Compiling gate networks on an Ising quantum computer

Here we describe a simple mechanical procedure for compiling a quantum gate network into the natural gates (pulses and delays) for an Ising quantum computer. The aim is not necessarily to generate the most efficient pulse sequence, but rather to develop an efficient compilation algorithm that can be easily implemented in large spin systems. The key observation is that it is not always necessary to refocus all the undesired couplings in a spin system. Instead the coupling evolution can simply be tracked and then corrected at some later time. Although described within the language of NMR the algorithm is applicable to any design of quantum computer based on Ising couplings.Comment: 5 pages RevTeX4 including 4 figures. Will submit to PR

Single qubit gates by selective excitation with Jump and Return sequences

We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180 degree rotation in a two spin system. Finally we show how these two approaches can be combined to produce more accurate frequency selective rotations.Comment: Revised and extended at request of referee; now in press at Physical Review A. 6 pages RevTex including 3 figure

Effect of noise on geometric logic gates for quantum computation

We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how it could be implemented with superconducting charge qubits. While it may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on non-adiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.Comment: 8 pages, 4 figures; published versio

State transfer in dissipative and dephasing environments

By diagonalization of a generalized superoperator for solving the master equation, we investigated effects of dissipative and dephasing environments on quantum state transfer, as well as entanglement distribution and creation in spin networks. Our results revealed that under the condition of the same decoherence rate $\gamma$, the detrimental effects of the dissipative environment are more severe than that of the dephasing environment. Beside this, the critical time $t_c$ at which the transfer fidelity and the concurrence attain their maxima arrives at the asymptotic value $t_0=\pi/2\lambda$ quickly as the spin chain length $N$ increases. The transfer fidelity of an excitation at time $t_0$ is independent of $N$ when the system subjects to dissipative environment, while it decreases as $N$ increases when the system subjects to dephasing environment. The average fidelity displays three different patterns corresponding to $N=4r+1$, $N=4r-1$ and $N=2r$. For each pattern, the average fidelity at time $t_0$ is independent of $r$ when the system subjects to dissipative environment, and decreases as $r$ increases when the system subjects to dephasing environment. The maximum concurrence also decreases as $N$ increases, and when $N\rightarrow\infty$, it arrives at an asymptotic value determined by the decoherence rate $\gamma$ and the structure of the spin network.Comment: 12 pages, 6 figure

Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.Comment: 12 pages, 4 figure

Evolutionary history of copy-number-variable locus for the low-affinity Fcy receptor: mutation rate, autoimmune disease, and the legacy of helminth infection

Both sequence variation and copy-number variation (CNV) of the genes encoding receptors for immunoglobulin G (Fcg receptors) have been genetically and functionally associated with a number of autoimmune diseases. However, the molecular nature and evolutionary context of this variation is unknown. Here, we describe the structure of the CNV, estimate its mutation rate and diversity, and place it in the context of the known functional alloantigen variation of these genes. Deletion of Fcg receptor IIIB, associated with systemic lupus erythematosus, is a result of independent nonallelic homologous recombination events with a frequency of approximately 0.1%. We also show that pathogen diversity, in particular helminth diversity, has played a critical role in shaping the functional variation at these genes both between mammalian species and between human populations. Positively selected amino acids are involved in the interaction with IgG and include some amino acids that are known polymorphic alloantigens in humans. This supports a genetic contribution to the hygiene hypothesis, which states that past evolution in the context of helminth diversity has left humans with an array of susceptibility alleles for autoimmune disease in the context of a helminth-free environment. This approach shows the link between pathogens and autoimmune disease at the genetic level and provides a strategy for interrogating the genetic variation underlying autoimmunedisease risk and infectious-disease susceptibility

Stictopleurus punctatonervosus (Goeze, 1778) (Hem.: Rhopalidae) rediscovered in Britain and new to Essex

Volume: 111Start Page: 135End Page: 13

Evolutionary history of the low-affinity Fc gamma receptor copy number variable locus: diversity, disease and helminth infection

Low-affinity Fc receptors for immunoglobulin G (IgG) are expressed on a variety of leucocytes and play an important role in immune responses to pathogens. Copy number and functional single nucleotide variation in the low affinity FCGR region is associated with lupus, malaria, and possibly rheumatoid arthritis. We analysed variation at this locus in a global survey of 946 individuals from 51 populations. We found no large differences in copy number distribution together with little association with flanking SNP haplotypes suggesting a high recurrent mutation rate of this CNV. Coalescent analysis of population data suggests a mutation rate of about 0.1% per generation. A model of recurrent duplication and deletion mediated by non-allelic homologous recombination is supported by breakpoint mapping of homozygous deletions. Given the functional relevance of the sequence variation typed, infectious disease burden may be involved in shaping variation. Indeed, helminth pathogen richness is significantly correlated with the frequency of the NA1 variant of FCGR3B (P=0.0018) and an active form of the FCGR2C receptor (P=0.0005). Maximum-likelihood analysis of sequence evolution in mammals supports a model where positive selection acted on lineages with high levels of helminth infection (P= 0.006). Positive selection has acted on a subset of amino acids in FCGR3 which were mapped to the crystal structure and formed three patches on the receptor likely to influence the interaction with IgG