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The Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers is crucial for spintronics. However, it is also significant even in symmetric ones, and unveiling its atomic-level origin remains an issue. We use electron microscopy to propose defect-mediated bulk DMI in Pt/Co/Pt. We find an enhancement of the net DMI by increasing sputter gas pressure. The samples have a compositional gradient, but their compositional asymmetry is weak. Our analysis suggests that the asymmetric distribution of dislocations in the compositional gradient regions generates bulk DMI. Our results indicate the importance of bulk DMI in multilayers and could facilitate the development of spintronic devices.

Magnetic racetrack memory (RTM) uses a series of either domains or skyrmions as data bits along nanowires. However, it lacks reading error detection capability in nanowires, which requires high electric current density for the deterministic motion of domain walls (DWs) or skyrmions. Here, we propose a method of a reading error-detectable RTM and explore domain-stored skyrmion structures for this RTM. This method uses domains as memory cells and assigns the presence and absence of a skyrmion in a domain to different bits, enabling the electrical signal of any memory cells to output the opposite sign to that of the adjacent memory cells. Using simulations and Lorentz microscopy, we demonstrate that perpendicularly magnetized nanowires with relatively large Dzyaloshinskii-Moriya interaction can achieve domain-stored skyrmion structures. Additionally, our simulations show that when DWs approach to skyrmions during spin-orbit torque-induced motion, angular momentum transfers from DWs to skyrmions, resulting in fast motion of skyrmions.

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly correctable, and aim to maximize a performance functional that combines a modified channel fidelity with a tuneable regularization term that promotes simpler codes. With this choice optimization is performed only over the set of codes, and not over the set of recovery operators. The set of codes of fixed dimensions is parametrized as the complex-valued Stiefel manifold of the same dimension: the resulting non-convex optimization problem is then solved by gradient-based local algorithms. When perfectly correctable codes cannot be found, a second optimization routine is run on the recovery Kraus map, also parametrized in a suitable Stiefel manifold via Stinespring representation. To test the approach, correctable codes are sought in different scenarios and compared to existing ones: three qubits subjected to bit-flip errors (single and correlated), four qubits undergoing local amplitude damping and five qubits subjected to local depolarizing channels. Approximate codes are found and tested for the previous examples as well pure non-Markovian dephasing noise acting on a $7/2$ spin, induced by a $1/2$ spin bath, and the noise of the first three qubits of IBM's \texttt{ibm\_kyoto} quantum computer. The fidelity results are competitive with existing iterative optimization algorithms, with respect to which we maintain a strong computational advantage, while obtaining simpler codes.

The Kalman filter is indispensable for state estimation across diverse fields but faces computational challenges with higher dimensions. Approaches such as Riccati equation approximations aim to alleviate this complexity, yet ensuring properties like bounded errors remains challenging. Yamada and Ohki introduced low-rank Kalman-Bucy filters for continuous-time systems, ensuring bounded errors. This paper proposes a discrete-time counterpart of the low-rank filter and shows its system theoretic properties and conditions for bounded mean square error estimation. Numerical simulations show the effectiveness of the proposed method., Comment: 6 pages, submitted

The Kalman-Bucy filter is extensively utilized across various applications. However, its computational complexity increases significantly in large-scale systems. To mitigate this challenge, a low-rank approximated Kalman--Bucy filter was proposed, comprising Oja's principal component flow and a low-dimensional Riccati differential equation. Previously, the estimation error was confirmed solely for linear time-invariant systems with a symmetric system matrix. This study extends the application by eliminating the constraint on the symmetricity of the system matrix and describes the equilibrium points of the Oja flow along with their stability for general matrices. In addition, the domain of attraction for a set of stable equilibrium points is estimated. Based on these findings, we demonstrate that the low-rank approximated Kalman--Bucy filter with a suitable rank maintains a bounded estimation error covariance matrix if the system is controllable and observable., Comment: fixed a few typos

