Counterdiabatic driving for long-lived singlet state preparation.

The quantum adiabatic method, which maintains populations in their instantaneous eigenstates throughout the state evolution, is an established and often a preferred choice for state preparation and manipulation. Although it minimizes the driving cost significantly, its slow speed is a severe limitation in noisy intermediate-scale quantum era technologies. Since adiabatic paths are extensive in many physical processes, it is of broader interest to achieve adiabaticity at a much faster rate. Shortcuts to adiabaticity techniques, which overcome the slow adiabatic process by driving the system faster through non-adiabatic paths, have seen increased attention recently. The extraordinarily long lifetime of the long-lived singlet states (LLS) in nuclear magnetic resonance (NMR), established over the past decade, has opened several important applications ranging from spectroscopy to biomedical imaging. Various methods, including adiabatic methods, are already being used to prepare LLS. In this article, we report the use of counterdiabatic driving (CD) to speed up LLS preparation with faster drives. Using NMR experiments, we show that CD can give stronger LLS order in shorter durations than conventional adiabatic driving.

Tomographic entanglement indicators from NMR experiments.

In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state nuclear magnetic resonance (NMR) experiments and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments and carry out a similar comparative assessment of the performance of tomographic indicators. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.

Star-topology registers: NMR and quantum information perspectives.

Quantum control of large spin registers is crucial for many applications ranging from spectroscopy to quantum information. A key factor that determines the efficiency of a register for implementing a given information processing task is its network topology. One particular type, called star-topology, involves a central qubit uniformly interacting with a set of ancillary qubits. A particular advantage of the star-topology quantum registers is in the efficient preparation of large entangled states, called NOON states, and their generalized variants. Thanks to the robust generation of such correlated states, spectral simplicity, ease of polarization transfer from ancillary qubits to the central qubit, as well as the availability of large spin-clusters, the star-topology registers have been utilized for several interesting applications over the last few years. Here we review some recent progress with the star-topology registers, particularly via nuclear magnetic resonance methods.

NMR studies of quantum chaos in a two-qubit kicked top.

Quantum chaotic kicked top model is implemented experimentally in a two-qubit system comprising of a pair of spin-1/2 nuclei using nuclear magnetic resonance techniques. The essential nonlinear interaction was realized using indirect spin-spin coupling, while the linear kicks were realized using radio-frequency pulses. After a variable number of kicks, quantum state tomography was employed to reconstruct the single-qubit reduced density matrices, using which we could extract von Neumann entropies and Husimi distributions. These measures enabled the study of correspondence with classical phase space as well as probing distinct features of quantum chaos, such as symmetries and temporal periodicity in the two-qubit kicked top.

Temporal Order in Periodically Driven Spins in Star-Shaped Clusters.

We experimentally study the response of star-shaped clusters of initially unentangled N=4, 10, and 37 nuclear spin-1/2 moments to an inexact π-pulse sequence and show that an Ising coupling between the center and the satellite spins results in robust period-2 magnetization oscillations. The period is stable against bath effects, but the amplitude decays with a timescale that depends on the inexactness of the pulse. Simulations reveal a semiclassical picture in which the rigidity of the period is due to a randomizing effect of the Larmor precession under the magnetization of surrounding spins. The timescales with stable periodicity increase with net initial magnetization, even in the presence of perturbations, indicating a robust temporal ordered phase for large systems with finite magnetization per spin.

Bang-bang optimal control of large spin systems: Enhancement of 13C-13C singlet-order at natural abundance.

Using a bang-bang optimal control technique, we transfer polarization from a set of abundant high-γ nuclei directly to singlet order of a low-γ spin-pair. This approach is analogous to algorithmic cooling (AC) procedure used in quantum state purification. Specifically, we apply this method for enhancing the singlet order in a natural abundant 13C- 13C spin pair by exploiting nine equivalent protons of an 11-spin system. Compared to the standard method not involving polarization transfer, we find an enhancement of singlet order by about 3.4 times. In addition, since the singlet magnetization is contributed by the faster relaxing protons, the recycle delay is halved. Thus effectively we observe a reduction in the overall experimental time by a factor of 23. We also discuss a possible extension of AC, known as heat-bath algorithmic cooling (HBAC).

