Protecting the √SWAP operation from general and residual errors by continuous dynamical decoupling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Protecting the √SWAP operation from general and residual errors by continuous dynamical decoupling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A planar Penning trap

In this thesis I present theoretical and experimental results concern- ing the operation and properties of a new kind of Penning trap, the planar trap. It consists of circular electrodes printed on an isolating surface, with an homogeneous magnetic field pointing perpendicular to that surface. The motivation of such geometry is to be found in the construction of an array of planar traps for quantum informa- tional purposes. The open access to radiation of this geometry, and the long coherence times expected for Penning traps, make the planar trap a good candidate for quantum computation. Several proposals for quantum 2-qubit interactions are studied and estimates for their rates are given. An expression for the electrostatic potential is presented, and its fea- tures exposed. A detailed study of the anharmonicity of the potential is given theoretically and is later demonstrated by experiment and numerical simulations, showing good agreement. Size scalability of this trap has been studied by replacing the original planar trap by a trap twice smaller in the experimental setup. This substitution shows no scale effect apart from those expected for the scaling of the parameters of the trap. A smaller lifetime for trapped electrons is seen for this smaller trap, but is clearly matched to a bigger misalignment of the trap’s surface and the magnetic field, due to its more difficult hand manipulation. I also give a hint that this trap may be of help in studying non-linear dynamics for a sextupolarly perturbed Penning trap.

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Algoritmi quantistici e classi di complessità

Solitamente il concetto di difficoltà è piuttosto soggettivo, ma per un matematico questa parola ha un significato diverso: anche con l’aiuto dei più potenti computer può essere impossibile trovare la soluzione di un sudoku, risolvere l’enigma del commesso viaggiatore o scomporre un numero nei suoi fattori primi; in questo senso le classi di complessità computazionale quantificano il concetto di difficoltà secondo le leggi dell’informatica classica. Una macchina quantistica, però, non segue le leggi classiche e costituisce un nuovo punto di vista in una frontiera della ricerca legata alla risoluzione dei celebri problemi del millennio: gli algoritmi quantistici implementano le proprietà straordinarie e misteriose della teoria dei quanti che, quando applicate lucidamente, danno luogo a risultati sorprendenti.

Applicazioni e implementazioni della computazione quantistica

Questa tesi introduce le basi della teoria della computazione quantistica, partendo da un approccio teorico-matematico al concetto di qubit per arrivare alla schematizzazione di alcuni circuiti per algoritmi quantistici, analizzando la differenza tra le porte logiche classiche e la loro versione quantistica. Segue poi una lista descrittiva di possibili applicazioni dei computer quantistici, divise per categorie, e i loro vantaggi rispetto ai computer classici. Tra le applicazioni rientrano la crittografia quantistica, gli algoritmi di fattorizzazione e del logaritmo discreto di Shor, il teletrasporto di informazione quantistica e molte altre. La parte più corposa della tesi riguarda le possibili implementazioni, ovvero come realizzare praticamente un computer quantistico rendendo entità fisiche i qubit. Di queste implementazioni vengono analizzati i vari aspetti necessari alla computazione quantistica, ovvero la creazione di stati iniziali, la misura di stati finali e le trasformazioni unitarie che rappresentano le porte logiche quantistiche. Infine vengono elencate le varie problematiche del modello preso in considerazione. Infine vengono citati alcuni esperimenti e modelli recenti che potrebbero vedere una realizzazione su scala industriale nei prossimi anni.

Sulla Pseudo-Telepatia Quantistica

La tesi descrive il fenomeno della pseudo-telepatia quantistica; vengono spiegati quali avvenimenti storici hanno portato alla nascita di questa teoria. Attraverso vari esempi, in un primo momento si cerca di far capire cosa sia realmente il fenomeno analizzato, successivamente verrà dimostrato che la pseudo-telepatia è la migliore strategia esistente per la risoluzione di alcune particolari tipologie di compiti.

