Deep generative modeling for volume reconstruction in cryo-electron microscopy
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59 BASIC BIOLOGICAL SCIENCES↗
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Scalable Experimental Bounds for Entangled Quantum State Fidelities
Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is important for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as O(3 N for N-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma et al.established that the complexity could be drastically reduced when looking at fidelity lower bounds for states that exhibit symmetries, such as Dicke states and GHZ states. These bounds must still be tight enough for larger states to provide reasonable estimations on NISQ devices. For the first time and more than 15 years after the theoretical introduction, we report meaningful lower bounds for the state preparation fidelity of all Dicke states up to N=10 and all GHZ states up to N=20 on Quantinuum H1 ion-trap systems using efficient implementations of recently proposed scalable circuits for these states. Our achieved lower bounds match or exceed previously reported exact fidelities on superconducting systems for much smaller states. Furthermore, we provide evidence that for large Dicke states |$D^{N}_{N/2}\rangle$, we may resort to a GHZ-based approximate state preparation to achieve better fidelity. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.
97 MATHEMATICS AND COMPUTING↗
Effects of Acute Exposures to Carbon Dioxide Upon Cognitive Functions
Large quantities of carbon dioxide (CO2) originate from human metabolism and typically, within spacecraft, remain about 10-fold higher in concentration than at the earth's surface. There have been recurring complaints by crew members of episodes of "mental viscosity" adversely affecting their performance, and there is evidence from the International Space Station (ISS) that associates CO2 levels with reports of headaches by crewmembers. Additionally, there is concern that CO2 may contribute to vision impairment and intracranial pressure that has been observed in some crewmembers. Consequently, flight rules have been employed to control the level of CO2 below 4 mm Hg, which is well below the existing Spacecraft Maximum Allowable Concentration (SMAC) of 10 mm Hg for 24-hour exposures, and 5.3 mm Hg for exposures of 7 to 180 days. However, the flight rule imposed limit, which places additional demands upon resources and current technology, still exceeds the lower bound of the threshold range for reportable headaches (2 - 5 mm Hg). Headaches, while sometime debilitating themselves, are also symptoms that can provide evidence that physiological defense mechanisms have been breached. The causes of the headaches may elicit other subtle adverse effects that occur at CO2 levels well below that for headaches. The concern that CO2 may have effects at levels below the threshold for headaches appears to be substantiated in unexpected findings that CO2 at concentrations below 2 mm Hg substantially reduced some cognitive functions that are associated with the ability to make complex decisions in conditions that are characterized by volatility, uncertainty, complexity, ambiguity, and delayed feedback. These are conditions that could be encountered by crews in off-nominal situations or during the first missions beyond low earth orbit. If findings of the earlier study are confirmed in crew-like subjects, our findings would provide additional evidence that CO2 may need to be controlled at levels that are well below current spacecraft limits. Our study will extend the earlier study to determine if crew-like subjects are similarly effected by CO2. In addition to employing the Strategic Management Simulation tool, we will use the Cognition battery of psychometric measures that are being utilized aboard the ISS. It will be important to learn, by using Cognition, if additional cognitive domains are sensitive to concentrations of CO2 at or below limits currently controlled by flight rules. While spaceflight Cognition data will greatly enhance the knowledge base related to inflight behavioral health and performance, some of the measures may be influenced by fatigue (related to sleep deprivation and or workload) and changes in circadian rhythms. Therefore our use of this battery of tests in a well-controlled, ground-based study that is free of these potential confounding influences will establish a baseline terrestrial data set against which Cognition data collected in flight may be assessed. The findings from this study will be useful to the NASA Toxicology Office and the National Research Council Committee on Toxicology, which assists NASA in setting environmental standards, for revision of the SMAC for CO2, and for designing further studies on effects of CO2 upon cognitive functions.
