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BEYONDPLANCK VI. Noise characterization and modeling

We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous literature, we initially adopt a 1/ f model for the noise power spectral density (PSD), but find the need for an additional lognormal component in the noise model for the 30 and 44 GHz bands. We implement an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then use this procedure to both estimate the gapless correlated noise in the time-domain, n corr , and to sample the noise PSD parameters, ξ n = {σ 0 , f knee , α, A p }. In contrast to previous Planck analyses, we assume piecewise stationary noise only within each pointing period (PID), not throughout the full mission, but we adopt the LFI Data Processing Center (DPC) results as priors on α and f knee . On average, we find best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results reveals many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/ f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise not described by a 1/ f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/ f at the 2–3σ level in each one hour pointing period, motivating the addition of the lognormal noise component for these bands. For some periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/ f profile is not adequate to fully characterize the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data, and the current work is a first attempt at understanding and mitigating these issues.

79 ASTRONOMY AND ASTROPHYSICS↗

BeyondPlanck: V. Minimal ADC Corrections for Planck LFI

We describe the correction procedure for Analog-to-Digital Converter (ADC) differential non-linearities (DNL) adopted in the Bayesian end-to-end BEYONDPLANCK analysis framework. This method is nearly identical to that developed for the official Planck Low Frequency Instrument (LFI) Data Processing Center (DPC) analysis, and relies on the binned rms noise profile of each detector data stream. However, rather than building the correction profile directly from the raw rms profile, we first fit a Gaussian to each significant ADC-induced rms decrement, and then derive the corresponding correction model from this smooth model. The main advantage of this approach is that only samples which are significantly affected by ADC DNLs are corrected, as opposed to the DPC approach in which the correction is applied to all samples, filtering out signals not associated with ADC DNLs. The new corrections are only applied to data for which there is a clear detection of the non-linearities, and for which they perform at least comparably with the DPC corrections. Out of a total of 88 LFI data streams (sky and reference load for each of the 44 detectors) we apply the new minimal ADC corrections in 25 cases, and maintain the DPC corrections in 8 cases. All these corrections are applied to 44 or 70 GHz channels, while, as in previous analyses, none of the 30 GHz ADCs show significant evidence of non-linearity. By comparing the BEYONDPLANCK and DPC ADC correction methods, we estimate that the residual ADC uncertainty is about two orders of magnitude below the total noise of both the 44 and 70 GHz channels, and their impact on current cosmological parameter estimation is small. However, we also show that non-idealities in the ADC corrections can generate sharp stripes in the final frequency maps, and these could be important for future joint analyses with the Planck High Frequency Instrument (HFI), Wilkinson Microwave Anisotropy Probe (WMAP), or other datasets. We therefore conclude that, although the existing corrections are adequate for LFI-based cosmological parameter analysis, further work on LFI ADC corrections is still warranted.

79 ASTRONOMY AND ASTROPHYSICS↗

BeyondPlanck: XII. Cosmological parameter constraints with end-to-end error propagation

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK results are generally slightly closer to the high-ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-ℓ polarization information from LFI and WMAP, we find a best-fit value of τ = 0.066 ± 0.013, which is higher than the low value of τ = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the BEYONDPLANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

79 ASTRONOMY AND ASTROPHYSICS↗

BeyondPlanck: VII. Bayesian estimation of gain and absolute calibration for cosmic microwave background experiments

We present a Bayesian calibration algorithm for cosmic microwave background (CMB) observations as implemented within the global end-to-end BEYONDPLANCK framework and applied to the Planck Low Frequency Instrument (LFI) data. Following the most recent Planck analysis, we decomposed the full time-dependent gain into a sum of three nearly orthogonal components: one absolute calibration term, common to all detectors, one time-independent term that can vary between detectors, and one time-dependent component that was allowed to vary between one-hour pointing periods. Each term was then sampled conditionally on all other parameters in the global signal model through Gibbs sampling. The absolute calibration is sampled using only the orbital dipole as a reference source, while the two relative gain components were sampled using the full sky signal, including the orbital and Solar CMB dipoles, CMB fluctuations, and foreground contributions. We discuss various aspects of the data that influence gain estimation, including the dipole-polarization quadrupole degeneracy and processing masks. Comparing our solution to previous pipelines, we find good agreement in general, with relative deviations of -0.67% (-0.84%) for 30 GHz, 0.12% (-0.04%) for 44 GHz and -0.03% (-0.64%) for 70 GHz, compared to Planck PR4 and Planck 2018, respectively. We note that the BEYONDPLANCK calibration was performed globally, which results in better inter-frequency consistency than previous estimates. Additionally, WMAP observations were used actively in the BEYONDPLANCK analysis, which both breaks internal degeneracies in the Planck data set and results in an overall better agreement with WMAP. Finally, we used a Wiener filtering approach to smoothing the gain estimates. We show that this method avoids artifacts in the correlated noise maps as a result of oversmoothing the gain solution, which is difficult to avoid with methods like boxcar smoothing, as Wiener filtering by construction maintains a balance between data fidelity and prior knowledge. Although our presentation and algorithm are currently oriented toward LFI processing, the general procedure is fully generalizable to other experiments, as long as the Solar dipole signal is available to be used for calibration.

