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NASA NTRSDate not supplied

Applying the System Complexity Metric (SCM)

A fundamental cause of difficulty in larger engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, so that there is no obvious mental model that correctly predicts its behavior. Higher complexity is usually associated with higher cost and higher failure rate. Complexity is indicated by a system having more and diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and often the emergence of unanticipated failure modes. Identifying and removing these signs of complexity should reduce complexity and improve performance. Here we limit complexity measurement to the number of components and their interactions. A System Complexity Metric (SCM) is defined as equal to the sum of the number of parts in a system, N, plus the sum of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of system block diagrams. Previous work found that life support system cost was directly proportional to SCM and that failure rate increased faster than SCM squared. SCM can be used to compare systems or to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems will be analyzed using SCM, cost, and failure rate.

Harry W Jones↗
NASA NTRS2021

Vegetation structural complexity and biodiversity in the Great Smoky Mountains

Vegetation structural complexity and biodiversity tend to be positively correlated, but understanding of this relationship is limited in part by structural metrics tending to quantify only horizontal or vertical variation, and that do not reflect internal structure. We developed new metrics for quantifying internal vegetation structural complexity using terrestrial LiDAR scanning and applied them to 12 NEON forest plots across an elevational gradient in Great Smoky Mountains National Park, USA. We asked (1) How do our newly developed structure metrics compare to traditional metrics? (2) How does forest structure vary with elevation in a high-biodiversity, high topographic complexity region? (3) How do forest structural metrics vary in the strength of their relationships with vascular plant biodiversity? Our new measures of canopy density (Depth) and structural complexity (σDepth), and their canopy height-normalized counterparts, were sensitive to structural variations and effectively summarized horizontal and vertical dimensions of structural complexity. Forest structure varied widely across plots spanning the elevational range of GRSM, with taller, more structurally complex forests at lower elevation. Vascular plant biodiversity was negatively correlated with elevation and more strongly positively correlated with vegetation structure variables. The strong correlations we observed between canopy structural complexity and biodiversity suggest that structural complexity metrics could be used to assay plant biodiversity over large areas in concert with airborne and spaceborne platforms.

Jonathan A. Walter↗
DOE OSTI2021

Binary Complex Neural Network Acceleration on FPGA

Being able to learn from complex data with phase information is imperative for many signal processing applications. Today’s real-valued deep neural networks (DNNs) have shown efficiency in latent information analysis but fall short when applied to the complex domain. Deep complex networks (DCN) , in contrast, can learn from complex data, but have high computational costs; therefore, they cannot satisfy the instant decision making requirements of many deployable systems dealing with short observations or short signal bursts. Recent, Binarized Complex Neural Network (BCNN), which integrates DCNs with binarized neural networks (BNN), shows great potential in classifying complex data in real-time. In this paper, we propose a structural pruning based accelerator of BCNN, which is able to provide more than 5000 frames/s inference throughput on edge devices. The high performance comes from both the algorithm and hardware sides. On the algorithm side, we conduct structural pruning to the original BCNN models and obtain 20 × pruning rates with negligible accuracy loss; on the hardware side, we propose a novel 2D convolution operation accelerator for the binary complex neural network. Experimental results show that the proposed design works with over 90% utilization and is able to achieve the inference throughput of 5882 frames/s and 4938 frames/s for complex NIN-Net and ResNet-18 using CIFAR-10 dataset and Alveo U280 Board.

Peng, Hongwu↗
DOE OSTI2024

Synthesis and Characterization of Uranium Complexes Supported by Substituted Aryldimethylsilylanilide Ligands

