Robust Control of Quantum Information

Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that ``refocuses'' them. They are due to reproducible spatial or temporal variations in the system's Hamiltonian, so that information on the variations is encoded in the system's spatiotemporal state and can be used to correct them. In this paper liquid-state nuclear magnetic resonance (NMR) is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radio-frequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians' underlying distribution.Comment: 14 pages, 6 figure

Demography of botfly (Cuterebra fontinella) parasitism in white-footed mice (Peromyscus leucopus) in Kansas

Botflies (Diptera: Cuterebra sp.) are widely distributed and seasonally abundant parasites of small mammals in North America. To assess their effect on rodent survival, we studied the demography of botfly parasitism on small mammals in northeastern Kansas during 1995–1999. Additional comparisons on botflies parasitizing small mammals were made to a nearby old-field grid where mark–recapture studies continued from 1975 to 2003. White-footed mice, Peromyscus leucopus, were infected by botfly larvae (Cuterebra fontinella) each year during our study. The period of infection for P. leucopus was June–December, with the highest proportion of mice infected in July and August. A smaller, second peak of infection in October and November indicated that C. fontinella reproduced bimodally at this latitude with distinct summer and autumn population peaks. During the botfly seasons of the 5 years, 140 (23.3%) of 602 P. leucopus captured were infected. The percentages of individuals infected during 1995, 1996, 1997, and 1999 were not significantly different (22.4, 17.3, 17.1, and 22.7%, respectively). However, in 1998, 32.4% individuals were infected with a higher incidence of multiple infections and a greater number of botfly larvae per host. Nearly half (47%) of the infected individuals caught in 1998 had infections in both summer and autumn, compared with 25% during the 1995–1997 seasons. In 1999, 63% of infected mice had at least a 2nd infection during the autumn. For all 5 years, 82%, 14%, and 4% of the infected mice had 1, 2, or 3 botflies, respectively. In 1998, 24% of the infected mice carried 2 or more botflies at one time, compared to 14% from 1995–1997 and 11% in 1999. Overall 94% percent of the infected mice were adults, with no differences between sexes. The variation seen in the prevalence of botfly parasitism of white-footed mice correlates to yearly weather fluctuations. Other demographic aspects of the infected mice, such as sex ratio, age, and longevity of those infected did not change year to year. Our data suggest that infection with Cuterebra has little negative or positive impact upon populations of white-footed mice. Tábanos (Diptera; Cuterebra) son un grupo de moscas parásitas con variable abundancia estacional en Norte América. Para determinar su efecto en la supervivencia de roedores, estudiamos la demografía del parasitismo por tábanos en mamíferos pequeños en el noreste de Kansas desde 1995 hastas 1999. Comparaciones adicionales del parasitismo de larvas de tábanos fueron realizadas usando una retícula de trampas en una zona aledaña, donde estudios de marca-recaptura fueron realizados desde 1975 hasta 2003. El ratón de patas blancas (Peromyscus leucopus), fue parasitado por larvas de tábanos (Cuterebra fontinella) todos los años de nuestro estudio. El período de infección para P. leucopus es entre Junio y Diciembre, con una mayor proporción de ratones infectados entre Julio y Agosto. Un segundo pico menor de infección sucede entre Octubre y Noviembre, indicando que C. fontinella es bimodal en la latitud de nuestro estudio, con picos poblacionales diferenciables en el verano y el otoño. Para los tábanos registradas por 5 años, 140 (23.3%) de 602 P. leucopus capturados presentaron infecciones. El porcentaje de individuos infectados en los años 1995, 1996, 1997, y 1999 no fueron diferentes (22.4%, 17.3%, 17.1%, y 22.7%, respectivamente). Sin embargo, en 1998, un total de 32.4% individuos fueron infectados, con una alta incidencia de infecciones múltiples, y un número mayor de larvas de tábano por hospedero. Casi la mitad (47%) de los individuos infectados capturados en 1998 tuvieron infecciones tanto en el verano como en el otoño, comparado con 25% durante 1995–1997. En 1999, 63% de los ratones infectados tuvieron al menos una segunda infección durante la misma estación. Para todos los 5 años, 82%, 14%, y 4% de los ratones infectados tuvieron 1, 2, o 3 larvas respectivamente. En 1998, 24% de los ratones infectados transportaron dos o más larvas al mismo tiempo, comparado con 14% durante 1995–1997 y 11% en 1999. En general, 94% de los ratones infectados fueron adultos, y no observamos diferencias en infección entre sexos. La variación observada en la prevalencia de parasitismo está correlacionada con fluctuaciones climáticas anuales. Otros aspectos de la demografía de parasitismo en ratones, por ejemplo, proporción de sexos, edad, longevidad de individuos infectados, no cambiaron entre años. Nuestros datos sugieren que infección por Cuterebra tiene pequeño impacto negativo o positivo en la población de ratones de patas blancas

