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A minimal Kitaev chain, consisting of two quantum dots connected via a superconductor, can host highly localized near-zero-energy states, known as poor man's Majoranas (PMMs). These states have been proposed as promising candidates to study Majorana bound states (MBSs) in a highly tunable setup. However, it is unclear whether and how PMMs observed in real systems are actually connected to the topological phase of the full Kitaev chain. Here, we study PMMs using a microscopic model and show that, in the long chain limit, not all PMMs are related to topological states. Rather, in long chains, some PMMs evolve into trivial highly localized low-energy states. We provide an analytical explanation for the occurrence of these states and show that there is no clear conductance signature that is able to distinguish PMMs that evolve into true topological states from PMMs that evolve into trivial states., Comment: 4 pages main text, 5 figures. 14 pages supplementary material, 54 figures

Prior work on the Image Quality Transfer on Diffusion MRI (dMRI) has shown significant improvement over traditional interpolation methods. However, the difficulty in obtaining ultra-high resolution Diffusion MRI scans poses a problem in training neural networks to obtain high-resolution dMRI scans. Here we hypothesise that the inclusion of structural MRI images, which can be acquired at much higher resolutions, can be used as a guide to obtaining a more accurate high-resolution dMRI output. To test our hypothesis, we have constructed a novel framework that incorporates structural MRI scans together with dMRI to obtain high-resolution dMRI scans. We set up tests which evaluate the validity of our claim through various configurations and compare the performance of our approach against a unimodal approach. Our results show that the inclusion of structural MRI scans do lead to an improvement in high-resolution image prediction when T1w data is incorporated into the model input.

Poor man's Majoranas (PMMs) hold the promise to engineer Majorana bound states in a highly tunable setup consisting of a chain of quantum dots that are connected via superconductors. Due to recent progress in controlling the amplitudes of elastic cotunneling (ECT) and crossed Andreev reflection (CAR), two vital ingredients for PMMs, experimental investigations of PMMs have gained significant interest. Previously, analytic conditions for the "sweet spots" that result in PMMs have focused on systems with infinite Zeeman energy. Here, we derive analytically a sweet spot condition for PMMs in a system with finite Zeeman energy in the absence of Coulomb interaction. We then consider two numerical models, one in which ECT and CAR are transmitted via superconducting bulk states and one in which they are transmitted via an Andreev bound state. In both models we find numerically near zero-energy states that are highly localized, even in the presence of finite Coulomb interaction. These states can be related to the analytic sweet spot derived in this work. However, we also find that in these more realistic models such states do not perfectly satisfy the characteristics of PMMs, rather they exist only within a "region of threshold" where PMM characteristics are approximately achieved.

Crossed Andreev reflection (CAR) is a nonlocal transport phenomenon that creates/detects Cooper-pair correlations between distant places. It is also the basis of Cooper-pair splitting to generate remote entanglement. Although CAR has been extensively studied in semiconductors proximity-coupled to a superconductor, it has been very difficult to observe it in a topological insulator (TI). Here we report the first observation of CAR in a proximitized TI nanowire (TINW). We performed local and nonlocal conductance spectroscopy on mesoscopic TINW devices in which superconducting (Nb) and metallic (Pt/Au) contacts are made on a bulk-insulating TINW. The local conductance detected a hard gap, accompanied by the appearance of Andreev bound states that can reach zero-bias, while a negative nonlocal conductance was occasionally observed upon sweeping the chemical potential, giving evidence for CAR. Surprisingly, the CAR signal was detected even over 1.5 $\mu$m, which implies that pair correlations extend over a length scale much longer than the expected superconducting coherence length of either Nb or the proximitised TINW. Such a long-range CAR effect is possibly due to an intricate role of disorder in proximitized nanowires. Also, our 0.9-$\mu$m device presented a decent Cooper-pair splitting efficiency of up to 0.5., Comment: 37 pages total; 28 pages of main text with 6 figures, 9 pages of supplement with 6 figures. The raw data and codes are available at the online depository Zenodo with the identifier DOI:10.5281/zenodo.12611922

