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.
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…
An embedded selective recoupling method is proposed which is based on the idea of embedding the recently proposed deterministic selective recoupling scheme of Yamaguchi et al. [quant-ph/0411099] into a stochastic dynamical decoupling method, such as the recently proposed Pauli-random-error-correction-(PAREC) scheme [Eur. Phys. J. D 32, 153, quant-ph/0407262]. The recoupling scheme enables the implementation of elementary quantum gates in a quantum information processor by partial suppression of the unwanted interactions. The random dynamical decoupling method cancels a significant part of the …
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme d…
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…
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.
During recent years, dynamical decoupling (DD) has gained relevance as a tool for manipulating quantum systems and extracting information from them. This is particularly relevant for spins involved in nuclear magnetic resonance (NMR), where DD sequences can be used to prolong quantum coherences, or for selectively couple/decouple the effects imposed by random environmental fluctuations. In this Letter, we show that one can exploit these concepts in order to selectively recouple diffusion processes in restricted spaces. The ensuing method provides a novel tool to measure restriction lengths in …
The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for single-qubit operations in a large subset of quantum computer proposals: those governed by isotropic and XXZ,XY-type anisotropic exchange interactions. Our method employs an encoding of one logical qubit into two physical qubits, while logic operations are performed using an analogue of the NMR selective recoupling method.
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.
Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e., memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling(recoupling) method, which is turn off(on) the couplings and also Solovay-Kitaev techniques to decompose Hamiltonian and Lindbladians into effi…
Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional NMR is an essential technique to characterize correlations between nuclei and, hence, molecule structures. Towards the ultimate goal of single-molecule NMR, dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the detection of single nuclear spins and nanoscale NMR. However, there is still the lack of a standard method in DD-based quantum sensing to characterize correlations between nuclear spins in single molecules. Here we present a scheme of two-dimensional DD-based quantum sensing, as a universal met…
Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen-vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nu…
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…
The thesis is centred on the theory of experimental methods in solid-state Nuclear Magnetic Resonance (ssNMR) spectroscopy, which deals with the interaction of electromagnetic radiation with nuclei in a magnetic field and possessing a fundamental quantum mechanical property called spin. Orientation-dependent interactions in ssNMR, while offering a wealth of information, lead to broad indistinct signal and therefore are averaged out, predominantly by Magic-Angle Spinning (MAS). Reintroduction of the coupling interactions is achieved through radio frequency recoupling pulse sequences. NMR experi…
We embarked upon the task of experimental protection of different classes of tripartite entangled states, namely the maximally entangled GHZ and W states and the ${\rm W \bar{W}}$ state, using dynamical decoupling. The states were created on a three-qubit NMR quantum information processor and allowed to evolve in the naturally noisy NMR environment. Tripartite entanglement was monitored at each time instant during state evolution, using negativity as an entanglement measure. It was found that the W state is most robust while the GHZ-type states are most fragile against the natural decoherence …
Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demo…
We present a solution to the problem of broadband decoupling of a coupled homonuclear two-spin system. We describe a pulse sequence that creates an effective field perpendicular to the coupling interaction with a magnitude propotional to the chemical shift of the spins over a broad range of chemical shifts. When the chemical shift difference as imprinted on the perpendicular field is greater than the coupling between the spins, we get effective decoupling. The pulse sequence may be useful in various NMR applications.
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 …
The recently developed formalism of Markovian master equations for quantum open systems with external periodic driving is applied to the theory of dynamical decoupling by periodic control. This new approach provides a more detailed quantitative picture of this phenomenon applicable both to traditional NMR spectroscopy and to recent attempts of decoherence reduction in quantum devices. For popular choices of bath spectral densities and a two-level system, exact formulas for the relaxation rates are available. In the context of NMR imaging, the obtained formulas allow the extraction of a new par…
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…
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 …
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We first introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state wi…
The discovery of the intriguing phenomenon that certain kinds of quantum correlations remain impervious to noise up to a specific point in time and then suddenly decay, has generated immense recent interest. We exploit dynamical decoupling sequences to prolong the persistence of time-invariant quantum discord in a system of two NMR qubits decohering in independent dephasing environments. We experimentally prepare two-qubit Bell-diagonal quantum states that interact with individual dephasing channels and demonstrate the effect of dynamical decoupling on the preservation of both quantum and clas…
Coupled pairs of spin-1/2 nuclei support one singlet state and three triplet states. In many circumstances the nuclear singlet order, defined as the difference between the singlet population and the mean of the triplet populations, is a long-lived state which persists for a relatively long time in solution. Various methods have been proposed for generating singlet order, starting from nuclear magnetization. This requires the stimulation of singlet-to-triplet transitions by modulated radiofrequency fields. We show that a recently described pulse sequence, known as PulsePol (Schwartz $\textit{et…
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…
Conventional control strategies for NV centers in quantum sensing are based on a two-level model of their triplet ground state. However, this approach fails in regimes of weak bias magnetic fields or strong microwave pulses, as we demonstrate. To overcome this limitation, we propose a novel control sequence that exploits all three levels by addressing a hidden Raman configuration with microwave pulses tuned to the zero-field transition. We report excellent performance in typical dynamical decoupling sequences, opening up the possibility for nano-NMR operation in low-field environments.