Experimental Implementation of a Concatenated Quantum Error-Correcting Code

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct against phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error-correcting codes offers a practical tool to handle realistic noise contributed by both independent and correlated errors.Comment: 4 pages, 2 encapsulated eps figures. REVTeX4 styl

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

Study of localization in the quantum sawtooth map emulated on a quantum information processor

Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.Comment: 20 pages, 9 figure

Error tolerance in an NMR Implementation of Grover's Fixed-Point Quantum Search Algorithm

We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for either one or two matching items in an unsorted database of four items. In this new algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, and so the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.Comment: 5 Pages RevTex4 including three figures. Changes made at request of referees; now in press at Phys Rev

Separability of very noisy mixed states and implications for NMR quantum computing

We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable. The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. We also discuss the implications of the bounds for NMR quantum computing.Comment: 4 pages, extensively revised, references adde

Complete quantum teleportation using nuclear magnetic resonance

Quantum mechanics provides spectacular new information processing abilities (Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called quantum teleportation (Bennett et al 1993) that allows the quantum state of a system to be transported from one location to another, without moving through the intervening space. Partial implementations of teleportation (Bouwmeester et al 1997, Boschi et al 1998) over macroscopic distances have been achieved using optical systems, but omit the final stage of the teleportation procedure. Here we report an experimental implementation of the full quantum teleportation operation over inter-atomic distances using liquid state nuclear magnetic resonance (NMR). The inclusion of the final stage enables for the first time a teleportation implementation which may be used as a subroutine in larger quantum computations, or for quantum communication. Our experiment also demonstrates the use of quantum process tomography, a procedure to completely characterize the dynamics of a quantum system. Finally, we demonstrate a controlled exploitation of decoherence as a tool to assist in the performance of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published versio

Cognitive Function is Unaffected during Acute Hypoxic Exposure but was Improved Following Exercise

International Journal of Exercise Science 15(5): 1481-1491, 2022. To investigate the effects of two levels of acute hypoxic exposure and exercise compared to normoxia on the Stroop color word test. A total of 14 (4 females and 10 males) active participants with a self-reported (mean±SEM) 8.54±1.44 h/week of physical activity, performed a 3-repetition maximum hex/trap bar deadlift, Hand-Release Push-Up, and Leg Tuck events from the Army Combat Fitness Test at normoxia and normobaric hypoxia of fraction of inspired oxygen (FiO2) of 16% and 14.3%. The Stroop color-word test was administered on a touch screen device before and after the exercise battery, where participants were given congruent (word and ink color matching) and incongruent (non-matching) prompts. Peripheral oxygen saturation (SpO2) and heart rate were recorded at pre- and post-exercise. Variables obtained from the Stroop color word test were not influenced as a result of acute hypoxic exposure but did improve after an exercise battery. Peripheral oxygen saturation was greater during normoxia compared to acute hypoxic exposure which indicated a systemic change in oxygenation. The results of the present study indicated that the Stroop color-word test is not influenced by an FiO2 16% or 14.3%, however, exercise did improve Stroop score and response time