Here, we report the synthesis and characterization of substituted aryldimethylsilyldiisopropylanilide ligands and their respective bisamido complexes of U(III), (3,5-R 2 -PhMe 2 SiNDipp) 2 UI(dioxane) x (1, R = H, x= 0; 2, R = Me, x = 0; 3, R = t Bu, x = 1). We found that the steric bulk of the 3,5-R 2 -Ph ring affects the hapticity of the U–arene interaction. In the solid-state, 1 is a U–(η 6 -arene) complex, while 2 is a bis(U–(η 1 -arene)) complex. Theoretically calculated bond orders at PBE0 and PBE0-D3 levels of theory support these hapticity assignments. The 3,5- t Bu 2 -Ph rings of 3 are too bulky to interact with U and solid-state metrical parameters initially suggested a U–(η 1 -arene) interaction with one of the Dipp rings. However, bond order calculations show that this interaction is even weaker than in the previously reported ((PhMe 2 Si) 2 N) 3 U complex, leading to the conclusion that 3 is best described as a U–(η o -arene) complex. Molecular orbital analyses in conjunction with electron localization methods reveal that the U–(η 6 -arene) bonding in 1 is primarily electrostatic in nature. Some charge transfer takes place from the arene π orbitals to the U 6d/5f hybrid orbitals in addition to subtle δ-back-bonding. In 2 and 3, both π and δ interactions are substantially weaker, in agreement with the differences in the U–arene coordination modes. Surprisingly, attempts to generate less sterically bulky (3,5-R 2 -PhMe 2 SiNPh) 2 UI complexes results in disproportionation to homoleptic tetraamido (3,5-R 2 -PhMe 2 SiNPh) 4 U(IV) (4, R = H; 5, R = Me) complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Preparation, characterization, and structural studies of new ruthenium(II) and ruthenium(III) complexes incorporating pyrazole ligands

Multimetallic complexes containing disparate metals have been established to have practical utilities. We previously reported a strategy for preparing such species by using combinations of neutral pyrazole (Hpyz, C 3 N 2 H 4 ) and anionic pyrazolyl ligands (pyz, C 3 N 2 H 3 – ), and herein are reported several new complexes that should be capable of incorporating a second metal center. Two of the complexes, [Ru(1,5-cod)(Hpyz) 3 Cl][BPh 4 ] and Ru(1,5-cod)(Hpyz) 2 (pyz) 2 (cod = cyclooctadiene), were prepared from [Ru(cod)Cl 2 ] 2 , while [Ru(tmeda)(Hpyz) 2 Cl 2 ][BF 4 ] (tmeda = tetramethylethylenediamine) was prepared from the neutral Ru(II) complex Ru(tmeda)(Hpyz) 2 Cl 2 via one electron oxidation by the ferricinium ion. The first two complexes, one cationic and the other uncharged, involve Ru(II), while the tmeda complex involves Ru(III). Finally, all three species have been structurally characterized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Selective deuteration of an RNA:RNA complex for structural analysis using small-angle scattering

The structures of RNA:RNA complexes regulate many biological processes. Despite their importance, protein-free RNA:RNA complexes represent a tiny fraction of experimentally determined structures. Here, we describe a joint small-angle X-ray and neutron scattering (SAXS/SANS) approach to structurally interrogate conformational changes in a model RNA:RNA complex. Using SAXS, we measured the solution structures of the individual RNAs and of the overall RNA:RNA complex. With SANS, we demonstrate, as a proof of principle, that isotope labeling and contrast matching (CM) can be combined to probe the bound state structure of an RNA within a selectively deuterated RNA:RNA complex. Furthermore, we show that experimental scattering data can validate and improve predicted AlphaFold 3 RNA:RNA complex structures to reflect its solution structure. In conclusion, our work demonstrates that in silico modeling, SAXS, and CM-SANS can be used in concert to directly analyze conformational changes within RNAs when in complex, enhancing our understanding of RNA structure in functional assemblies.

HIV-1 dimerization initiation site↗
DOE OSTI2024

Spectroscopic and Computational Evidence of Uranium Dihydrogen Complexes

Dihydrogen complexation, a phenomenon with robust precedent in the transition metal series, is spectroscopically detected for a uranium(III) complex and thereby extended for the first time to the 5f series. The vacant coordination site and low valence of (C 5 H 4 SiMe 3 ) 3 U prove to be key to the reversible formation of (C 5 H 4 SiMe 3 ) 3 U–H 2 (complex 1), and the paramagnetism of the f 3 center facilitates the detection of complex 1 by NMR spectroscopy. Density functional theory calculations reveal that the delocalization of the 5f electron density from (C 5 H 4 SiMe 3 ) 3 U onto the side-on dihydrogen ligand is crucial to complex formation, an unusual bonding situation for an actinide acid–base complex. Here, the spectroscopic and computational results are compared to those reported for lanthanide metallocenes to yield insight into the nature of–and future possibilities for–f-element dihydrogen complexation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

An Impedance-Based Complexity Metric for Unmanned Aircraft System Traffic Scenario Classification

