Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Ancilla-assisted quantum state tomography in multiqubit registers

The standard method of quantum state tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla-assisted QST (AAQST) proposed by Nieuwenhuizen and co-workers Phys. Rev. Lett. 92, 120402 (2004)] greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. Here we describe methods for explicit construction of AAQST experiments in multiqubit registers. We also report nuclear magnetic resonance studies on AAQST of (i) a two-qubit input register using a one-qubit ancilla in an isotropic liquid-state system and (ii) a three-qubit input register using a two-qubit ancilla register in a partially oriented system. The experimental results confirm the effectiveness of AAQST in such multiqubit registers.

Experimental Test of the Quantum No-Hiding Theorem

The no-hiding theorem says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the Universe with no information being hidden in the correlation between these two subsystems. Here, we report an experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance. We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

An evolutionary formalism for weak quantum measurements

Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs, which is consistent with the well-established framework of quantum mechanics. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of the Born rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution.

Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use C-13 nuclear spins as qubits and an environment of H-1 nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 mu s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

We present thermal and electrical transport measurements of low-density (10(14) m(-2)), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We find that even in the supposedly strongly localized regime, where the electrical resistivity of the system is two orders of magnitude greater than the quantum of resistance h/e(2), the thermopower decreases linearly with temperature indicating metallicity. Remarkably, the magnitude of the thermopower exceeds the predicted value in noninteracting metallic 2DESs at similar carrier densities by over two orders of magnitude. Our results indicate a new quantum state and possibly a novel class of itinerant quasiparticles in dilute 2DESs at low temperatures where the Coulomb interaction plays a pivotal role.

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si: P and Ge: P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Non-Abelian gauge redundancy and entropic ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping

Topological crystalline insulators (TCIs) are a new quantum state of matter in which linearly dispersed metallic surface states are protected by crystal mirror symmetry. Owing to its vanishingly small bulk band gap, a TCI like Pb0.6Sn0.4Te has poor thermoelectric properties. Breaking of crystal symmetry can widen the band gap of TCI. While breaking of mirror symmetry in a TCI has been mostly explored by various physical perturbation techniques, chemical doping, which may also alter the electronic structure of TCI by perturbing the local mirror symmetry, has not yet been explored. Herein, we demonstrate that Na doping in Pb0.6Sn0.4Te locally breaks the crystal symmetry and opens up a bulk electronic band gap, which is confirmed by direct electronic absorption spectroscopy and electronic structure calculations. Na doping in Pb0.6Sn0.4Te increases p-type carrier concentration and suppresses the bipolar conduction (by widening the band gap), which collectively gives rise to a promising zT of 1 at 856 K for Pb0.58Sn0.40Na0.02Te. Breaking of crystal symmetry by chemical doping widens the bulk band gap in TCI, which uncovers a route to improve TCI for thermoelectric applications.

Effect of inter-edge Coulomb interactions on transport through a point contact in nu=5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G(H) = 1/2e(2)/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G(H) = 5/2e(2)/h) and the fully disconnected case (G(H) = 0).

Buckled nano rod - a two state system: quantum effects on its dynamics

We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from the harmonic to the double well regime. The two minima in potential energy curve describe two possible buckled states. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain epsilon = 4 epsilon c the simple TST rate diverges. We suggest a method to correct this divergence for quantum calculations. We also find that zero point energy contributions can be quite large so that single mode calculations can lead to large errors in the rate.

Spin State Selective Excitation of Single Quantum Transitions Using Multiple Quantum Spectroscopy- an Aid to Analyse Complex Proton NMR spectra of Oriented Molecules

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)−single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.