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Nonreciprocal transport effects can occur in the normal state of conductors and in superconductors when both inversion and time-reversal symmetry are broken. Here, we consider systems where magnetochiral anisotropy (MCA) of the energy spectrum due to an externally applied magnetic field results in a rectification effect in the normal state and a superconducting (SC) diode effect when the system is proximitised by a superconductor. Focussing on nanowire systems, we obtain analytic expressions for both normal state rectification and SC diode effects that reveal the commonalities - as well as differences - between these two phenomena. Furthermore, we consider the nanowire brought into an (almost) helical state in the normal phase or a topological superconducting phase when proximitised. In both cases this reveals that the topology of the system considerably modifies its nonreciprocal transport properties. Our results provide new insights into how to determine the origin of nonreciprocal effects and further evince the strong connection of nonreciprocal transport with the topological properties of a system., Comment: Main text: 5 pages, 3 figures. Supplemental material: 4 pages, 1 figure

Recent developments in diffusion models have advanced conditioned image generation, yet they struggle with reconstructing out-of-distribution (OOD) images, such as unseen tumors in medical images, causing "image hallucination" and risking misdiagnosis. We hypothesize such hallucinations result from local OOD regions in the conditional images. We verify that partitioning the OOD region and conducting separate image generations alleviates hallucinations in several applications. From this, we propose a training-free diffusion framework that reduces hallucination with multiple Local Diffusion processes. Our approach involves OOD estimation followed by two modules: a "branching" module generates locally both within and outside OOD regions, and a "fusion" module integrates these predictions into one. Our evaluation shows our method mitigates hallucination over baseline models quantitatively and qualitatively, reducing misdiagnosis by 40% and 25% in the real-world medical and natural image datasets, respectively. It also demonstrates compatibility with various pre-trained diffusion models.

Low-field (LF) MRI scanners (<1T) are still prevalent in settings with limited resources or unreliable power supply. However, they often yield images with lower spatial resolution and contrast than high-field (HF) scanners. This quality disparity can result in inaccurate clinician interpretations. Image Quality Transfer (IQT) has been developed to enhance the quality of images by learning a mapping function between low and high-quality images. Existing IQT models often fail to restore high-frequency features, leading to blurry output. In this paper, we propose a 3D conditional diffusion model to improve 3D volumetric data, specifically LF MR images. Additionally, we incorporate a cross-batch mechanism into the self-attention and padding of our network, ensuring broader contextual awareness even under small 3D patches. Experiments on the publicly available Human Connectome Project (HCP) dataset for IQT and brain parcellation demonstrate that our model outperforms existing methods both quantitatively and qualitatively. The code is publicly available at \url{https://github.com/edshkim98/DiffusionIQT}.

In this Reply we respond to the comment by Antipov et al. from Microsoft Quantum on Hess et al., PRL 130, 207001 (2023). Antipov et al. reported only a single simulation and claimed it did not pass the Microsoft Quantum topological gap protocol (TGP). They have provided no parameters or data for this simulation (despite request). Regardless, in this reply we demonstrate that the trivial bulk gap reopening mechanism outlined in Hess et al., in combination with trivial ZBPs, passes the TGP and therefore can result in TGP false positives., Comment: Updated to include remarks, submitted to PRL, showing that Fig. 1 of Microsoft Quantum's comment was demonstrably false. Microsoft Quantum's comment has subsequently been rejected