Seawater carbonate chemistry and biological processes of oysters Crassostrea virginica during experiments, 2010

Estuarine organisms are exposed to periodic strong fluctuations in seawater pH driven by biological carbon dioxide (CO2) production, which may in the future be further exacerbated by the ocean acidification associated with the global rise in CO2. Calcium carbonate-producing marine species such as mollusks are expected to be vulnerable to acidification of estuarine waters, since elevated CO2 concentration and lower pH lead to a decrease in the degree of saturation of water with respect to calcium carbonate, potentially affecting biomineralization. Our study demonstrates that the increase in CO2 partial pressure (pCO2) in seawater and associated decrease in pH within the environmentally relevant range for estuaries have negative effects on physiology, rates of shell deposition and mechanical properties of the shells of eastern oysters Crassostrea virginica (Gmelin). High CO2 levels (pH ~7.5, pCO2 ~3500 µatm) caused significant increases in juvenile mortality rates and inhibited both shell and soft-body growth compared to the control conditions (pH ~8.2, pCO2 ~380 µatm). Furthermore, elevated CO2 concentrations resulted in higher standard metabolic rates in oyster juveniles, likely due to the higher energy cost of homeostasis. The high CO2 conditions also led to changes in the ultrastructure and mechanical properties of shells, including increased thickness of the calcite laths within the hypostracum and reduced hardness and fracture toughness of the shells, indicating that elevated CO2 levels have negative effects on the biomineralization process. These data strongly suggest that the rise in CO2 can impact physiology and biomineralization in marine calcifiers such as eastern oysters, threatening their survival and potentially leading to profound ecological and economic impacts in estuarine ecosystems.

Seawater carbonate chemistry, nutrients and growth rate during experiments with coral Astrangia poculata and field observations, 2010

Zooxanthellate colonies of the scleractinian coral Astrangia poculata were grown under combinations of ambient and elevated nutrients (5 µM NO, 0.3 µM PO4, and 2nM Fe) and CO2 (780 ppmv) treatments for a period of 6 months. Coral calcification rates, estimated from buoyant weights, were not significantly affected by moderately elevated nutrients at ambient CO2 and were negatively affected by elevated CO2 at ambient nutrient levels. However, calcification by corals reared under elevated nutrients combined with elevated CO2 was not significantly different from that of corals reared under ambient conditions, suggesting that CO2 enrichment can lead to nutrient limitation in zooxanthellate corals. A conceptual model is proposed to explain how nutrients and CO2 interact to control zooxanthellate coral calcification. Nutrient limited corals are unable to utilize an increase in dissolved inorganic carbon (DIC) as nutrients are already limiting growth, thus the effect of elevated CO2 on saturation state drives the calcification response. Under nutrient replete conditions, corals may have the ability to utilize more DIC, thus the calcification response to CO2 becomes the product of a negative effect on saturation state and a positive effect on gross carbon fixation, depending upon which dominates, the calcification response can be either positive or negative. This may help explain how the range of coral responses found in different studies of ocean acidification can be obtained.

Seawater carbonate chemistry and biological processes during experiments with calcifiing organisms, 2009

Anthropogenic elevation of atmospheric carbon dioxide (pCO2) is making the oceans more acidic, thereby reducing their degree of saturation with respect to calcium carbonate (CaCO3). There is mounting concern over the impact that future CO2-induced reductions in the CaCO3 saturation state of seawater will have on marine organisms that construct their shells and skeletons from this mineral. Here, we present the results of 60 d laboratory experiments in which we investigated the effects of CO2-induced ocean acidification on calcification in 18 benthic marine organisms. Species were selected to span a broad taxonomic range (crustacea, cnidaria, echinoidea, rhodophyta, chlorophyta, gastropoda, bivalvia, annelida) and included organisms producing aragonite, low-Mg calcite, and high-Mg calcite forms of CaCO3. We show that 10 of the 18 species studied exhibited reduced rates of net calcification and, in some cases, net dissolution under elevated pCO2. However, in seven species, net calcification increased under the intermediate and/or highest levels of pCO2, and one species showed no response at all. These varied responses may reflect differences amongst organisms in their ability to regulate pH at the site of calcification, in the extent to which their outer shell layer is protected by an organic covering, in the solubility of their shell or skeletal mineral, and whether they utilize photosynthesis. Whatever the specific mechanism(s) involved, our results suggest that the impact of elevated atmospheric pCO2 on marine calcification is more varied than previously thought.

