its (pseudo-pure) ground state and the effective Hamiltonian varied in such a way that the Heisenberg chain is taken from a product state to an entangled state and finally to a different product state.
Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to real world problems is a subject of active investigation. Analysis of many-body quantum system is particularly challenging for classical computers due to the exponential scaling of Hilbert space dimension with the number of particles. Hence, solving problems relevant to chemistry and condensed matter physics are expected to be the first successful applicatio…
In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves a time-reversal procedure to assess the effect of perturbations in a quantum excitation dynamics. However, when addressing macroscopic systems one is repeatedly confronted with limitations that seem insurmountable. This led to formulate the \textit{central hypothesis of irreversibility} stating that the time-scale of decoherence, $T_3$, is proportional to th…
We consider the quantum discord in a two-particle spin-1/2 system (dimer) governed by the standard multiple quantum (MQ) Hamiltonian and reveal the relation between the discord and the intensity of the second-order MQ coherence. Since the coherence intensities may be measured in experiment, we obtain a method of detecting the quantum discord in experiment. Comparison of discord and concurrence is represented.
The multiple-quantum NMR spectroscopy has an extensive application in determination of the bio-macro-molecular structures and in the investigation of the properties of a variety of physical materials. In quantum computation the multiple-quantum transition processes have been used to construct the quantum circuits, quantum algorithms, and quantum simulations. The multiple-quantum operator algebra spaces are closely related to the symmetries of a multiple-spin quantum system. They may have an important effect on the multiple-quantum transition processes and the multiple-quantum NMR spectroscopy …
The effects of shot noise on the quantum computation of NMR spectra
Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学与技术中心）；HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；The University of Nottingham（诺丁汉大学）
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…
We study the decay of multiple quantum (MQ) NMR coherences in systems with the large number of equivalent spins. As being created on the preparation period of MQ NMR experiment, they decay due to the dipole-dipole interactions (DDI) on the evolution period of this experiment. It is shown that the relaxation time decreases with the increase in MQ coherence order {(according to the known results)} and in the number of spins. We also consider the modified preparation period of MQ NMR experiment (G.A.Alvarez, D.Suter, PRL {\bf 104}, 230403 (2010)) concatenating the short evolution periods under th…
Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are well-established techniques that provide valuable information in a diverse set of disciplines but are currently limited to macroscopic sample volumes. Here we demonstrate nanoscale NMR spectroscopy and imaging under ambient conditions of samples containing multiple nuclear species, using nitrogen-vacancy (NV) colour centres in diamond as sensors. With single, shallow NV centres in a diamond chip and samples placed on the diamond surface, we perform NMR spectroscopy and one-dimensional MRI on few-nanometre-sized samples c…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the …
This letter presents a two-dimensional nuclear magnetic resonance(NMR) approach for constructing a two-logical-qubit decoherence-free subspace (DFS) based on the fact that the three protons in a CH3 spin system can not be resolved in one-dimension NMR spectroscopy, but to a certain extent, can be distinguished by two-dimensional multiple-quantum NMR. We used four noisy physical nuclear spins, including three protons and one carbon in the CH3 spin system, to generate two decoherence-free logical quantum bits. It made full use of the unaddressed spins which could not be used in one-dimensional s…
Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new meas…
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…
We experimentally emulate interaction induced blockade and local spin freezing in two and three qubit Nuclear Magnetic Resonance (NMR) architecture. These phenomena are identical to the Rydberg blockade and Rydberg biased freezing. In Rydberg blockade, the simultaneous excitation of two or more atoms is blocked due to the level shift induced by the strong Van der Waal's interaction. In such a strong interaction regime, one can also observe Rydberg biased freezing, wherein the dynamics is confined to a subspace, with the help of multiple drives with unequal amplitudes. Here we drive NMR qubits …
Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design a circuit that acts as an efficient quantum generative model, providing samples out of the spectral function of high rank observables in polynomial time. This includes many experimentally relevant spectra such as the dynamic structure factor, the optical conductivity or the NMR spectrum. Experimental realization of the algorithm, apart from logarithmic overh…
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…
Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ-coherences of different orders and distortions. The only effect of such transfer is scaling of the certain blocks of sender's density matrix (matrices of MQ-coherences of different order). Such a block-scaled transfer is an alternative to the perfect state transfer. In particular, equal scaling of higher order MQ-coherences matrices is possible. Moreover, there are states which can be transferred to the receiver preserving …
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…
The non-local nature of the correlations possessed by quantum systems may be revealed by experimental demonstrations of the violation of Bell-type inequalities. Recent work has placed bounds on the correlations that quantum systems can possess in an actual experiment. These bounds were limited to a composite quantum system comprising of a few lower-dimensional subsystems. In a more general approach, it has been shown that fewer body correlations can reveal the non-local nature of the correlations arising from a quantum mechanical description of nature. Such tests on the correlations can be tra…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation of the Hamiltonian do not work in this setting. In fact, since the inception of Magnus' expansion in 1954, no fundamentally novel mathematical approach capable of solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here of an entirely different non-perturbative approach, termed path-sum, which is always guarant…
While a bit is the fundamental unit of binary classical information, a qubit is the fundamental unit of quantum information. In quantum information processing (QIP), it is customary to call the qubits under study as system qubits, and the additional qubits as ancillary qubits. In this thesis, I describe various schemes to exploit the ancillary qubits to efficiently perform many QIP tasks and their experimental demonstrations in nuclear magnetic resonance (NMR) systems. Particularly, we have showed that, in the presence of sufficient ancillary qubits, it is possible to completely characterize a…
Pursuit and Review of Magnetic Resonance Imaging (MRI) based Quantum Computing -- Qubit Generation, Spin Purification, Tailored RF Pulses and MRI Sequences for Quantum Computing
Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.