Scully, R. R.↗
Predictions of a population of cataclysmic variables in globular clusters
We have studied the number of cataclysmic variables (CVs) that should be active in globular clusters during the present epoch as a result of binary formation via two-body tidal capture. We predict the orbital period and luminosity distributions of CVs in globular clusters. The results arebased on Monte Carlo simulations combined with evolution calculations appropriate to each system formed during the lifetime of two specific globular clusters, omega Cen and 47 Tuc. From our study of these two clusters, which represent the range of core densities and states of mass segregation that are likely to be interesting, we extrapolate our results to the Galactic globlular cluster system. Although there is at present little direct observational evidence of CVs in globular clusters, we find that there should be a large number of active systems. We predict that there should be more than approximately 100 CVs in both 47 Tuc and omega Cen and several thousand in the Galactic globular cluster system. These numbers are based on two-body processes alone and represent a lower bound on the number of systems that may have been formed as a result of stellar interaction within globular clusters. The relation between these calculations and the paucity of optically detected CVs in globular clusters is discussed. Should future observations fail to find convincing evidence of a substantial population of cluster CVs, then the two-body tidal capture scenario is likely to be seriously constrained. Of the CVs we espect in 47 Tuc and omega Cen, approximately 45 and 20, respectively, should have accretion luminosities above 10(exp 33) ergs/s. If one utilizes a relation for converting accretion luminosity to hard X-ray luminosity that is based on observations of Galactic plane CVs, even these sources will not exhibit X-ray luminosities above 10(exp 33) ergs/s. While we cannot account directly for the most luminous subset of the low-luminosity globular cluster X-ray sources without assuming an evolutionary pattern that is different from that of the majority of CVs in the disk, we are able to account for all of the observed lower luminosity subset of these sources, many of which have been recently discovered through ROSAT observations. In order for our predicted integrated cluster X-ray luminosities to be consistent with observational upper limits, the relation between accretion and X-ray luminosities should be something like that inferred from the Galactic plane population of CVs. Our calculations predict a large number of systems with L(sub acc) is less than 10(exp 32) ergs/s. Although our calculations imply that globular clusters should have an enhancement of CVs relative to the number thought to be present in the Galactic disk, this enhancement is at most roughly an order of magnitude, not comparable to the factor of approximately 100 for low-mass X-ray binaries (LMXBs).
Di Stefano, R.↗
Methods and Results of a Search for Gravitational Waves Associated with Gamma-Ray Bursts Using the GEO 600, LIGO, and Virgo Detectors
In this paper we report on a search for short-duration gravitational wave bursts in the frequency range 64 Hz-1792 Hz associated with gamma-ray bursts (GRBs), using data from GEO600 and one of the LIGO or Virgo detectors. We introduce the method of a linear search grid to analyze GRB events with large sky localization uncertainties such as the localizations provided by the Fermi Gamma-ray Burst Monitor (GBM). Coherent searches for gravitational waves (GWs) can be computationally intensive when the GRB sky position is not well-localized, due to the corrections required for the difference in arrival time between detectors. Using a linear search grid we are able to reduce the computational cost of the analysis by a factor of O(10) for GBM events. Furthermore, we demonstrate that our analysis pipeline can improve upon the sky localization of GRBs detected by the GBM, if a high-frequency GW signal is observed in coincidence. We use the linear search grid method in a search for GWs associated with 129 GRBs observed satellite-based gamma-ray experiments between 2006 and 2011. The GRBs in our sample had not been previously analyzed for GW counterparts. A fraction of our GRB events are analyzed using data from GEO600 while the detector was using squeezed-light states to improve its sensitivity; this is the first search for GWs using data from a squeezed-light interferometric observatory. We find no evidence for GW signals, either with any individual GRB in this sample or with the population as a whole. For each GRB we place lower bounds on the distance to the progenitor, assuming a fixed GW emission energy of 10(exp -2)Stellar Mass sq c, with a median exclusion distance of 0.8 Mpc for emission at 500 Hz and 0.3 Mpc at 1 kHz. The reduced computational cost associated with a linear search grid will enable rapid searches for GWs associated with Fermi GBM events in the Advanced detector era.
methods↗
The Contribution of Ionizing Starts to the Far-Infrared and Radio Emission in the Milky Way: Evidence for a Swept-up Shell and Diffuse Ionized Halo Around the W4 Chimney/Supershell
Normandeau have proposed that W4 is a galactic chimney, the only chimney to-date identified in our Galaxy. Using the recent approx. 1 min resolution IGA (Infrared Galaxy Atlas) and DRAO (Dominion Royal Astrophysical Observatory) CGPS (Canadian Galactic Plane Survey) galactic plane surveys we analyze the far-infrared and radio structure of the W 4 chimney/supershell. We show W4 has a swept-up partially ionized shell of gas and dust which is powered by the OCl 352 star cluster. Analysis of the dust column density establishes there is dense interstellar material below the shell, directly showing the dense material which caused the lower shell expansion to stall. Due to much lower densities above the Galactic plane, the upper W4 shell achieved 'breakout' to form a Galactic chimney. Although the shell appears ionization bounded, it is very inhomogenous and an ionized halo provides evidence of significant Lyman continuum leakage. A large fraction of the OCl 352 cluster photons escape to large distances and are available to ionize the WIM (warm ionized medium) component of the interstellar medium.