This paper introduces an impedance-based metric to capture the complexity of a given unmanned aircraft system traffic scenario. The metric accounts for both the number of aircraft and the traffic flow pattern. The work presented here extends an earlier approach that introduced another scenario complexity metric based on the number of potential conflicts weighted by the conflict resolution cost associated. Complexity measurements for randomly-generated scenarios were produced through high-fidelity fast-time simulations and treated as baseline. Then the impedance based metric was evaluated, for the same scenarios, without the need for an actual flight simulation and a conflict resolution method. The results show that the impedance-based metric has a strong correlation to the baseline data and performs marginally better than the weighted conflict-based complexity metric introduced in the earlier work. The metric computation generates impedance maps which are useful for identifying high complexity regions in a scenario, where flight plan changes might be necessitated. This metric can therefore be used, in conjunction with other complexity metrics, to inform adequate traffic management strategies and classify a traffic scenario as acceptable, unacceptable or acceptable with changes made to flight plans that pass through the high complexity regions. The metric can also be used as a guidance metric for strategic conflict management methods.

Complexity↗
DOE OSTI2022

Conjugated Polyelectrolyte-Based Complex Fluids as Aqueous Exciton Transport Networks

The ability to assemble artificial systems that mimic aspects of natural light-harvesting functions is fascinating and attractive for materials design. Given the complexity of such a system, a simple design pathway is desirable. Here, we argue that associative phase separation of oppositely charged conjugated polyelectrolytes (CPEs) can provide such a path in an environmentally benign medium: water. We find that complexation between an exciton–donor and acceptor CPE leads to formation of a complex fluid. We interrogate exciton transfer from the donor to the acceptor CPE within the complex fluid and find that transfer is highly efficient. We also find that excess molecular ions can tune the modulus of the inter-CPE complex fluid. Even at high ion concentrations, CPEs remain complexed with significantly delocalized electronic wavefunctions. In conclusion, our work lays the rational foundation for complex, tunable aqueous light-harvesting systems via the intrinsic thermodynamics of associative phase separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Half‐sandwich ruthenium complex with a very low overpotential and excellent activity for water oxidation under acidic conditions

Abstract Molecular catalysts are acknowledged for the ability to design reaction sites within well‐defined structures to achieve high catalytic activities. However, in many cases, molecular catalysts undergo structural changes to some other form(s), which are finally the real catalysts. Here, we report two half‐sandwich ruthenium complexes; [Ru([9]aneN3)(bpy)Cl] + 3 and [Ru([9]aneN3)(pic)OH 2 ] 2+ 4 , based on the macrocyclic 1,4,7‐triazacyclononane ([9]aneN3) ligand for water oxidation (WO). The two complexes have similar core but different ancillary ligands, which greatly affected their stability as well as activity for WO. Complex 3 retained high stability and excellent activity (turnover number [TON] = 1250) in chemical WO and first‐order reaction kinetics with respect to [Ce IV ] with a calculated rate constant ( k cat ) of 34.59 s −1 . Further, the complex demonstrated very low overpotential of ~210 mV in electrochemical WO. At an overpotential of only 400 mV, turnover frequency (TOF) of complex 3 was electrochemically estimated to be 131.2 s −1 . In contrast, complex 4 underwent picolinate ligand dissociation, as a deactivation pathway, to form the tri‐aqua derivative. Density functional theory (DFT) calculations are used to explain the dissociation mechanism of picolinate ligand in complex 4 , which happens through a stepwise dissociation mechanism.

Younus, Hussein A.↗
DOE OSTI2024

Elucidating the Structure of the Eu‐EDTA Complex in Solution at Various Protonation States

Abstract Ethylenediaminetetraacetic acid (EDTA), which has two amine and four carboxylate protonation sites, forms stable complexes with lanthanide ions. This work analyzes the coordination structure, in atomic resolution, of the Eu 3+ ion complexed with EDTA in all its protonation states in aqueous solution. Eu‐EDTA complexes were modeled using classical molecular dynamics (MD) simulations using force field parameters optimized with ab initio molecular dynamics (AIMD) simulations. Structures from the MD simulations were used to predict extended X‐ray absorption fine structure (EXAFS) spectra and compared with EXAFS measurements of the Eu 3+ aqua ion and Eu‐EDTA complexes at pH 3 and 11. This work details how Eu‐EDTA complex coordination structures change with increasing protonation of the EDTA ligand in the complex, from the tightly bound unprotonated complex to the unbinding of the fully protonated EDTA ligand from the Eu 3+ ion as both become solvated by water. Agreement between predicted and measured EXAFS spectra supports the findings from simulation.