The fusion of non-Abelian anyons or topological defects is a fundamental operation in measurement-only topological quantum computation. In topological superconductors, this operation amounts to a determination of the shared fermion parity of Majorana zero modes. As a step towards this, we implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined nanowire. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1 fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7 $\mu$s at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. These results are consistent with a measurement of the fermion parity encoded in a pair of Majorana zero modes that are separated by approximately 3 $\mu$m and subjected to a low rate of poisoning by non-equilibrium quasiparticles. The large capacitance shift and long poisoning time enable a parity measurement error probability of 1%., Comment: Added data on a second measurement of device A and a measurement of device B, expanded discussion of a trivial scenario. Refs added, author list updated

Measurements of nucleon and nuclei Electric Dipole Moments (EDMs) play an important role in probing CP violation and exploring physics beyond the Standard Model. We extract the neutron EDM by measuring the energy shift of the nucleon two-point correlation function in the presence of a background field. The UV divergence of the topological charge density operator is mitigated using gradient flow, and the diffusion effect induced by the gradient flow process is included into the fit ansatz. Our calculations were carried out on two 2+1 DWF fermion, Iwasaki, gauge field ensembles generated by the RBC/UKQCD collaborations with inverse lattice spacing 1.73 GeV and pion masses of about 340 and 420 MeV., Comment: 8 pages, 3 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we highlight the key role of dynamical invariance of the target: if the perturbation preserves invariance, it is possible to prove that it also preserves its attractivity, under some additional assumptions. In addition, we prove boundedness in mean of the solutions of perturbed systems under open-loop protocols. For the feedback strategies, in the general case without assumptions on invariance, we provide bounds on the perturbation effect in expectation and in probability, as well as specific bounds for non-demolition nominal systems.

We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a specific relation between different CP asymmetries. The resultant relation is similar to the one obtained in GUT baryogenesis and sphaleron processes, where we also obtain a required condition for generating particle number asymmetry in CP-like symmetric models. In addition, we propose a generalization of a CP-like transformation for continuous symmetry groups. Since the CP transformation is an outer automorphism, which depends on the internal symmetry group, it turns out that the physical CP and CP-like symmetries can be mutually converted through the spontaneous symmetry breaking (SSB) of the internal symmetry. We investigate properties of physical CP asymmetry in both CP and CP-like symmetric phases, and find that the spontaneous CP violation and restoration can be observed even in models with continuous groups. We demonstrate that CP-like symmetric models with continuous Lie groups can be naturally realized in physical CP symmetric models through the SSB., Comment: 50 pages, 1 figure

We develop an energy trading system, EDISON-X, that uses blockchain technology to manage the buying and selling of electricity usage rights, i.e., tokens. UPX and SPX tokens purchase electricity from the utility company's distribution lines and the photovoltaic panels. On July 1, 17 students in our school dormitory participated in an experiment to confirm the operation of the EDISON-X system. Based on the results of this experiment, we discuss the energy trading system using blockchain technology for the effective usage of renewable energy. We develop topology and network science methodologies to understand the characteristics of energy trading. We test the hypothesis that market transactions become less active when ``cavities'' appear using persistent homology. The preliminary result implies that the hypothesis could be adopted. We, however, need more data samples.

In usual (non-stochastic) tensor network calculations, the truncated singular value decomposition (SVD) is often used for approximating a tensor, and it causes systematic errors. By introducing stochastic noise in the approximation, however, one can avoid such systematic errors at the expense of statistical errors which can be straightforwardly controlled. Therefore in principle, exact results can be obtained even at finite bond dimension up to the statistical errors. A previous study of the unbiased method implemented in tensor renormalization group (TRG) algorithm, however, showed that the statistical errors for physical quantity are not negligible, and furthermore the computational cost is linearly proportional to a system volume. In this paper, we introduce a new way of stochastic noise such that the statistical error is suppressed, and moreover, in order to reduce the computational cost we propose common noise method whose cost is proportional to the logarithm of volume. We find that the method provides better accuracy for the free energy compared with the truncated SVD when applying to TRG for Ising model on square lattice. Although the common noise method introduces systematic error originated from a correlation of noises, we show that the error can be described by a simple functional form in terms of the number of noises, thus the error can be straightforwardly controlled in an actual analysis. We also apply the method to the graph independent local truncation algorithm and show that the accuracy is further improved., Comment: 34 pages, 19 figures, 2 tables, version published in Phys.Rev.D