Terebey, Susan↗
Sharpening the Distance Conjecture in diverse dimensions
The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ||$\phi$|| as m ~ exp(–λ||$\phi$||), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $1/\sqrt{d-2}$. In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $1/\sqrt{d-2}$ discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $1/\sqrt{d-2}$, thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Influence of residual chlorine on Ru/TiO 2 active sites during CO 2 methanation
Titania-supported ruthenium (Ru/TiO 2 ) is an established catalyst for the hydrogenation of carbon dioxide to methane (Sabatier reaction). Chlorine contamination, owed to the RuCl 3 precursor, is demonstrated to have a detrimental impact on methanation activity. After calcination and reduction the catalyst contains residual chlorine, shown by XPS. An aqueous ammonia wash removes Cl without leaching Ru. The washed catalysts exhibit improvements in CH 4 site-time yields. Low Ru loading catalysts encounter the greatest activity enhancements after washing (~4.5-fold). DFT calculations indicate that chlorine and CO 2 directly compete for adsorption on Ru step sites, with Cl impeding the adsorption of CO 2 at under-coordinated sites and at higher Cl coverages. H 2 -chemisorption/TPR show that Cl removal lowers the onset of low temperature H 2 dissociation on Ru. Finally, DRIFTS provide evidence that the removal of Cl facilitates low temperature dissociative binding of CO 2 , indicated by the formation of surface bound linear CO species.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by the Interplanetary Network
We present the results of a search for gravitational waves associated with 223 gamma ray bursts (GRBs) detected by the InterPlanetary Network (IPN) in 2005-2010 during LIGO's fifth and sixth science runs and Virgo's first, second, and third science runs. The IPN satellites provide accurate times of the bursts and sky localizations that vary significantly from degree scale to hundreds of square degrees. We search for both a well-modeled binary coalescence signal, the favored progenitor model for short GRBs, and for generic, unmodeled gravitational wave bursts. Both searches use the event time and sky localization to improve the gravitational wave search sensitivity as compared to corresponding all-time, all-sky searches. We find no evidence of a gravitational wave signal associated with any of the IPN GRBs in the sample, nor do we find evidence for a population of weak gravitational wave signals associated with the GRBs. For all IPN-detected GRBs, for which a sufficient duration of quality gravitational wave data are available, we place lower bounds on the distance to the source in accordance with an optimistic assumption of gravitational wave emission energy of 10(exp−2) solar mass c(exp 2) at 150 Hz, and find a median of 13 Mpc. For the 27 short-hard GRBs we place 90% confidence exclusion distances to two source models: a binary neutron star coalescence, with a median distance of 12 Mpc, or the coalescence of a neutron star and black hole, with a median distance of 22 Mpc. Finally, we combine this search with previously published results to provide a population statement for GRB searches in first-generation LIGO and Virgo gravitational wave detectors and a resulting examination of prospects for the advanced gravitational wave detectors.
gravitational wave detectors↗
Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO–Virgo Run O3a
We search for gravitational-wave transients associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the first part of the third observing run of Advanced LIGO and Advanced Virgo (2019 April 1 15:00 UTC–2019 October 1 15:00 UTC). A total of 105 GRBs were analyzed using a search for generic gravitational-wave transients; 32 GRBs were analyzed with a search that specifically targets neutron star binary mergers as short GRB progenitors. We find no significant evidence for gravitational-wave signals associated with the GRBs that we followed up, nor for a population of unidentified subthreshold signals. We consider several source types and signal morphologies, and report for these lower bounds on the distance to each GRB.
R. Abbott↗
Bounding Extreme Spacecraft Charging in the Lunar Environment
Robotic and manned spacecraft from the Apollo era demonstrated that the lunar surface in daylight will charge to positive potentials of a few tens of volts because the photoelectron current dominates the charging process. In contrast, potentials of the lunar surface in darkness which were predicted to be on the order of a hundred volts negative in the Apollo era have been shown more recently to reach values of a few hundred volts negative with extremes on the order of a few kilovolts. The recent measurements of night time lunar surface potentials are based on electron beams in the Lunar Prospector Electron Reflectometer data sets interpreted as evidence for secondary electrons generated on the lunar surface accelerated through a plasma sheath from a negatively charged lunar surface. The spacecraft potential was not evaluated in these observations and therefore represents a lower limit to the magnitude of the lunar negative surface potential. This paper will describe a method for obtaining bounds on the magnitude of lunar surface potentials from spacecraft measurements in low lunar orbit based on estimates of the spacecraft potential. We first use Nascap-2k surface charging analyses to evaluate potentials of spacecraft in low lunar orbit and then include the potential drops between the ambient space environment and the spacecraft to the potential drop between the lunar surface and the ambient space environment to estimate the lunar surface potential from the satellite measurements.
