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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.
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.
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.
Focal polarization is necessary for finely arranged cell-cell interactions. The yeast mating projection, with its punctate polarisome, is a good model system for this process. We explored the critical role of the polarisome scaffold protein Spa2 during yeast mating with a hypothesis motivated by mathematical modeling and tested by in vivo experiments. Our simulations predicted that two positive feedback loops generate focal polarization, including a novel feedback pathway involving the N-terminal domain of Spa2. We characterized the latter using loss-of-function and gain-of-function mutants. The N-terminal region contains a Spa2 Homology Domain (SHD) which is conserved from yeast to humans, and when mutated largely reproduced the spa2Δ phenotype. Our work together with published data show that the SHD domain recruits Msb3/4 that stimulates Sec4-mediated transport of Bud6 to the polarisome. There, Bud6 activates Bni1-catalyzed actin cable formation, recruiting more Spa2 and completing the positive feedback loop. We demonstrate that disrupting this loop at any point results in morphological defects. Gain-of-function perturbations partially restored focal polarization in a spa2 loss-of-function mutant without restoring localization of upstream components, thus supporting the pathway order. Thus, we have collected data consistent with a novel positive feedback loop that contributes to focal polarization during pheromone-induced polarization in yeast.
The National Reactor Innovation Center (NRIC) at Idaho National Laboratory (INL) in Idaho Falls, Idaho, was authorized under the Nuclear Energy Innovation Capabilities Act (Public Law 115–248) to provide private sector technology developers with resources and infrastructure for testing, demonstration, and performance assessment to accelerate deployment of new advanced reactor technology concepts. NRIC’s mission is to enable clean, affordable, reliable energy by supporting U.S. government investments in nuclear energy research, development, demonstration, and commercialization of new nuclear energy systems. It intends to provide existing facilities and other undeveloped and previously developed sites at INL to advanced reactor vendors for prototype technology testing and deployment. Some of these demonstration projects may be subject to DOE authorization, while other projects may require approval by the U.S. Nuclear Regulatory Commission (NRC) prior to construction and operation. NRIC and INL are considering whether to pursue one or more ESPs to help facilitate new reactor deployment at the INL Site. An ESP would allow early investment in licensing infrastructure in advance of a reactor design being ready to deploy. Through the ESPs, NRIC would help reduce the cost and time required to deploy demonstration reactors at the INL Site. This also will allow INL to bring its nuclear and siting experience to the ESP development process allowing for better and more efficient improvements and utilization of the Site. A preapproved ESP at INL will also remove the uncertainty of NRC siting approvals from the demonstration project proponents, who may not be well positioned to complete the analyses in a timely manner. The purpose of this NRIC ESP roadmap is to provide rigor and understanding needed for INL and DOE decision-makers to make data-informed decisions on pursuing NRC ESPs in support of future advanced reactor demonstrations at INL. The roadmap provides a structured method for addressing potential challenges and identifying options for resolution.
To understand how the composition of novel lubricant additives and their ash interact with gasoline particulate filters (GPFs), an accelerated aging protocol was conducted using three lubricant additive formulations and two GPF types. The additive packages (adpaks) consisted of Ca+Mg detergent in a 3:1 or 0:1 ratio and an anti-wear component—either zinc dialkyl dithiophosphate (ZDDP) or a novel phosphonium-phosphinate ionic liquid (IL) substitute. The particulate sampling captured amount/compositions of particulate matter (PM) generated, total particulate number, and size distribution. Five ash loadings were completed. GPF position and adpak composition affected the backpressure, ash composition, ash morphology, and captured mass. The particulate sampling indicated that the ash component consisted primarily of particles less than 50 nm in size and that the Mg-only adpak resulted in more particulate of 50–400 nm in size. Postmortem materials characterization indicated GPFs in the underfloor position had deeper penetration of ash into the walls compared to the close-coupled position. Additionally, the Mg-only adpak had a higher filter collection efficiency (>90%) and the ash particles consisted of a higher concentration of dense ash material. In contrast, four of the 3:1 Ca:Mg lubricant adpaks resulted in a collection efficiency of only 40–50%. Although the collection efficiency was higher with the Mg-only adpak, the ash layer in the GPF was not thicker, nor was the penetration into the wall more significant, and surprisingly the full useful life (FUL) backpressure was lower than with Ca:Mg adpaks. The higher density of the Mg-derived ash was the only detectable difference. A possible explanation of this observation is that Mg ash has a lower melting point and is more susceptible to densification during combustion or GPF regeneration. The substitution of IL in place of the ZDDP did not lead to any notable changes in collection efficiency or location of the ash.