Exquisite sensitivities are a prominent advantage of quantum sensors. Ramsey sequences allow precise measurement of direct current fields, while Hahn-echo-like sequences measure alternating current fields. However, the latter are restrained for use with high-frequency fields (above approximately $1$ kHz) due to finite coherence times, leaving less-sensitive noncoherent methods for the low-frequency range. In this paper, we propose to bridge the gap with a fitting-based algorithm with a frequency-independent sensitivity to coherently measure low-frequency fields. As the algorithm benefits from coherence-based measurements, its demonstration with a single nitrogen-vacancy center gives a sensitivity of $9.4$ nT Hz$^{-0.5}$ for frequencies below about $0.6$ kHz down to near-constant fields. To inspect the potential in various scenarios, we apply the algorithm at a background field of tens of nTs, and we measure low-frequency signals via synchronization., Comment: 12 pages, 5 figures; supp 14 pages, 9 figures

To determine how electron correlations open a gap in two-dimensional massless Dirac electrons in the organic compounds $\alpha$-(BEDT-TTF)$_2$I$_3$ [$\alpha$-(ET)$_2$I$_3$] and $\alpha$-(BEDT-TSeF)$_2$I$_3$ [$\alpha$-(BETS)$_2$I$_3$], we derive and analyze $ab$ $initio$ low-energy effective Hamiltonians for these two compounds. We find that the horizontal stripe charge ordering opens a gap in the massless Dirac electrons in $\alpha$-(ET)$_2$I$_3$, while an insulating phase without explicit symmetry breaking appears in $\alpha$-(BETS)$_2$I$_3$. We clarify that the combination of the anisotropic transfer integrals and the electron correlations induces a dimensional reduction in the spin correlations, i.e., one-dimensional spin correlations develop in $\alpha$-(BETS)$_2$I$_3$. We show that the one-dimensional spin correlations open a gap in the massless Dirac electrons. Our finding paves the way for opening gaps for massless Dirac electrons using strong electronic correlations., Comment: 9 pages, 2 tables, and 6 figures. The input and output files of the ab initio and the mVMC calculations are available at https://isspns-gitlab.issp.u-tokyo.ac.jp/k-yoshimi/alpha-salts

Silicon-vacancy (SiV) centers in diamond are a promising candidate for all-optical nanoscale high-sensitivity thermometry because they have sufficient sensitivity to reach the subkelvin precision required for application to biosystems. It is expected that nanodiamonds with SiV centers can be injected into cells to measure the nanoscale local temperatures of biosystems such as organelles. However, the smallest particle size used to demonstrate thermometry using SiV centers is a few hundred nanometers. We recently developed SiV-center-containing nanodiamonds via a detonation process that is suitable for large-scale production. Here, we investigate the spectral response of SiV-center-containing detonation nanodiamonds (SiV-DNDs) to temperature. We used air-oxidized and polyglycerol-coated SiV-DNDs with a mean particle size of around 20 nm, which is the smallest size used to demonstrate thermometry using color centers in nanodiamond. We found that the zero-phonon line for SiV-DND is linearly red-shifted with increasing temperature in the range of 22.0 to 40.5 $^\circ C$. The peak sensitivity to temperature was 0.011 $\pm$ 0.002 nm/K, which agrees with the reported high sensitivity of SiV centers in bulk diamond. A temperature sensitivity analysis revealed that SiV-DND thermometry can achieve subkelvin precision. All-optical SiV-DND thermometry will be important for investigating nanosystems such as organelles in living cells., Comment: 35 pages, 7 figures, 3 tables