Minow, Joseph I.↗
Synthesis of regional crust and upper-mantle structure from seismic and gravity data
Analyses of regional gravity and magnetic patterns, LANDSAT images and geological information revealed two major lineaments crossing western Pennsylvania and parts of surrounding states. These lineaments are inferred to be expressions of fracture zones which penetrare deeply into the crust and possibly the upper mantle. The extensions of the Tyron-Mt. Union and the Pittsburgh-Washington lineaments bound a distinct crustal block (Lake Erie-Maryland block) over 100 km wide and probably more than 600 km in length. Evidence exists for the lateral displacement of this block at least 60 km northwestward during late Precambrian to Lower Ordovician time. Subsequent movements have been mainly vertical with respect to neighboring blocks. A possible crustal block that passes through eastern Kentucky, proposed by a TVA study on tectonics in the southern Appalachians, was also investigated. Finally, the use of regional gravity and magnetic data in identifying major crustal structures beneath western Pennsylvania is discussed.
Alexander, S. S.↗
Constraints on Axions from Cosmic Distance Measurements
Axion couplings to photons could induce photon-axion conversion in the presence of magnetic fields in the Universe. This conversion could impact various cosmic distance measurements, such as luminosity distances to type Ia supernovae and angular distances to galaxy clusters, in different ways. In this paper we consider different combinations of the most up-to-date distance measurements to constrain the axion-photon coupling. Employing the conservative cell magnetic field model for the magnetic fields in the intergalactic medium (IGM) and ignoring the conversion in the intracluster medium (ICM), we find the upper bounds on axion-photon couplings to be around 5 × 10^(−12) (nG/B) √(Mpc/s) Ge/V for axion masses m(a) below 10^(−13) eV, where B is the strength of the IGM magnetic field, and s is the comoving size of the magnetic domains. When including the conversion in the ICM, the upper bound is lowered and could reach 5 × 10^(−13) Ge/V for m(a) < 5 × 10^(−12) eV. While this stronger bound depends on the ICM modeling, it is independent of the strength of the IGM magnetic field, for which there is no direct evidence yet. These constraints could be placed on firmer footing with an enhanced understanding and control of the astrophysical uncertainties associated with the IGM and ICM. All the bounds are determined by the shape of the Hubble rate as a function of redshift reconstructable from various distance measurements, and insensitive to today’s Hubble rate, of which there is a tension between early and late cosmological measurements. As an appendix, we discuss the model building challenges of the use of photon-axion conversion to make type Ia supernovae brighter to alleviate the Hubble problem/crisis.
Cosmology of Theories beyond the SM↗
Testing Scale-Dependent Modified Gravity with DESI DR1
The Dark Energy Spectroscopic Instrument (DESI) provides an unprecedented opportunity to test deviations from general relativity (GR) that introduce a new physical scale within its redshift range. Using the connection between a Yukawa-like potential and the Hu-Sawicki $f(R)$ model, we place strong constraints on the range of a hypothetical fifth force mediated by a massive scalar field. We analyze the power spectrum measurements from DESI Data Release 1 using a baseline EFT model that employs the fkpt approach for the loop integrals. We find no evidence for deviations from GR and obtain the constraint $\log_{10} |f_{R_0}| < -4.59$ (95% C.L.). This corresponds to an upper bound at redshift zero on the scale at which corrections to GR become important, $λ< 17.81$ Mpc, or equivalently, a lower bound on the mass of the additional gravitational mediator of $m_ϕ> 3.60 \times 10^{-31}$ eV. We find that the modified gravity parameter $f_{R_0}$ is largely orthogonal to the cosmological parameters in the model, such that no additional projection effects relative to the GR case are introduced in this Full-Shape analysis. Furthermore, a second modified gravity parameter, the power index $n$, which modulates the time-variation of the associated mass, is found to be consistent with previous analyses that fixed it to unity. Adding DESI BAO data or other cosmological probes does not significantly change these results. The conclusions remain similar if the background evolution is described by evolving dark energy instead of a cosmological constant. Additionally, we test the robustness of the baseline model by varying the maximum wavenumber used in the Full-Shape analysis and analyzing the DESI targets separately. Finally, we analyze the degeneracies between the modified-gravity parameters and the sum of neutrino masses.
