Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR computing, however, a net improvement in the signal-to-noise would require very high polarization. The experiment implemented the 3-bit code for phase errors in liquid state state NMR.Comment: 5 pages, three figure

Protein interfaces are thought to be distinguishable from the rest of the protein surface by their greater degree of residue conservation. We test the validity of this approach on an expanded set of 64 proteinprotein interfaces using conservation scores derived from two multiple sequence alignment types, one of close homologs/orthologs and one of diverse homologs/paralogs. Overall, we find that the interface is slightly more conserved than the rest of the protein surface when using either alignment type, with alignments of diverse homologs showing marginally better discrimination. However, using a novel surface-patch definition, we find that the interface is rarely significantly more conserved than other surface patches when using either alignment type. When an interface is among the most conserved surface patches, it tends to be part of an enzyme active site. The most conserved surface patch overlaps with 39% (± 28%) and 36% (± 28%) of the actual interface for diverse and close homologs, respectively. Contrary to results obtained from smaller data sets, this work indicates that residue conservation is rarely sufficient for complete and accurate prediction of protein interfaces. Finally, we find that obligate interfaces differ from transient interfaces in that the former have significantly fewer alignment gaps at the interface than the rest of the protein surface, as well as having buried interface residues that are more conserved than partially buried interface residues.

We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.PACS numbers: 03.67.-a,76.60.-k In 1982, Richard Feynman proposed that a quantum system would be more efficiently simulated by a computer based on the principles of quantum mechanics rather than by one based on classical mechanics [1]. Recently, it has been pointed out that it should be possible to efficiently approximate any desired Hamiltonian within the standard model of a quantum computer by a sparsely coupled array of two-state systems [2][3][4]. Many of the concepts of quantum simulation are implicit in the average Hamiltonian theory developed by Waugh and colleagues to design NMR pulse sequences which implement a specific desired effective NMR Hamiltonian [5]. Here we show the first explicit simulation of one quantum system by another; namely the simulation of the kinematics and dynamics of a truncated quantum oscillator by an NMR quantum information processor [6,7]. Quantum simulations are shown for both an undriven harmonic oscillator and a driven anharmonic oscillator.A general scheme for quantum simulation is summarized by the following diagram:The object is to simulate the effect of the evolution |s U −→ |s(T ) using the physical system P . To do this, S is related to P by an invertible map φ which determines a correspondence between all the operators and states of S and of P . In particular, the propagator U maps to V T = φ −1 U φ. The challenge is to implement V T using propagators V i arising from the available external interactions with intervening periods of natural evolution esufficient class of simple operations (logic gates) are implementable in the physical system, the Universal Computation Theorem [8][9][10] guarantees that any operator (in particular V T ) can be composed of natural evolutions in P and external interactions. For unitary maps φ, we may write V T = e −iHpT /h where H p ≡ φ −1 H s φ can be identified with the average Hamiltonian of Waugh. After |p VT −→ |p T , the final map φ −1 takes |p T → |s(T ) thereby effecting the simulation |s → |s(T ) . Note that H s (T ) can be a time dependent Hamiltonian and that T is viewed as a parameter when mapped to P . This implies that the physical times t i (T ) are parameterized by the simulated time T .Liquid state NMR quantum computers are well suited for quantum simulations because they have long spin relaxation times (T 1 and T 2 ) as well as the flexibility of using a variety of molecular samples. In particular, the coupling between the nuclear spins, usually dominated by the 'scalar' coupling (J), may be reduced at will by means of radiofrequency pulses. Typically spin 1/2 nuclei are used. Thus, the kinematics of any 2 N level quantum system could be simulated using a given N -spin molecule.We ...

This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the Dirac equation, operators and monogenics, the Hydrogen atom, propagators and scattering theory, spin precession, tunnelling times, spin measurement, multiparticle quantum mechanics, relativistic multiparticle wave equations, and semiclassical mechanics.

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 σzσzσz corresponding to a three body interaction.