79 ASTRONOMY AND ASTROPHYSICS↗

BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗

BEYONDPLANCK X. Planck Low Frequency Instrument frequency maps with sample-based error propagation

We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg 0 /g 0 = 5 x 10 -5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B-mode experiments aiming at nanokelvin precision.

79 ASTRONOMY AND ASTROPHYSICS↗

BeyondPlanck: I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BEYONDPLANCK project in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building directly on experience from ESA’s Planck mission, we implemented a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a full joint posterior distribution P(ω | d), where ω represents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-ℓ CMB polarization reconstruction with Planck LFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/f correlated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth to τ = 0.066 ± 0.013, with a low-resolution CMB-based χ 2 probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in the Planck LFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide COSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.

79 ASTRONOMY AND ASTROPHYSICS↗

BEYONDPLANCK IV. On end-to-end simulations in CMB analysis — Bayesian versus frequentist statistics

End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before BEYONDPLANCK, most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BEYONDPLANCK represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The BEYONDPLANCK posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level BEYONDPLANCK algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.

79 ASTRONOMY AND ASTROPHYSICS↗

Principles to adapt financing mechanisms for fully integrated hybrid energy systems

As the electricity sector evolves, and as all energy types (thermal, electric, chemical, etc.) become more coupled, there has been increased interest to develop and deploy hybrid energy systems (HES). This work focuses on fully integrated HES, where there are multiple energy sources and multiple energy products, often coupled through a storage buffer. A significant amount of the available literature on this work describes technology pathways for fully integrated HES; however, it is unclear how financial institutions should treat these systems. Fully integrated HES represent an increase in complexity from their stand-alone counterparts, but they also potentially mitigate financial risk and provide value to the energy system, which has not yet been accounted for in financing mechanisms that could help to enable such systems. This paper provides some examples of fully integrated HES and proposes principles to help adapt financing to adequately capture the value of such systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Radio frequency and DC high voltage breakdown of high pressure helium, argon, and xenon

Motivated by the possibility of guiding daughter ions from double beta decay events to single-ion sensors for barium tagging, the NEXT collaboration is developing a program of R&D to test radio frequency (RF) carpets for ion transport in high pressure xenon gas. This would require carpet functionality in regimes at higher pressures than have been previously reported, implying correspondingly larger electrode voltages than in existing systems. This mode of operation appears plausible for contemporary RF-carpet geometries due to the higher predicted breakdown strength of high pressure xenon relative to low pressure helium, the working medium in most existing RF carpet devices. In this paper we present the first measurements of the high voltage dielectric strength of xenon gas at high pressure and at the relevant RF frequencies for ion transport (in the 10 MHz range), as well as new DC and RF measurements of the dielectric strengths of high pressure argon and helium gases at small gap sizes. We find breakdown voltages that are compatible with stable RF carpet operation given the gas, pressure, voltage, materials and geometry of interest.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Reflectance and fluorescence characteristics of PTFE coated with TPB at visible, UV, and VUV as a function of thickness

Polytetrafluoroethylene (PTFE) is an excellent diffuse reflector widely used in light collection systems for particle physics experiments. In noble element systems, it is often coated with tetraphenyl butadiene (TPB) to allow detection of vacuum ultraviolet scintillation light. Here, in this work this dependence is investigated for PTFE coated with TPB in air for light of wavelengths of 200 nm, 260 nm, and 450 nm. The results show that TPB-coated PTFE has a reflectance of approximately 92% for thicknesses ranging from 5 mm to 10 mm at 450 nm, with negligible variation as a function of thickness within this range. A cross-check of these results using an argon chamber supports the conclusion that the change in thickness from 5 mm to 10 mm does not affect significantly the light response at 128 nm. Our results indicate that pieces of TPB-coated PTFE thinner than the typical 10 mm can be used in particle physics detectors without compromising the light signal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NEXT-CRAB-0: a high pressure gaseous xenon time projection chamber with a direct VUV camera based readout

The search for neutrinoless double beta decay(0νββ) remains one of the most compelling experimentalavenues for the discovery in the neutrino sector.Electroluminescent gas-phase time projection chambers are wellsuited to 0νββ searches due to their intrinsicallyprecise energy resolution and topological event identificationcapabilities. Scalability to ton- and multi-ton masses requiresreadout of large-area electroluminescent regions with fine spatialresolution, low radiogenic backgrounds, and a scalable dataacquisition system. This paper presents a detector prototype thatrecords event topology in an electroluminescent xenon gas TPC viaVUV image-intensified cameras. This enables an extendable readoutof large tracking planes with commercial devices that reside almostentirely outside of the active medium. Following furtherdevelopment in intermediate scale demonstrators, this technique mayrepresent a novel and enlargeable method for topological eventimaging in 0νββ.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Design, characterization and installation of the NEXT-100 cathode and electroluminescence regions