We experimentally demonstrate the efficacy of a three-layer nested Uhrig dynamical decoupling (NUDD) sequence to preserve arbitrary quantum states in a two-dimensional subspace of the four-dimensional two-qubit Hilbert space, on an NMR quantum information processor. The effect of the state preservation is studied first on four known states, including two product states and two maximally entangled Bell states. Next, to evaluate the preservation capacity of the NUDD scheme, we apply it to eight randomly generated states in the subspace. Although, the preservation of different states varies, the …
Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and $in$ $vivo$ MRS. In the present survey, a general expression for ch…
The nitrogen vacancy (NV) color center in diamond is an enormously important platform for the development of quantum sensors, including for single spin and single molecule NMR. Detection of weak single-spin signals is greatly enhanced by repeated sequences of microwave pulses; in these dynamical decoupling (DD) techniques, the key control parameters swept in the experiment are the time intervals, $τ$, between pulses. Here we show that, in fact, the pulse duration offers a powerful additional control parameter. While previously, a non-negligible pulse-width has been considered simply a source o…
Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrate…
This thesis deals with the generation, estimation and preservation of novel quantum states of two and three qubits, on an NMR quantum information processor. Using the maximum likelihood ansatz, we have developed a method for state estimation such that the reconstructed density matrix does not have negative eigenvalues and the errors are within the space of valid density operators. Due to interactions with the environment, unwanted changes occur in the system, leading to decoherence. Controlling decoherence is one of the biggest challenges to be overcome to build quantum computers. We have used…
Single-molecule nuclear magnetic resonance (NMR) is a crown-jewel challenge in the field of magnetic resonance spectroscopy and has important applications in chemical analysis and in quantum computing. Recently, it becomes possible to tackle this grand challenge thanks to experimental advances in preserving quantum coherence of nitrogen-vacancy (NV) center spins in diamond as a sensitive probe and theoretical proposals on atomic-scale magnetometry via dynamical decoupling control. Through decoherence measurement of NV centers under dynamical decoupling control, sensing of single $^{13}\textbf{…
Methods that preserve coherence broadly impact all quantum information processing and metrology applications. Dynamical decoupling methods accomplish this by protecting qubits in noisy environments but are typically constrained to the limit where the qubits themselves are non-interacting. Here we consider the alternate regime wherein the inter-qubit couplings are of the same order as dephasing interactions with the environment. We propose and demonstrate a multi-pulse protocol that protects transverse spin states by suitably Hamiltonian engineering the inter-spin coupling while simultaneously …
Coherence time is an essential parameter for quantum sensing, quantum information, and quantum computation. In this work, we demonstrate electron spin coherence times as long as 0.1 s for an ensemble of rubidium atoms trapped in a solid parahydrogen matrix. We explore the underlying physics limiting the coherence time. The properties of these matrix isolated atoms are very promising for future applications, including quantum sensing of nuclear spins. If combined with efficient single-atom readout, this would enable NMR and magnetic resonance imaging of single molecules cotrapped with alkali-me…
Single-molecule sensitivity of nuclear magnetic resonance (NMR) and angstrom resolution of magnetic resonance imaging (MRI) are the highest challenges in magnetic microscopy. Recent development in dynamical-decoupling- (DD) enhanced diamond quantum sensing has enabled single-nucleus NMR and nanoscale NMR. Similar to conventional NMR and MRI, current DD-based quantum sensing utilizes the frequency fingerprints of target nuclear spins. The frequency fingerprints by their nature cannot resolve different nuclear spins that have the same noise frequency or differentiate different types of correlati…
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…
Refocusing of a quantum system in NMR and quantum information processing can be achieved by application of short pulses according to the methods of spin echo and dynamical decoupling. However, these methods are strongly limited by the requirement that the evolution of the system between pulses be suitably small. Here we show how refocusing may be achieved for arbitrary (but time-independent) evolution of the system between pulses. We first illustrate the procedure with one-qubit systems, and then generalize to $d$-dimensional quantum systems. We also give an application of this result to quant…
We theoretically analyze the performance of the nuclear magnetic resonance (NMR) spectroscopy with a superconducting flux qubit (FQ). Such NMR with the FQ is attractive because of the possibility to detect the relatively small number of nuclear spins in a local region ($\simμ$m) with low temperatures ($\sim$ mK) and low magnetic fields ($\sim$ mT), in which other types of quantum sensing schemes cannot easily access. A sample containing nuclear spins is directly attached on the FQ, and the FQ is used as a magnetometer to detect magnetic fields from the nuclear spins. Especially, we consider tw…
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest requirements still present daunting experimental challenges. The goal of this Dissertation is to reduce various resources required for robust quantum computation, focusing on quantum error correcting codes and solution NMR quantum computation. A variety of techniques have been developed, including high rate quantum codes for amplitude damping, relaxed criteria for q…