A review on balya action mentioned in Ayurveda.

Medicinal and dietary substances have been used for various purposes including nutritional from time immemorial. Various activities such as immunomodulator, bulk promoting, nutritional, etc. that enhance strength, immunity, bulk of the body resulted by the use of medicinal or dietary substances are termed in total as Balya in Ayurveda. The term Balya originally stands for all those actions that enhance the "Bala". The word "Bala" refers to the strength and ability of the body or part of the body to cope up with various physical stressors. This term "Bala" refers to various body components and functions as per the science of Ayurveda. Even in the presence of modern scientific knowledge regarding body strength, Ayurveda concepts add varied dimensions to provide detailed explanation of Balya term. The balya action is critically analyzed and discussed in this review.

Investigation of the Leggett-Garg inequality for precessing nuclear spins.

We report experimental implementation of a protocol for testing the Leggett-Garg inequality (LGI) for nuclear spins precessing in an external magnetic field. The implementation involves certain controlled operations, performed in parallel on pairs of spin-1/2 nuclei (target and probe) from molecules of a nuclear magnetic resonance ensemble, which enable evaluation of temporal correlations from an LG string. Our experiment demonstrates violation of the LGI for time intervals between successive measurements, over which the effects of relaxation on the quantum state of target spin are negligible. Further, it is observed that the temporal correlations decay, and the same target spin appears to display macrorealistic behavior consistent with LGI.

Density matrix tomography of singlet states.

First direct and quantitative study of singlet states using density matrix tomography is reported. A robust scheme for the tomography of a general density matrix of two spin 1/2 nuclei is introduced for this purpose. The study is carried out at different spin-lock conditions and the results are compared.

NMR implementation of adiabatic SAT algorithm using strongly modulated pulses.

NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.

Gelation of covalently edge-modified laponites in aqueous media. 1. rheology and nuclear magnetic resonance.

We describe the covalent modification of the edges of laponite with organic groups and the influence of this modification on gelation behavior. We compare three materials: an unmodified laponite, a laponite edge modified with a trimethyl moiety (MLap), and an octyldimethyl moiety (OLap). Gelation is investigated using rheology and NMR T1 relaxation measurements and nuclear Overhauser enhancement spectroscopy (NOESY). MLap and OLap show qualitatively different gelation. Gelation of MLap is very similar to laponite: MLap gels over the same time scale as laponite and has about the same solid modulus, and the MLap gel is almost as transparent as laponite. In contrast, OLap gels rapidly relative to laponite and forms a weak, turbid gel. We believe that gelation in laponite and MLap results from the formation of a network of well-dispersed platelets (or a few platelets), while in OLap, gelation results from a network of stacks of several platelets. NMR relaxation measurements indicate that gelation does not affect the average relaxation of water protons. However, T1 increases marginally for the protons in the organic moieties in MLap and decreases for protons in the organic moieties in OLap. Relaxation measurements, analyses of line width, and NOESY taken together suggest that, in OLap, gelation is a consequence of association of the organic moieties on the laponite edges, and that this association strengthens with time. Thus, the time-dependent changes in NMR suggest a structural origin for the time-dependent changes in the rheological behavior.

Spins as qubits: quantum information processing by nuclear magnetic resonance.

Storing information in quantum mechanical degrees of freedom and processing it by unitary transformation promises a new class of computers that can efficiently solve problems for which no efficient classical algorithms are known. The most straightforward implementation of this type of information processing uses nuclear spins to store the information and nuclear magnetic resonance for processing it. We discuss the basics of quantum information processing by NMR, with an emphasis on two fields of research: the design and implementation of robust logical gate operations and the loss of quantum information, which is known as decoherence.

Benchmarking quantum control methods on a 12-qubit system.

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.

Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses.

Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase-shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase-shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and quantum Fourier transform by simulations and experiments using transition selective pulses.

Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses.

Quantum logical operations using two-dimensional NMR have recently been described using the scalar coupling evolution technique [J. Chem. Phys. 109, 10603 (1998)]. In the present paper, we describe the implementation of quantum logical operations using two-dimensional NMR, with the help of spin- and transition-selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are also implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. The Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been implemented using spin- and transition-selective pulses after creating a coherent superposition state in the two-dimensional methodology.