NEXT-100 is currently being constructed at the Laboratorio Subterráneo de Canfranc in the Spanish Pyrenees and will search for neutrinoless double beta decay using a high-pressure gaseous time projection chamber (TPC) with 100 kg of xenon. Charge amplification is carried out via electroluminescence (EL) which is the process of accelerating electrons in a high electric field region causing secondary scintillation of the medium proportional to the initial charge. The NEXT-100 EL and cathode regions are made from tensioned hexagonal meshes of 1 m diameter. This paper describes the design, characterization, and installation of these parts for NEXT-100. Simulations of the electric field are performed to model the drift and amplification of ionization electrons produced in the detector under various EL region alignments and rotations. Measurements of the electrostatic breakdown voltage in air characterize performance under high voltage conditions and identify breakdown points. Furthermore, the electrostatic deflection of the mesh is quantified and fit to a first-principles mechanical model. Measurements were performed with both a standalone test EL region and with the NEXT-100 EL region before its installation in the detector. Finally, we describe the parts as installed in NEXT-100, following their deployment in Summer 2023.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

High voltage delivery and distribution for the NEXT-100 Time Projection Chamber

A critical element in the realization of large liquid andgas time projection chambers (TPCs) is the delivery and distributionof high voltages into and around the detector. Such experimentsrequire of order tens of kilovolts to enable electron drift overmeter-scale distances. This paper describes the design andoperation of the cathode feedthrough and high voltage distributionthrough the field cage of the NEXT-100 experiment, an undergroundTPC that will search for neutrinoless double beta decay0νββ. The feedthrough has been demonstrated to holdpressures up to 20 bar and sustain voltages as high as -65 kV.The TPC is operating stably at its design high voltages. The systemhas been realized within the constraints of a stringent radiopuritybudget and is now being used to execute a suite of sensitive doublebeta decay analyses.

Adams, C. [Argonne]↗

Integrated assessment model diagnostics: key indicators and model evolution

Integrated assessment models (IAMs) form a prime tool in informing climate mitigation strategies. Diagnostic indicators that allow to compare these models can help to describe and explain differences in model projections. This also increases transparency and comparability. Earlier, the IAM community has developed an approach to diagnose models (Kriegler et al., 2015). Here we build on this, by proposing a selected set of well-defined indicators as a community standard, similar to metrics used for other modeling communities such as climate models. These indicators are the relative abatement index (RAI), emission reduction type index (ERT), inertia timescale (IT), fossil fuel reduction (FFR), transformation index (TI) and cost per abatement value (CAV). We apply the approach to 17 IAMs, including both older version as well as their latest versions, as applied in the IPCC 6th Assessment Report (AR6). The study shows that the approach can be easily applied and allows for comparison of model versions in time. The indicators and their trends can often be explained in terms of model characteristics and changes. We show that together, the set of six indicators can provide an useful indication of the main traits of the model and can roughly indicate the general model behavior. The results also show that there is often a considerable spread across the models. Interestingly, the diagnostic values often change for different model versions, but there does not seem to be a distinct trend across the different models.

54 ENVIRONMENTAL SCIENCES↗

Measurement of the 136 Xe two-neutrino double-β-decay half-life via direct background subtraction in NEXT

Here, we report a measurement of the half-life of the 136 Xe two-neutrino double-β decay performed with a novel direct-background-subtraction technique. The analysis relies on the data collected with the NEXT-White detector operated with 136 Xe-enriched and 136 Xe-depleted xenon, as well as on the topology of double-electron tracks. With a fiducial mass of only 3.5 kg of Xe, a half-life of 2.34$_{-0.46}^{+0.80}$(stat)$_{-0.17}^{+0.30}$(sys)×10 21 yr is derived from the background-subtracted energy spectrum. The presented technique demonstrates the feasibility of unique background-model-independent neutrinoless double-β-decay searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Robust Measurements of n -Point Correlation Functions of Driven-Dissipative Quantum Systems on a Digital Quantum Computer

We propose and demonstrate a unified hierarchical method to measure n -point correlation functions that can be applied to driven, dissipative, or otherwise open or nonequilibrium quantum systems. In this method, the time evolution of the system is repeatedly interrupted by interacting an ancilla qubit with the system through a controlled operation, and measuring the ancilla immediately afterward. We discuss the robustness of this method as compared to other ancilla-based interferometric techniques (such as the Hadamard test), and highlight its advantages for near-term quantum simulations of open quantum systems. We implement the method on a quantum computer in order to measure single-particle Green’s functions of a driven-dissipative fermionic system. This Letter shows that dynamical correlation functions for driven-dissipative systems can be robustly measured with near-term quantum computers. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Playing Nonlocal Games across a Topological Phase Transition on a Quantum Computer

Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this Letter, we introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. Unlike previous examples, quantum advantage persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. We demonstrate this robustness experimentally on Quantinuum’s H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits leveraging midcircuit measurements and unitary feedback. We are thus able to tune through a topological phase transition—witnessed by the loss of robust quantum advantage—on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed Greenberger-Horne-Zeilinger states, for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit. Lastly, we discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players.

97 MATHEMATICS AND COMPUTING↗