Gonzalez, D. [Guanajuato U.; UNAM, CCF] (ORCID:000↗
Extremely Low Passive Microwave Brightness Temperatures Due to Thunderstorms
Extreme events by their nature fall outside the bounds of routine experience. With imperfect or ambiguous measuring systems, it is appropriate to question whether an unusual measurement represents an extreme event or is the result of instrument errors or other sources of noise. About three weeks after the Tropical Rainfall Measuring Mission (TRMM) satellite began collecting data in Dec 1997, a thunderstorm was observed over northern Argentina with 85 GHz brightness temperatures below 50 K and 37 GHz brightness temperatures below 70 K (Zipser et al. 2006). These values are well below what had previously been observed from satellite sensors with lower resolution. The 37 GHz brightness temperatures are also well below those measured by TRMM for any other storm in the subsequent 16 years. Without corroborating evidence, it would be natural to suspect a problem with the instrument, or perhaps an irregularity with the platform during the first weeks of the satellite mission. Automated quality control flags or other procedures in retrieval algorithms could treat these measurements as errors, because they fall outside the expected bounds. But the TRMM satellite also carries a radar and a lightning sensor, both confirming the presence of an intense thunderstorm. The radar recorded 40+ dBZ reflectivity up to about 19 km altitude. More than 200 lightning flashes per minute were recorded. That same storm's 19 GHz brightness temperatures below 150 K would normally be interpreted as the result of a low-emissivity water surface (e.g., a lake, or flood waters) if not for the simultaneous measurements of such intense convection. This paper will examine records from TRMM and related satellite sensors including SSMI, AMSR-E, and the new GMI to find the strongest signatures resulting from thunderstorms, and distinguishing those from sources of noise. The lowest brightness temperatures resulting from thunderstorms as seen by TRMM have been in Argentina in November and December. For SSMI sensors carried on five DMSP satellites examined so far, the lowest thunderstorm-related brightness temperatures have been from Argentina in November - December and from Minnesota in June-July. The Minnesota cases were associated with spotter reports of large hail, significant severe wind, and tornadoes. Those locations have the record-holders for each satellite. The lowest AMSR-E 36.5 GHz brightness temperatures associated with deep convection have been in Argentina; the lowest 89.0 GHz brightness temperatures were from Typhoon Bolaven in the Philippine Sea. This paper will show examples of cases with the lowest brightness temperatures, and map the locations of these and other storms with brightness temperatures nearly as low. The study is largely motivated by the new GMI sensor on the Global Precipitation Mission core satellite, launched in February 2014, with its high resolution expected to reveal unprecedented low brightness temperatures when extreme events are encountered.
Cecil, Daniel J.↗
Radar Observations of Asteroid 10115 (1992 SK)
The approach of 1992 SK to within 0.056 AU of Earth on 1999 March 26 provided an excellent opportunity for radar observations. We observed it daily between March 22-26 at Goldstone at a transmitter frequency of 8560 MHz (3.50 cm). Weighted, optimally smoothed sums of cw (Doppler-only) echoes achieve a signal-to-noise ratio of about 300. Our highest resolution cw setup places up to approx. 30 0.5-Hz Doppler cells on the target at echo powers exceeding two standard deviations of the noise. Our highest resolution imaging setup places about 20 0.25-us (37.5 m) x 2.0 Hz pixels on 1992 SK at echo powers above the same threshold. We completed nearly 300 runs with each setup and obtained thorough rotational phase coverage (period = 7.320 h, P. Pravec, pers. comm.). The dispersion of the echoes in time delay indicates a lower bound on 1992 SK's maximum pole-on breadth of approx. 0.4 km that is consistent with the echo bandwidth and rotation period. Variations in the cw spectral bandwidths and shapes and in the delay-Doppler images as a function of rotation phase are evident on each day, are consistent in bandwidth with each other and with the rotation period, and indicate that the asteroid is asymmetric and modesty elongated.
Benner, L. A. M.↗
A new reeling technique for very long extension scanning in the stratosphere
A balloon-borne winching system has been developed for extending a very long tether with payload down into the stratosphere and recovering it, this has been flight proven by being carrried to an altitude of 40 km, lowering a 62-kg stratospheric photochemistry experiment 12 km at a descent velocity of about 6-8 m/sec and recovering it at comparable velocities. During the first flight, the data gave no evidence of dynamic instabilities due to the system or the stratospheric interactions. The future utility of this payload is discussed with attention to the design factors that bound the range of performance of this type of system.
Hazen, N. L.↗
Perturbative Stability and Error-Correction Thresholds of Quantum Codes
Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.
quantum error correction↗