In superconductors, the combination of broken time-reversal and broken inversion symmetries can result in a critical current being dependent on the direction of current flow. This phenomenon is known as superconducting diode effect (SDE) and has great potential for applications in future low-temperature electronics. Here, we investigate how magnetic textures such as domain walls or skyrmions on a racetrack can be used to control the SDE in a Josephson junction and how the SDE can be used as a low-temperature read-out of the data in racetrack memory devices. First, we consider a two-dimensional electron gas (2DEG) with strong spin-orbit-interaction (SOI) coupled to a magnetic racetrack, which forms the weak-link in a Josephson junction. In this setup, the exchange coupling between the magnetic texture and the itinerant electrons in the 2DEG breaks time-reversal symmetry and enables the SDE. When a magnetic texture, such as a domain wall or skyrmion enters the Josephson junction, the local exchange field within the junction is changed and, consequently, the strength of the SDE is altered. In particular, depending on the position and form of the magnetic texture, moving the magnetic texture can cause the SDE coefficient to change its sign, enabling a Josephson transistor effect with potentially fast switching frequencies. Further, we find that the SDE is enhanced if the junction length-scales are comparable with the length-scale of the magnetic texture. Furthermore, we show that, under certain circumstances, the symmetry breaking provided by particular magnetic textures, such as skyrmions, can lead to an SDE even in the absence of Rashba SOI in the 2DEG. Our results provide a basis for new forms of readout in low-temperature memory devices as well as demonstrating how a Josephson transistor effect can be achieved even in the absence of an external magnetic field and intrinsic Rashba SOI., Comment: 16 pages, 11 figures, 1 table

Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using simulations on modern-day devices. Therefore, the inherent physical limitations of the device on the parameters of the simulation must be understood. This analysis examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. These errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian. A general framework for quantifying these errors is introduced and applied to several proposed time evolution methods, including Trotter-like methods and Floquet-engineered constant-field approaches. The limitations placed on the accuracy of time evolution methods by current devices are discussed. Characterization of the scaling of coherent effects of different error sources provides a way to extend the presented Hamiltonian engineering methods to take advantage of forthcoming device capabilities., Comment: 19 pages, 8 figures, comments welcome

Inducing Cooper pairing in a thin ferromagnetic topological insulator in the quantum anomalous Hall state (called quantum anomalous Hall insulator, QAHI) is a promising way to realize topological superconductivity with associated chiral Majorana edge states. However, finding evidence of superconducting proximity effect in a QAHI has proven to be a considerable challenge due to inherent experimental difficulties. Here we report the observation of crossed Andreev reflection (CAR) across a narrow superconducting Nb electrode contacting the chiral edge state of a QAHI, evinced by a negative nonlocal voltage measured downstream from the grounded Nb electrode. This is an unambiguous signature of induced superconducting pair correlation in the chiral edge state. Our theoretical analysis demonstrates that CAR processes of the chiral edge are not strongly dependent on the nature of the superconductivity that mediates them. Nevertheless, the characteristic length of the CAR process is found to be much longer than the superconducting correlation length in Nb, which suggests that the CAR is in fact mediated by superconductivity induced on the QAHI surface. The approach and results presented here provide a foundation for future studies of topological superconductivity and Majorana physics, as well as for the search for non-Abelian zero modes., Comment: 45 pages total; 27 pages of main text with 4 figures, 18 pages of supplement with 9 figures

In this Reply we respond to the comment by Das Sarma and Pan [1] on Hess et al., Phys. Rev. Lett. 130, 207001, "Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires" [2]. First, we note that Das Sarma and Pan reproduce the key results of Hess et al., substantiating that our findings are entirely valid. Next, we clarify the incorrect statement by Das Sarma and Pan that the main result of Hess et al. requires a "contrived periodic pristine system", pointing out the extensive discussion of positional disorder in the Hess et al. We also demonstrate that nonlocal conductance features are generically reduced by disorder. This applies to both an Andreev band and to a genuine topological bulk gap reopening signature (BRS). In fact, the suppression of nonlocal conductance of a genuine BRS by disorder was discussed in, e.g., Pan, Sau, Das Sarma, PRB 103, 014513 (2021) [3]. We conclude that, contrary to the claims of Das Sarma and Pan, the minimal model of Hess et al. is relevant to current realistic nanowire devices where only a few overlapping ABSs would be required to mimic a BRS., Comment: 2 pages, 1 figure

