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We design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Here, our methods preserves complete positivity and are trace preserving.
Participation of U.S. scientists on the COPERNIC (COmplete Positive ions, Electrons and Ram Negative Ion measurements near Comet Halley) plasma experiment on the Giotto mission is described. The experiment consisted of two detectors: the EESA (electron electrostatic analyzer) which provided three-dimensional measurements of the distribution of electrons from 10 eV to 30 keV, and the PICCA (positive ion cluster composition analyzer) which provided mass analysis of positively charged cold cometary ions from mass 10 to 210 amu. In addition, a small 3 deg wide sector of the EESA looking in the ram direction was devoted to the detection of negatively charged cold cometary ions. Both detectors operated perfectly up to near closest approach (approx. 600 km) to Halley, but impacts of dust particles and neutral gas on the spacecraft contaminated parts of the data during the last few minutes. Although no flight hardware was fabricated in the U.S., The U.S. made very significant contributions to the hardware design, ground support equipment (GSE) design and fabrication, and flight and data reduction software required for the experiment, and also participated fully in the data reduction and analysis, and theoretical modeling and interpretation. Cometary data analysis is presented.
Accurate modeling of decoherence errors in quantum processors is crucial for analyzing and improving gate fidelities. To increase the accuracy beyond that of the Lindblad dynamical map, several generalizations have been proposed, and the exploration of simpler and more systematic frameworks is still ongoing. In this paper, we introduce a decoherence model based on the Keldysh formalism. This formalism allows us to include non-periodic drives and correlated quantum noise in our model. In addition to its wide range of applications, our method is also numerically simple, and yields a CPTP map. These features allow us to integrate the Keldysh map with quantum-optimal-control techniques. We demonstrate that this strategy generates pulses that mitigate correlated quantum noise in qubit state-transfer and gate operations.
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional C* -algebras. In other words, we prove an analogue of Bayes' theorem in the joint classical and quantum context. Our analogue is justified by recent advances in categorical probability theory, which have provided an abstract formulation of the classical Bayes' theorem. In the process, we further develop non-commutative almost everywhere equivalence and illustrate its important role in non-commutative Bayesian inversion. The construction of such Bayesian inverses, when they exist, involves solving a positive semidefinite matrix completion problem for the Choi matrix. This gives a solution to the open problem of constructing Bayesian inversion for completely positive unital maps acting on density matrices that do not have full support. In conclusion, we illustrate how the procedure works for several examples relevant to quantum information theory.
Highlights: • Non-Markovian master equation for open quantum system with power-law memory is proposed. • Non-Markovian dynamics of two-level quantum system with memory is described. • Solutions of non-Markovian quantum master equations are derived. • Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. • Exact solution of non-Markovian equations of system with memory is proposed. In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.
Recent advances in the Global Positioning System (GPS) technology have initiated a new era in aerospace navigation and control. GPS receivers have become increasingly compact and affordable, and new developments have made attitude determination using subcentimeter positioning among two or more antennas feasible for real-time applications. GPS-based attitude control systems will become highly portable packages which provide time, navigation, and attitude information of sufficient accuracy for many aerospace needs. A typical spacecraft application of GPS attitude determination is a gravity gradient stabilized satellite in low Earth orbit that employs a GPS receiver and four body mounted patch antennas. The coupled, linearized equations of motion enable complete position and attitude information to be extracted from only two antennas. A discussion of the various error sources for spaceborne GPS attitude measurement systems is included. Attitude determination of better than 0.3 degrees is possible for 1 meter antenna separation. Suggestions are provided to improve the accuracy of the attitude solution.
Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.
We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional C* -algebras.
We provide a theory, algorithms, and simulations of nonequilibrium quantum systems using a one-dimensional (1D) completely positive (CP), matrix-product (MP) density-operator (𝜌) representation. By generalizing the matrix product state's orthogonality center, to additionally store positive classical mixture correlations, the MP𝜌 factorization naturally emerges. In this setting, we analytically and numerically examine the virtual gauge freedoms associated with the representation of quantum density operators. Based on this perspective, we simplify algorithms in certain limits to speed up the integration of the canonical-form master-equation dynamics. This enables us to quickly evolve under the dynamics of two-body quantum channels without resorting to optimization-based methods. In addition to this technical advance, we also scale up numerical examples and discuss implications for accurately modeling hardware architectures and predicting their performance in the near term. This includes an example of the quantum to classical transition of informationally leaky, i.e., decohering, qubits. In this setting, because of loss from environmental interactions, nonlocal complex coherence correlations are converted into global incoherent classical statistical mixture correlations. Lastly, the representation of both global and local correlations is discussed. We expect this work to have applications in additional nonequilibrium settings, beyond qubit engineering.