Quantum phase transitions occur at zero temperature, when the ground state of a Hamiltonian undergoes a qualitative change as a function of a control parameter. We consider a particularly interesting system with competing one-, two- and three-body interactions. Depending on the relative strength of these interactions, the ground state of the system can be a product state, or it can exhibit genuine tripartite entanglement. We experimentally simulate such a system in an NMR quantum simulator and observe the different ground states. By adiabatically changing the strength of one coupling constant,…
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…
Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences (MQCs). Here we investigate the $α$-MQCs, a novel class of multiple quantum coherences which is based on $α$-relative purity, an information-theoretic quantifier analogous to quantum fidelity and closely related to Rényi relative entropy of order $α$. Our framework enables linking $α$-MQCs to Wigner-Yanase-Dyson skew information (WYDSI), an asymmetry monoto…
Conventional nuclear magnetic resonance (NMR) spectroscopy relies on acquiring signal from a macroscopic ensemble of molecules to gain information about molecular structure and dynamics. Transferring this technique to nanoscale sample sizes would enable molecular analysis without the effects of averaging over spatial and temporal inhomogeneities and without the need for macroscopic volumes of analyte, both inherent to large ensemble measurements. Nanoscale NMR based on nitrogen vacancy (NV) centers inside bulk diamond chips achieves single nuclear spin sensitivity and the resolution required t…
The paper describes the multiple rotating frame technique for designing modulated rf-fields, that perform broadband heteronuclear decoupling in solution NMR spectroscopy. The decoupling is understood by performing a sequence of coordinate transformations, each of which demodulates a component of the Rf-field to a static component, that progressively averages the chemical shift and dipolar interaction. We show that by increasing the number of modulations in the decoupling field, the ratio of dispersion in the chemical shift to the strength of the rf-field is successively reduced in progressive …
A multiple round quantum dense coding (MRQDC) scheme based on the quantum phase estimation algorithm is proposed. Using an $m+1$ qubit system, Bob can transmit $2^{m+1}$ messages to Alice, through manipulating only one qubit and exchanging it between Alice and Bob for $m$ rounds. The information capacity is enhanced to $m+1$ bits. We have implemented the scheme in a three- qubit nuclear magnetic resonance (NMR) quantum computer. The experimental results show a good agreement between theory and experiment.
Understanding the interplay between quantum coherence and non-Hermitian features would enable the devising of quantum technologies based on dissipative systems. In turn, quantum coherence can be characterized in terms of the language of multiple quantum coherences (MQCs) originally developed in solid-state nuclear magnetic resonance (NMR), nowadays applied to the detection of quantum chaos, and to the study of criticality in many-body quantum systems. Here we show the usefulness of MQCs for probing equilibrium phase transitions in non-Hermitian systems. To do so, we investigate the connection …
We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $π$ pulses can reduce dipolar interactions between spins of the same species in solids. Our simulations of pulsed electron spin resonance (ESR) experiments show that $π$ rotations with small ($<$~10\%) imperfections refocus instantaneous diffusion. Here, the intractable N-body problem of interacting dipoles is approximated by the average evolution of a single spin in a changing mean field. These calculations agree well with experiments and do not require powerful hardware. Our results add to past attempts to explain similar …