Low-dimensional germanium hole devices are promising systems with many potential applications such as hole spin qubits, Andreev spin qubits, and Josephson junctions, and can serve as a basis for the realization of topological superconductivity. This vast array of potential uses for Ge largely stems from the exceptionally strong and controllable spin-orbit interaction (SOI), ultralong mean free paths, long coherence times, and compatibility with complementary metal-oxide-semiconductor (CMOS) technology. However, when brought into proximity with a superconductor (SC), metallization normally diminishes many useful properties of a semiconductor, for instance, typically reducing the g factor and SOI energy, as well as renormalizing the effective mass. In this paper, we consider metallization of a Ge nanowire (NW) in proximity to a SC, explicitly taking into account the three-dimensional (3D) geometry of the NW. We find that proximitized Ge exhibits a unique phenomenology of metallization effects, where the 3D cross section plays a crucial role. For instance, in contrast to expectations, we find that SOI can be enhanced by strong coupling to the superconductor. We also show that the thickness of the NW plays a critical role in determining both the size of the proximity-induced pairing potential and metallization effects, since the coupling between the NW and SC strongly depends on the distance of the NW wave function from the interface with the SC. In the absence of electrostatic effects, we find that a sizable gap opens only in thin NWs ($d \lesssim 3$ nm). In thicker NWs, the wave function must be pushed closer to the SC by electrostatic effects in order to achieve a sizable proximity gap such that the required electrostatic field strength can simultaneously induce a strong SOI.

The human thalamus is a highly connected subcortical grey-matter structure within the brain. It comprises dozens of nuclei with different function and connectivity, which are affected differently by disease. For this reason, there is growing interest in studying the thalamic nuclei in vivo with MRI. Tools are available to segment the thalamus from 1 mm T1 scans, but the contrast of the lateral and internal boundaries is too faint to produce reliable segmentations. Some tools have attempted to incorporate information from diffusion MRI in the segmentation to refine these boundaries, but do not generalise well across diffusion MRI acquisitions. Here we present the first CNN that can segment thalamic nuclei from T1 and diffusion data of any resolution without retraining or fine tuning. Our method builds on a public histological atlas of the thalamic nuclei and silver standard segmentations on high-quality diffusion data obtained with a recent Bayesian adaptive segmentation tool. We combine these with an approximate degradation model for fast domain randomisation during training. Our CNN produces a segmentation at 0.7 mm isotropic resolution, irrespective of the resolution of the input. Moreover, it uses a parsimonious model of the diffusion signal at each voxel (fractional anisotropy and principal eigenvector) that is compatible with virtually any set of directions and b-values, including huge amounts of legacy data. We show results of our proposed method on three heterogeneous datasets acquired on dozens of different scanners. An implementation of the method is publicly available at https://freesurfer.net/fswiki/ThalamicNucleiDTI., Comment: Under review

We consider superconductor-normal-superconductor-normal-superconductor (SNSNS) planar Josephson junctions in hole systems with spin-orbit interaction that is cubic in momentum (CSOI). Using only the superconducting phase difference, we find parameter regimes where junctions of experimentally achievable transparency can enter a topological superconducting phase with Majorana bound states (MBSs) at the junction ends. In planar germanium heterostructures CSOI can be the dominant form of SOI and extremely strong. We show analytically and numerically that, within experimental regimes, our results provide an achievable roadmap for a new MBS platform with low disorder, minimal magnetic fields, and very strong spin-orbit interaction, overcoming many of the key deficiencies that have so far prevented the conclusive observation of MBSs., Comment: main text: 4 pages, 3 figures. Appendix: 8 pages, 7 figures

When a charge current is injected into the surface state of a topological insulator (TI), the resulting shift of the spin-momentum-locked Fermi surface leads to the appearance of a net spin polarization. The helical spin structure of the Dirac-cone surface state of a TI should lead to a fixed sign of this spin polarization for a given current direction, but experimentally, both signs that agree and disagree with the theory expectation for the surface state Dirac cone have been observed in the past. Although the origin of the wrong sign has not been conclusively elucidated, this observation points to the possibility that one may switch the spin polarization at will to realize a spin transistor operation. Here we report the observation of both signs of spin polarization in the very same device and demonstrate the tunability between the two by electrostatic gating, which gives a proof of principle of a topological insulator spin transistor. This switching behaviour is explained using a minimal model of competing contributions from the topological surface state and trivial Rashba-split states., Comment: Main text: 8 pages, 3 figs. SI: 6 pages, 4 figs

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.