We present a noise deconvolution technique for obtaining noiseless expectation values of noisy observables at the output of multiqubit quantum channels. For any number of qubits or in the presence of correlations, our protocol applies to any mathematically invertible noise model, even when its inverse map is not physically implementable, i.e., when it is neither completely positive nor trace preserving. For a generic observable affected by Pauli noise it provides a quadratic speedup, always producing a rescaling of its Pauli basis components. We show that it is still possible to achieve the deconvolution while experimentally estimating the noise parameters, whenever these are unknown (bypassing resource-heavy techniques such as quantum process tomography). We provide a simulation, with examples for both Pauli and non-Pauli channels.
Here we show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the R(SIC) matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of circuits.
Here, we introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.
Remote actuation of a gripper shaft affects vertical engagement between a drive shaft and control rod. A secondary function of the gripper is to provide remote indication of positive completion of the gripping or ungripping operation.
The Giotto Complete Positive ion, Electron and Ram Negative Ion measurements near Comet Halley plasma experiment identified regions in which the solar wind interaction with the cometary plasma displayed characteristic features. Beginning 4.6 million km from the comet there is an upstream region with sporadic connection to the comet. An electron foreshock is present up to 250,000 km away from the bow shock. A bow shock is detected at 1.15 million km. Between the bow shock and the cometopause the outer regions can be divided into three parts. A cometopause is found at 135,000 km, and a density decrease is detected at 45,000 km from the comet. The detailed plasma features associated with these regions are described.
Three-dimensional plasma electron (22 eV to 30 keV) observations upstream of Comet Halley bow shock, obtained by the RPA-1 COPERNIC (Reme Plasma Analyzer - Complete Positive Ion, Electron and Ram Negative Ion Measurements near Comet Halley) experiment on the Giotto spacecraft are reported. Besides electron distributions typical of the undisturbed solar wind and backstreaming electrons observed when the magnetic field line intersects the cometary bow shock, a new type of distribution, characterized by enhanced low energy (less than 100 eV) flux which peaks at 90-deg pitch angles is found. These are most prominent when the spacecraft is on field lines which pass close to but are not connected to the bow shock. The 90-deg pitch angle electrons appear to have been adiabatically heated by the increase in the magnetic field strength resulting from the compression of the upstream solar wind plasma by the cometary mass loading. A model calculation of this effect which agrees qualitatively with the observed 90-deg flux enhancements is presented.
This investigation involved the analysis of electron plasma and heavy ion composition measurements made by the COPERNIC (COmplete Positive ion, Electron, and Ram Negative Ion measurements near Comet Halley) plasma experiment during the close fly-by of Halley by the European Space Agency's Giotto spacecraft. The experiment provided measurements of the full 3-dimensional distribution of 10 eV-30 keV electrons, and mass analysis of cold cometary ions from 10-210 amu. The analysis of the COPERNIC data has yielded some remarkable results, including: The discovery of negatively charged ions in the inner coma; the discovery of far heavier (mass is greater than 50 amu) ions than predicted, dominated by complex molecular ions made up of C, H, O, and N; the discovery of an adiabatic heating effect on electrons from the compression of the solar wind plasma; the identification of several organic and sulfur bearing ions; and the discovery of a new 'mystery region' where electrons are accelerated to high energies. These discoveries were in addition to the detailed analysis of 'expected' features at Comet Halley. Although this grant has expired, analysis continues on the data at a low (unfunded) level, and it is expected that more significant results will be obtained. A bibliography of the papers resulting from this research is attached, and a copy of each paper is included.
The three-dimensional electron spectrometer of the Reme plasma analyzer-complete positive ion, electron and ram negative ion measurements near comet Halley (RPA-COPERNIC) experiment aboard the Giotto spacecraft, although damaged during the comet Halley encounter in March 1986, has provided very new results during the encounter on July 10, 1992, with the weakly active comet Grigg-Skjellerup (G-S). The main characteristic features of the highly structured interaction region extending from approximately 26,500 km inbound to approximately 37,200 km outbound are presented. These results are compared to the results obtained by the same instrument during the Giotto comet Halley fly-by. Despite the large difference in the size of the interaction regions (approximately 60,000 km for G-S, approximately 2000,000 km for Halley) due to 2 orders of magnitude difference in cometary neutral gas production rate, there are striking similarities in the solar wind interactions with the two comets.
Complete nucleotide sequences are presented for 5S rRNA from Bacillus subtilis, B. firmus, B. pasteurii, B. brevis, Lactobacillus brevis, and Streptococcus faecalis, and 5S rRNA oligonucleotide catalogs and partial sequence data are given for B. cereus and Sporosarcina ureae. These data demonstrate a striking consistency of 5S rRNA primary and secondary structure within a given bacterial grouping. An exception is B. brevis, in which the 5S rRNA sequence varies significantly from that of other bacilli in the tuned helix and the procaryotic loop. The localization of these variations suggests that B. brevis occupies an ecological niche that selects such changes. It is noted that this organism produces antibiotics which affect ribosome function.