Protein content of Calanus finmarchicus from the North Atlantic collected during Maria S. Merian cruise MSM26 in spring 2013

For the determination of water-soluble protein content of C. finmarchicus of the different stations the Qubit® Protein Assay Kit (Invitrogen) was used. Analysis was performed with extracts of 10 copepods. Working solution was prepared with Qubit® protein reagent and Qubit® protein buffer (1:200). 190 µL working solution was pipetted into each well of a micro plate and 10 µL of sample or Qubit® protein standard (0, 200 and 400 ng/µL) was added. Solutions were mixed and incubated for 15 min at room temperature. Measurements were conducted with a micro plate reader (TriStar LB 941, Berthold Technologies) at 485 nm excitation and 590 nm emission, using the software MikroWin2000 (Berthold Technologies).

Seawater carbonate chemistry, nutrients and growth rate during experiments with coral Astrangia poculata, 2010

Zooxanthellate colonies of the scleractinian coral Astrangia poculata were grown under combinations of ambient and elevated nutrients (5 µM NO, 0.3 µM PO4, and 2nM Fe) and CO2 (780 ppmv) treatments for a period of 6 months. Coral calcification rates, estimated from buoyant weights, were not significantly affected by moderately elevated nutrients at ambient CO2 and were negatively affected by elevated CO2 at ambient nutrient levels. However, calcification by corals reared under elevated nutrients combined with elevated CO2 was not significantly different from that of corals reared under ambient conditions, suggesting that CO2 enrichment can lead to nutrient limitation in zooxanthellate corals. A conceptual model is proposed to explain how nutrients and CO2 interact to control zooxanthellate coral calcification. Nutrient limited corals are unable to utilize an increase in dissolved inorganic carbon (DIC) as nutrients are already limiting growth, thus the effect of elevated CO2 on saturation state drives the calcification response. Under nutrient replete conditions, corals may have the ability to utilize more DIC, thus the calcification response to CO2 becomes the product of a negative effect on saturation state and a positive effect on gross carbon fixation, depending upon which dominates, the calcification response can be either positive or negative. This may help explain how the range of coral responses found in different studies of ocean acidification can be obtained.

Emaranhamento de feixes de fótons por meio do campo magnético

Foi proposta uma experiência na qual seria possível produzir um emaranhamento quântico de feixes de fótons com diferentes frequências, movendo-se em uma mesma direção, controlado por meio de um campo magnético externo. Nessa experiência, a interação entre o campo magnético e fótons é realizada por intermédio de elétrons, que interagem tanto com os fótons quanto com o campo magnético externo. Foi desenvolvida uma teoria que descreve processos físicos. Derivamos medidas de emaranhamento de informação e de Schmidt para um sistema geral de dois qubits e a medida residual para um sistema geral de três qubits. Usando a informação obtida da análise dos sistemas de dois e de três quase-fótons, calculamos medidas de emaranhamento. Criamos um programa para cálculo numérico, nesses casos, através do qual construímos gráficos de dependência das medidas de emaranhamentos em feixes de dois e de três fótons. Os resultados obtidos nos permitem ver como a medida de emaranhamento depende dos parâmetros, que caracterizam o sistema em questão. Por exemplo, se ambas as polarizações dos fótons coincidem, então, nenhum emaranhamento ocorre. O emaranhamento acontece apenas se as polarizações do fóton forem opostas.

Scaling of decoherence effects in quantum computers

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.

Robustness of quantum gates in the presence of noise

We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all bipartite unitary quantum gates, and it is found that the controlled-NOT gate is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being p(th)less than or equal to0.5.