The duality between color and kinematics brings many simplifications to the construction of scattering amplitudes. Here, we show that satisfaction of the tree-level Bern-Carrasco-Johansson relations can dramatically simplify loop computations even when the loop-level relations are not explicitly satisfied. We introduce an agglomerative algorithm, color-dual cut tiling, that builds the entire integrand from the simplest on-shell conditions applied to a seed of off-shell integrand information. Specifically, we demonstrate that for two-to-two scattering at three loops in the maximally supersymmetric gauge theory there is sufficient information contained in planar cuts—completely determined by positivity constraints—to generate all of the nonplanar sector. We further make use of the generalized double copy to generate a representation of maximally supersymmetric gravity as a functional of the planar SYM input. We close with comments on generalizations and possible applications of the approach. Published by the American Physical Society 2025
Virus-like particles (VLPs) are a class of biomaterials which serve as platforms for achieving the desired functionality through interior and exterior modifications. Through ionic strength-mediated electrostatic interactions, VLPs have been assembled into hierarchically ordered materials. This work builds on predictive models to prepare polymer-coated VLP dusters at very low ionic strength. Zeta potential measurements showed that the clusters carried a strongly positive charge, a complete charge reversal from the VLP building block. SAXS analysis confirmed polymer adsorption onto the VLP exterior. Furthermore, we then studied the activity of an encapsulated enzyme toward small molecular and macromolecular substrates to determine the effect of each component of the hierarchically assembled material. We found that while encapsulation and polymer coating did not have a large effect on access to the enzyme by its native, small molecular substrate, substrate modification with a macromolecule caused the polymer coating and encapsulation to affect the access to the enzyme.
We present a new class of AI models for the detection of quasi-circular, spinning, non-precessing binary black hole mergers whose waveforms include the higher order gravitational wave modes ($\ell$, |m|) = {(2,2), (2,1), (3,3), (3,2), (4,4)}, and mode mixing effects in the $\ell$ = 3, |m| = 2 harmonics. These AI models combine hybrid dilated convolution neural networks to accurately model both short- and long-range temporal sequential information of gravitational waves; and graph neural networks to capture spatial correlations among gravitational wave observatories to consistently describe and identify the presence of a signal in a three detector network encompassing the Advanced LIGO and Virgo detectors. We first trained these spatiotemporal-graph AI models using synthetic noise, using 1.2 million modeled waveforms to densely sample this signal manifold, within 1.7 h using 256 NVIDIA A100 GPUs in the Polaris supercomputer at the Argonne Leadership Computing Facility. This distributed training approach exhibited optimal classification performance, and strong scaling up to 512 NVIDIA A100 GPUs. With these AI ensembles we processed data from a three detector network, and found that an ensemble of 4 AI models achieves state-of-the-art performance for signal detection, and reports two misclassifications for every decade of searched data. We distributed AI inference over 128 GPUs in the Polaris supercomputer and 128 nodes in the Theta supercomputer, and completed the processing of a decade of gravitational wave data from a three detector network within 3.5 h. Finally, we fine-tuned these AI ensembles to process the entire month of February 2020, which is part of the O3b LIGO/Virgo observation run, and found 6 gravitational waves, concurrently identified in Advanced LIGO and Advanced Virgo data, and zero false positives. This analysis was completed in one hour using one NVIDIA A100 GPU.
‘Candidatus Liberibacter’ is a group of bacterial species that are obligate intracellular plant pathogens and cause Huanglongbing disease of citrus trees and Zebra Chip in potatoes. Here, we examined the extent of intra- and interspecific genetic diversity across the genus using comparative genomics. Our approach examined a wide set of Liberibacter genome sequences including five pathogenic species and one species not known to cause disease. By performing comparative genomics analyses, we sought to understand the evolutionary history of this genus and to identify genes or genome regions that may affect pathogenicity. With a set of 52 genomes, we performed comparative genomics, measured genome rearrangement, and completed statistical tests of positive selection. We explored markers of genetic diversity across the genus, such as average nucleotide identity across the whole genome. These analyses revealed the highest intraspecific diversity amongst the ‘Ca. Liberibacter solanacearum’ species, which also has the largest plant host range. We identified sets of core and accessory genes across the genus and within each species and measured the ratio of nonsynonymous to synonymous mutations (dN/dS) across genes. We identified ten genes with evidence of a history of positive selection in the Liberibacter genus, including genes in the Tad complex, which have been previously implicated as being highly divergent in the ‘Ca. L. capsica’ species based on high values of dN.
We report the dielectric constant of 1 M LiPF 6 in EC:EMC 3:7 w/w (ethylene carbonate/ethyl methyl carbonate) in addition to neat EC:EMC 3:7 w/w. Using three Debye relaxations, the static permittivity value, or dielectric constant, is extrapolated to 18.5, which is compared to 18.7 for the neat solvent mixture. The EC solvent is found to strongly coordinate with the Li + cations of the salt, which results in a loss of dielectric contribution to the electrolyte. However, the small amplitude and large uncertainty in relaxation frequency for EMC cloud definitive identification of the Li + solvation shell. Importantly, the loss of the free EC permittivity contribution due to Li + solvation is almost completely balanced by the positive contribution of the associated LiPF 6 salt, demonstrating that a significant quantity of dipolar ion pairs exists in 1 M LiPF 6 in EC:EMC 3:7.