Chemistry↗
DOE OSTI2020

Quantum complexity of time evolution with chaotic Hamiltonians

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum error correction from complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the “mutual purity” of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix ρAB is the difference $\mathcal{F}$ p ($A : B$) ≡ $\mathrm{T}$r $p^{2}_{AB}$ - $\mathrm{T}$r $p^{2}_{A}$ $\mathrm{T}$r $p^{2}_{B}$. We show that when the encoding complexity is small, the mutual purity is O(1) for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming O(1/N) for O(log N) encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of O(e -N ). We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion A with sufficiently high encoding complexity is robustly protected against low-rank errors acting on A with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region A despite being encoded in it.

1/N expansion↗
DOE OSTI2020

Bio-reduction of ferrihydrite-montmorillonite-organic matter complexes: Effect of montmorillonite and fate of organic matter

Organic matter (OM) is often associated with Fe (hydr)oxides such as ferrihydrite (Fh) in soils and sediments, forming binary Fh-OM complexes. Microbial reduction of Fh results in destabilization of the complexes and mineral/OM transformation. However, little is known about the role of clay minerals in such processes, despite their common co-existence with Fh and OM in natural environments. Here Fh-OM complexes were synthesized in the presence of montmorillonite (SWy-2), forming ternary Fh-(SWy-2)-OM complexes. A metal-reducing bacterium Geobacter sulfurreducens was used to reduce Fh in the complexes under circumneutral pH and anoxic conditions with or without H 2 as extra electron donor. Various spectroscopy and mass spectrometry methods were used to monitor the progress of Fh bio-reduction and mineral/OM transformation. Results showed that G. sulfurreducens utilized mineral-bound OM as electron donor and/or carbon source to couple with Fh reduction. Relative to Fh-OM complex, Addition of SWy-2 to Fh-OM complex enhanced the bio-reduction extent of Fh by increasing the proportion of bioavailable OM that was weakly bound to SWy-2. However, its effect on the bio-reduction rate was variable. SWy-2 initially decreased the rate, because it spatially separated OM (electron donor) from Fh (electron acceptor). During later incubation, SWy-2 increased the reduction rate by sorbing biogenic Fe 2+ that would otherwise passivate the Fh and cell surfaces. Bio-reduction transformed mineral-bound OM to microbial products (e.g. necromass, extracellular polymeric substances), but organic compounds with aromatic structures, carboxyl groups and large molecular weight were more resistant to desorption and oxidation. The persistence of these compounds against bio-reduction induced transformation is likely due to their stronger binding with minerals and/or lower nominal oxidation states of carbon relative to other compounds. Our results provide new insights into the role of clay minerals in regulating biogeochemical cycling of solid-phase Fe and transformation of mineral-associated OM in anoxic soil environments.

58 GEOSCIENCES↗
DOE OSTI2020

Reduction of uranyl and uranyl-organic complexes mediated by magnetite and ilmenite: A combined electrochemical AFM and DFT study

Reduction of mobile aqueous uranyl complexes can be hindered by the strength of the uranyl-ligand complex and the resistivity of the complexes to electron transfer. Semiconducting solids, such as magnetite (Fe 3 O 4 ) and ilmenite (FeTiO 3 ), can facilitate otherwise-slow electron transfer between the reductant and oxidant, especially if these species are adsorbed on their surfaces as inner-sphere complexes. Electrons can then be shuttled through the surface or the structure. This process can be facilitated by either finding a new electron transfer path or by weakening or destroying the ligand-uranyl complex. Using in situ electrochemical atomic force microscopy (EC-AFM), we imaged reduction products of uranyl as mediated by magnetite and ilmenite in the absence or presence of the organic ligands, ethylenediaminetetraacetate (EDTA) and oxalate. In situ images of uranyl reduction show gradual nucleation and growth of reduced uranium on the mineral surfaces with decreasing reduction potentials. X-ray photoelectron spectroscopy (XPS) measurements indicate pentavalent uranium as the dominant uranium species resulting from uranyl reduction mediated by magnetite and ilmenite. The reduction potentials of uranyl-organic species relevant to our reaction system, (U VI O 2 ∙oxalate) 0 and (U VI O 2 ∙HEDTA) - , are derived using quantum–mechanical modeling and compared with the midpoint potentials obtained from cyclic voltammetry measurements. The spectroscopic, electrochemical, and computational data suggest that the catalysis of Fe-bearing minerals facilitates the reduction of uranyl-organic complexes. U(VI)-oxalate complexes are redox-active and participate directly in the reduction mediated by magnetite. In the presence of EDTA, reduction of uranyl may proceed in concert with ligand exchange between metals (i.e., U and Fe) on the mineral surface. Finally, the proposed mechanism is the breaking of uranyl-organic bonds upon interaction with the mineral surface followed by the formation of Fe-organic bonds, thereby allowing the reduction of hexavalent uranyl to pentavalent one.