In a nanowire (NW) of a three-dimensional topological insulator (TI), the quantum-confinement of topological surface states leads to a peculiar subband structure that is useful for generating Majorana bound states. Top-down fabrication of TINWs from a high-quality thin film would be a scalable technology with great design flexibility, but there has been no report on top-down-fabricated TINWs where the chemical potential can be tuned to the charge neutrality point (CNP). Here we present a top-down fabrication process for bulk-insulating TINWs etched from high-quality (Bi$_{1-x}$Sb$_{x}$)$_2$Te$_3$ thin films without degradation. We show that the chemical potential can be gate-tuned to the CNP and the resistance of the NW presents characteristic oscillations as functions of the gate voltage and the parallel magnetic field, manifesting the TI-subband physics. We further demonstrate the superconducting proximity effect in these TINWs, preparing the groundwork for future devices to investigate Majorana bound states., Comment: 32 pages. 22 main text, 10 SI

In bulk superconductors or Josephson junctions formed in materials with spin-orbit interaction, the critical current can depend on the direction of current flow and applied magnetic field, an effect known as the superconducting (SC) diode effect. Here, we consider the SC diode effect in Josephson junctions in nanowire devices. We find that the $4\pi$-periodic contribution of Majorana bound states (MBSs) to the current phase relation (CPR) of single junctions results in a significant enhancement of the SC diode effect when the device enters the topological phase. Crucially, this enhancement of the SC diode effect is independent of the parity of the junction and therefore protected from parity altering events, such as quasiparticle poisoning, which have hampered efforts to directly observe the $4\pi$-periodic CPR of MBSs. We show that this effect can be generalized to SQUIDs and that, in such devices, the parity-protected SC diode effect can provide a highly controllable probe of the topology in a Josephson junction., Comment: 7 pages, 4 figures

The second workshop on the HEP Analysis Ecosystem took place 23-25 May 2022 at IJCLab in Orsay, to look at progress and continuing challenges in scaling up HEP analysis to meet the needs of HL-LHC and DUNE, as well as the very pressing needs of LHC Run 3 analysis. The workshop was themed around six particular topics, which were felt to capture key questions, opportunities and challenges. Each topic arranged a plenary session introduction, often with speakers summarising the state-of-the art and the next steps for analysis. This was then followed by parallel sessions, which were much more discussion focused, and where attendees could grapple with the challenges and propose solutions that could be tried. Where there was significant overlap between topics, a joint discussion between them was arranged. In the weeks following the workshop the session conveners wrote this document, which is a summary of the main discussions, the key points raised and the conclusions and outcomes. The document was circulated amongst the participants for comments before being finalised here.

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing.

We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes ($t_{ijk}^{abc}$). Through our method we can reduce the scaling of the (T) energy from the traditional O($N^{7}$) to a more modest O($N^{5}$). We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields sub-millihartree (mEh) differences from CCSD(T) when evaluating absolute energies, and sub-0.1 kcal/mol energy differences when evaluating relative energies. Finally, we demonstrate that this method converges to the true CCSD(T) energy through the systematic increasing of the rank or eigenvalue tolerance of the orthogonal projector, as well as exhibiting sub-linear to linear error growth with respect to system size.

We investigate non-linear transport signatures stemming from linear and cubic spin-orbit interactions in one- and two-dimensional systems. The analytical zero-temperature response to external fields is complemented by finite temperature numerical analysis, establishing a way to distinguish between linear and cubic spin-orbit interactions. We also propose a protocol to determine the relevant material parameters from transport measurements attainable in realistic conditions, illustrated by values for Ge heterostructures. Our results establish a method for the fast benchmarking of spin-orbit properties in semiconductor nanostructures., Comment: 7 pages, 3 figures

We consider a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the non-local conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature (BRS) in non-local conductance is essentially unaffected by the additional presence of trivial zero-bias peaks (ZBPs) in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial BRS and ZBPs mimics the basic features required to pass the so-called "topological gap protocol". Our results therefore provide a topologically trivial minimal model by which the applicability of this protocol can be benchmarked.