In nanoscale metrology applications, measurements are commonly limited by the performance of the sensor. Here we show that in nuclear magnetic resonance (NMR) spectroscopy measurements using single nitrogen-vacancy (NV) centers in diamond, the NV sensor electron spin limits spectral resolution down to a few hundred Hz, which constraints the characterization and coherent control of finite spin systems, and furthermore, is insufficient for high resolution NMR spectroscopy aiming at single molecule recognition and structure analysis of the latter. To overcome the limitation, we support an NV elec…
We present a method that implement directional, perfect state transfers within a branched spin network by exploiting quantum interferences in the time-domain. That provides a tool to isolate subsystems from a large and complex one. Directionality is achieved by interrupting the spin-spin coupled evolution with periods of free Zeeman evolutions, whose timing is tuned to be commensurate with the relative phases accrued by specific spin pairs. This leads to a resonant transfer between the chosen qubits, and to a detuning of all remaining pathways in the network, using only global manipulations. A…
Coherent optical control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways in order to manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of Quantum Information. Inspired by Nuclear Magnetic Resonance (NMR) spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent control techniques. Here we review related d…
For the implementation of a quantum computer it is necessary to exercise complete control over the Hamiltonian of the used physical system. For NMR quantum computing the effectively acting Hamiltonian can be manipulated via pulse sequences. Here we examine a register consisting of N selectively addressable spins with pairwise coupling between each spin pair. We show that complete decoupling of the spins is possible independent of the particular form of the spin-spin interaction. The proposed method based on orthogonal arrays is efficient in the sense that the effort regarding time and amount o…
Characterizing and understanding noise affecting quantum states has immense benefits in spectroscopy as well as in realizing quantum devices. Transverse relaxation times under a set of dynamical decoupling (DD) sequences with varying interpulse delays were earlier used for obtaining the noise spectral densities of single-qubit coherences. In this work, using a pair of homonuclear spins and NMR techniques, we experimentally characterize noise in certain decoherence-free subspaces. We also explore the noise of similar states in a heteronuclear spin pair. Further, using a 10-qubit system, we inve…
We experimentally emulate, in a controlled fashion, the non-Markovian dynamics of a pure dephasing spin-boson model at zero temperature. Specifically, we use a randomized set of external radio-frequency fields to engineer a desired noise power-spectrum to effectively realize a non-Markovian environment for a single NMR qubit. The information backflow, characteristic to the non-Markovianity, is captured in the nonmonotonicity of the decoherence function and von Neumann entropy of the system. Using such emulated non-Markovian environments, we experimentally study the efficiency of the Carr-Purce…
A quantum memory interacts with its environment and loses information via decoherence as well as incoherence. A robust quantum control that prepares, preserves, and manipulates nonclassical correlations even in the presence of environmental influence is of paramount importance in quantum information processing. A well-known technique to suppress decoherence, namely Dynamical Decoupling (DD), consists of a sequence of rapid flips applied to the system in order to refocus the system-environment interactions. In this work, we integrate DD with quantum gates using optimal control techniques to rea…
We report NMR experiments using high-power, RF decoupling techniques to show that a 29-Si nuclear spin qubit in a solid silicon crystal at room temperature can preserve quantum phase for 10^9 precessional periods. The coherence times we report are longer than for any other observed solid-state qubit by more than four orders of magnitude. In high quality crystals, these times are limited by residual dipolar couplings and can be further improved by isotopic depletion. In defect-heavy samples, we provide evidence for decoherence limited by 1/f noise. These results provide insight toward proposals…
Fault-tolerant hyper-Ramsey spectroscopy of optical clock transitions with dynamical decoupling
Centre for Quantum Technologies, Department of Physics, Sofia University（索非亚大学量子技术中心物理系）；Sorbonne Université CNRS, MONARIS, UMR 8233（索邦大学CNRS，MONARIS实验室）；MajuLab, International Research Laboratory IRL 3654, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University（新加坡国立大学-索邦大学-尼斯蔚蓝海岸大学南洋理工大学联合研究实验室）；Center for Quantum Technologies, Nanyang Technological University（南洋理工大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学理学院南洋量子枢纽）；Laboratoire de Physique des Lasers, CNRS, Université Sorbonne Paris Nord（巴黎北索邦大学CNRS激光物理实验室）
Multipulse sequences based on Carr-Purcell decoupling are frequently used for narrow-band signal detection in single spin magnetometry. We have analyzed the behavior of multipulse sensing sequences under real-world conditions, including finite pulse durations and the presence of detunings. We find that these non-idealities introduce harmonics to the filter function, allowing additional frequencies to pass the filter. In particular, we find that the XY family of sequences can generate signals at the 2fac, 4fac and 8fac harmonics and their odd subharmonics, where fac is the ac signal frequency. …
Persistent Quantum-Enhanced Frequency Sensing with T^{-3/2} Scaling
Department of Physics and Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文系）；Challenge Institute for Quantum Computation, University of California Los Angeles（加州大学洛杉矶分校挑战量子计算研究所）；Center for Quantum Science and Engineering, University of California Los Angeles（加州大学洛杉矶分校量子科学与工程中心）