58 GEOSCIENCES↗
DOE OSTI2022

S K-edge XAS of Cu Ⅱ , Cu Ⅰ , and Zn Ⅱ oxidized Dithiolene complexes: Covalent contributions to structure and the Jahn-Teller effect

We report reduced dithiolene ligands are bound to high valent Mo centers in the active site of the oxotransferase family of enzymes. Related model complexes have been studied with great insight by Prof. Holm and his colleagues. This study focuses on the other limit of dithiolene chemistry: an investigation of the 2-electron oxidized dithiolene bound to low-valent late transition metal (TM) ions (Zn II , Cu I , and Cu II ). The bonding descriptions of the oxidized dithiolene [N,N-dimethyl piperazine 2,3-dithione (Me 2 Dt 0 )] complexes are probed using S K-edge X-ray absorption spectroscopy (XAS) and the results are correlated to density functional theory (DFT) calculations. These experimentally supported calculations are then extended to explain the different geometric structures of the three complexes. The Zn II (Me 2 Dt 0 ) 2 complex has only ligand-ligand repulsion so it is stabilized at the D 2d symmetry limit. The Cu I (Me 2 Dt 0 ) 2 complex has additional weak backbonding thus distorts somewhat from D 2d toward D 2h symmetry. The Cu II (Me 2 Dt 0 ) 2 complex has a strong σ donor bond that leads to both a large Jahn-Teller stabilization to D 2h and an additional covalent contribution to the geometry. The combined strong stabilization results in the square planar, D 2h structure. This study quantifies the competition between the ligand-ligand repulsion and the change in electronic structures in determining the final geometric structures of the oxidized dithiolene complexes, and provides quantitative insights into the Jahn-Teller stabilization energy and its origin.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Physical structure of constitutional isomers influences antiproliferation activity of thiosemicarbazone-alkylthiocarbamate copper complexes

A series of hybrid thiosemicarbazone-alkylthiocarbamate copper complexes with similar electronic environments but distinct physical structures have been prepared, characterized, and evaluated for antiproliferation activity. The complexes include the constitutional isomers (1-phenylpropane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 1 ) and (1-phenylpropane-1-one-(N-methylthiosemicarbazonato)-2-imine-(O-ethylthiocarbamato))copper(II) (CuL 2 ) along with (1-propane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 3 ). Complexes CuL 1 and CuL 2 differ in the positions of the pendent thiosemicarbazone (TSC) and alkylthiocarbamate (ATC) moieties on the 1-phenylpropane backbone. Complex CuL 3 employs a propane backbone with the TSC in the 2-position as in CuL 1 . The isomer pair CuL 1 and CuL 2 have equivalent electronic environments with indistinguishable Cu II/I potentials (E 1/2 = -0.86 V vs. ferrocenium/ferrocene) and electron paramagnetic resonance (EPR) spectra (g ∥ = 2.26, g ⊥ = 2.08). The electronic structure of CuL 3 has a similar E 1/2 of -0.84 V and identical EPR parameters to CuL 1, 2 . Single crystal X-ray diffraction studies confirm a consistent donor environment with no substantial variation in the Cusingle bondN or Cusingle bondS bond distances and angles between the complexes. The antiproliferation activities of the CuL 1–3 were evaluated against the lung adenocarcinoma cell line (A549) and nonmalignant lung fibroblast cell line (IMR-90) using the MTT assay. CuL 1 had the highest A549 activity ( A549 EC 50 = 0.065 μM) and selectivity ( IMR-90 EC 50 / A549 EC 50 = 20). The constitutional isomer CuL 2 displayed decreased A549 activity (0.18 μM) and selectivity (10.6). The complex CuL 3 displayed activity (0.009 μM) similar to CuL 1 but with a lack of selectivity (1.0). Cellular copper loading determined by ICP-MS was consistent with the activity and selectivity trends. The complexes CuL 1–3 did not induce reactive oxygen species (ROS) generation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum complexity in gravity, quantum field theory, and quantum information science

Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. Here, we seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.

Baiguera, Stefano [Istituto Nazionale di Fisica Nu↗