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

Selective coherence transfers in homonuclear dipolar coupled spin systems

Mapping the physical dipolar Hamiltonian of a solid-state network of nuclear spins onto a system of nearest-neighbor couplings would be extremely useful for a variety of quantum information processing applications, as well as NMR structural studies. We demonstrate such a mapping for a system consisting of an ensemble of spin pairs, where the coupling between spins in the same pair is significantly stronger than the coupling between spins on different pairs. An amplitude modulated RF field is applied on resonance with the Larmor frequency of the spins, with the frequency of the modulation matched to the frequency of the dipolar coupling of interest. The spin pairs appear isolated from each other in the regime where the RF power (omega_1) is such that omega_weak << omega_1 << omega_strong. Coherence lifetimes within the two-spin system are increased from 19 us to 11.1 ms, a factor of 572.Comment: 4 pages. Paper re-submitted with minor changes to clarify that the scheme demonstrated is not an exact mapping onto a nearest neighbor system. However, this is the first demonstration of a controlled evolution in a subspace of an extended spin system, on a timescale that is much larger than the dipolar dephasing tim

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

Acute Treadmill Exercise Discriminately Improves the Skeletal Muscle Insulin-Stimulated Growth Signaling Responses in Mice Lacking REDD1

A loss of the regulated in development and DNA damage 1 (REDD1) hyperactivates mechanistic Target of Rapamycin Complex 1 (mTORC1) reducing insulin‐stimulated insulin signaling, which could provide insight into mechanisms of insulin resistance. Although aerobic exercise acutely inhibits mTORC1 signaling, improvements in insulin‐stimulated signaling are exhibited. The goal of this study was to determine if a single bout of treadmill exercise was sufficient to improve insulin signaling in mice lacking REDD1. REDD1 wildtype (WT) and REDD1 knockout (KO) mice were acutely exercised on a treadmill (30 min, 20 m/min, 5% grade). A within animal noninsulin‐to‐insulin‐stimulated percent change in skeletal muscle insulin‐stimulated kinases (IRS‐1, ERK1/2, Akt), growth signaling activation (4E‐BP1, S6K1), and markers of growth repression (REDD1, AMPK, FOXO1/3A) was examined, following no exercise control or an acute bout of exercise. Unlike REDD1 KO mice, REDD1 WT mice exhibited an increase (P \u3c 0.05) in REDD1 following treadmill exercise. However, both REDD1 WT and KO mice exhibited an increase (P \u3c 0.05) AMPK phosphorylation, and a subsequent reduction (P \u3c 0.05) in mTORC1 signaling after the exercise bout versus nonexercising WT or KO mice. Exercise increased (P \u3c 0.05) the noninsulin‐to‐insulin‐stimulated percent change phosphorylation of mTORC1, ERK1/2, IRS‐1, and Akt on S473 in REDD1 KO mice when compared to nonexercised KO mice. However, there was no change in the noninsulin‐to‐insulin‐stimulated percent change activation of Akt on T308 and FOXO1/3A in the KO when compared to WT or KO mouse muscle after exercise. Our data show that a bout of treadmill exercise discriminately improves insulin‐stimulated signaling in the absence of REDD1

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

The anatomy of exhumed river-channel belts: Bedform to belt‐scale river kinematics of the Ruby Ranch Member, Cretaceous Cedar Mountain Formation, Utah, USA

Many published interpretations of ancient fluvial systems have relied on observations of extensive outcrops of thick successions. This paper, in contrast, demonstrates that a regional understanding of palaeoriver kinematics, depositional setting and sedimentation rates can be interpreted from local sedimentological measurements of bedform and barform strata. Dune and bar strata, channel planform geometry and bed topography are measured within exhumed fluvial strata exposed as ridges in the Ruby Ranch Member of the Cretaceous Cedar Mountain Formation, Utah, USA. The ridges are composed of lithified stacked channel belts, representing at least five or six re‐occupations of a single‐strand channel. Lateral sections reveal well‐preserved barforms constructed of subaqueous dune cross‐sets. The topography of palaeobarforms is preserved along the top surface of the outcrops. Comparisons of the channel‐belt centreline to local palaeotransport directions indicate that channel planform geometry was preserved through the re‐occupations, rather than being obscured by lateral migration. Rapid avulsions preserved the state of the active channel bed and its individual bars at the time of abandonment. Inferred minimum sedimentation durations for the preserved elements, inferred from cross‐set thickness distributions and assumed bedform migration rates, vary within a belt from one to ten days. Using only these local sedimentological measurements, the depositional setting is interpreted as a fluvial megafan, given the similarity in river kinematics. This paper provides a systematic methodology for the future synthesis of vertical and planview data, including the drone‐equipped 2020 Mars Rover mission, to exhumed fluvial and deltaic strata

Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing

We describe a method for improving coherent control through the use of detailed knowledge of the system's Hamiltonian. Precise unitary transformations were obtained by strongly modulating the system's dynamics to average out unwanted evolution. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on multi-qubit systems. Compared to low power selective pulses, which cannot average out all unwanted evolution, these pulses are substantially shorter in time, thereby reducing the effects of relaxation. Liquid-state NMR techniques on homonuclear spin systems are used to demonstrate the accuracy of these gates both in simulation and experiment. Simulations of the coherent evolution of a 3-qubit system show that the control sequences faithfully implement the unitary operations, typically yielding gate fidelities on the order of 0.999 and, for some sequences, up to 0.9997. The experimentally determined density matrices resulting from the application of different control sequences on a 3-spin system have overlaps of up to 0.99 with the expected states, confirming the quality of the experimental implementation.Comment: RevTeX3, 11 pages including 2 tables and 5 figures; Journal of Chemical Physics, in pres

Foundations of space-time finite element methods: polytopes, interpolation, and integration

The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical foundation, or equivalently a numerical infrastructure. This foundation should include a collection of suitable elements (usually hypercubes, simplices, or closely related polytopes), numerical interpolation procedures (usually orthonormal polynomial bases), and numerical integration procedures (usually quadrature rules). It is well known that each of these areas has yet to be fully explored, and in the present article, we attempt to directly address this issue. We begin by developing a concrete, sequential procedure for constructing generic four-dimensional elements (4-polytopes). Thereafter, we review the key numerical properties of several canonical elements: the tesseract, tetrahedral prism, and pentatope. Here, we provide explicit expressions for orthonormal polynomial bases on these elements. Next, we construct fully symmetric quadrature rules with positive weights that are capable of exactly integrating high-degree polynomials, e.g. up to degree 17 on the tesseract. Finally, the quadrature rules are successfully tested using a set of canonical numerical experiments on polynomial and transcendental functions.Comment: 34 pages, 18 figure

Carotid Baroreflex Control of Heart Rate is Enhanced during Whole-body Heat Stress

Whole-body heat stress (WBH) reduces orthostatic tolerance. While impaired carotid baroreflex (CBR) function during WBH has been reported, study design considerations may limit interpretation of previous findings. We sought to test the hypothesis that CBR function is unaltered during WBH. CBR function was assessed in ten subjects using 5-sec trials of neck pressure (45, 30 and 15 Torr) and neck suction (-20, -40, -60 and - 80 Torr) during normothermia (NT) and passive WBH (Δ core temp ~1 °C). Analysis of stimulus response curves (4-parameter logistic model) for CBR control of heart rate (CBR-HR) and mean arterial pressure (CBR-MAP), as well as separate 2-way ANOVA of the hypo- and hypertensive stimuli (factor 1: thermal condition, factor 2: chamber pressure) were performed. For CBR-HR, maximal gain was increased during WBH (-0.73±0.37) compared to NT (-0.39±0.11, p=0.03). In addition, the CBR-HR responding range was increased during WBH (32±15) compared to NT (18±8 bpm, p=0.03). Separate analysis of hypertensive stimulation revealed enhanced HR responses during WBH at -40, -60 and -80 Torr (condition*chamber pressure interaction, p=0.049) compared to NT. For CBR-MAP, both logistic analysis and separate 2-way ANOVA revealed no differences during WBH. Therefore, despite marked orthostatic intolerance observed during WBH, CBR control of heart rate (enhanced) and arterial pressure (no change) is well-preserved