arXiv subjects

Amit Rotem

Publications and source records attributed to Amit Rotem.

14 recordsLinked to original sources

arXiv2026

The WaveHoltz Heterogeneous Multiscale Method

We consider the numerical solution of the wave equation in materials with rapidly varying coefficients, and time harmonic sources. For these problems, direct discretization is prohibitively costly, and instead multiscale methods are used. There are several multiscale methods that directly discretize in the frequency domain. In this work we instead start in the time-domain and combine a finite difference Heterogeneous Multiscale Method (HMM) for the wave equation with the WaveHoltz method. Each WaveHoltz iteration marches the wave equation towards the time-periodic Helmholtz solution. The advantages of the WaveHoltz method relative to traditional Helmholtz solvers carry over directly to the multiscale problems considered here. Since, in addition, the time-domain solver does not artificially impose boundary conditions on the micro-scale problems, no boundary errors from the micro-scale problems are present in the homogenized frequency domain solution.

math.NA↗

arXiv2026

Efficient Domain Decomposition for the Helmholtz Equation on GPUs

The Helmholtz equation governs wave propagation in acoustics, electromagnetics, and seismology, but its indefinite nature makes it difficult to solve with iterative methods. Domain decomposition methods are a natural fit for massively parallel architectures, yet mapping efficient Helmholtz solvers onto modern GPUs remains a challenge. We address both with two key contributions: (1) a block-level domain decomposition scheme, in which each subdomain is assigned to a single thread block and all solves run concurrently in a single kernel launch, and (2) WaveHoltz as the subdomain solver. WaveHoltz is a fixed-point iteration that is uniquely well-suited to the GPU execution model due to its minimal memory footprint and no reduction operations. Together, these eliminate device-level synchronizations and replace global memory traffic with shared memory and register-level operations, keeping subdomain data largely resident in L1 and L2 cache. We explore two threading strategies: one degree of freedom per thread for small subdomains, and multiple degrees of freedom per thread for larger ones. Benchmarks of our CUDA based implementation on a NVIDIA A100 show that WaveHoltz achieves 2x-25x speedup over MINRES, with the advantage growing with subdomain size. Crucially, evaluating the subdomain solver in single rather than double precision yields an additional 2x-10x speedup--a benefit largely unattainable by MINRES due to loss of Krylov vector orthogonality under reduced precision.

cs.DC↗

arXiv2025

High fidelity CNOT gates in photonic integrated circuits using composite segmented directional couplers

Integrated photonic circuits are a promising platform for scalable quantum information processing, but their performance is often constrained by component sensitivity to fabrication imperfections. Directional couplers, which are crucial building blocks for integrated quantum logic gates, are particularly prone to such limitations, with strong dependence on geometric and spectral parameters which reduces gate fidelity. Here, we demonstrate that composite segmented directional couplers (CSDC) offer a fabrication-tolerant alternative that enhances gate fidelity without active tuning. We design and fabricate a fully integrated photonic controlled-NOT (CNOT) gate using both uniform and composite coupler variants and compare their performance via simulation, classical characterization, and quantum two-photon interference. The composite design reduces the average error probability by nearly a factor of two and decreases variability fivefold. The residual error is primarily limited by photon indistinguishability. Classical matrix reconstruction confirms improved agreement with the ideal CNOT operation. These results establish CSDCs as compact, passive, and foundry-compatible building blocks for robust scalable quantum photonic circuits.

physics.optics↗

arXiv2025

Cavity-mediated cross-cross-resonance gate

We propose a cavity-mediated gate between two transmon qubits or other nonlinear superconducting elements. The gate is realized by driving both qubits at a frequency that is near-resonant with the frequency of the cavity. Since both qubits are subject to a cross-resonant drive, we call this gate a cross-cross-resonance gate. In close analogy with gates between trapped-ion qubits, in phase space, the state of the cavity makes a circle whose area depends on the state of the two qubits, realizing a controlled-phase gate. We propose two schemes for canceling the dominant error, which is the dispersive coupling. We also show that this cross-cross-resonance gate allows one to realize simultaneous gates between multiple pairs of qubits coupled via the same metamaterial composed of an array of coupled cavities or other linear mediators.

quant-ph↗

arXiv2025

High-Fidelity Integrated Quantum Photonic Logic Via Robust Directional Couplers

Scalable quantum information processing with integrated photonics requires quantum logic operations with high fidelity and robustness. Directional couplers, the fundamental elements enabling quantum interference and logic operations, are inherently sensitive to fabrication imperfections and environmental fluctuations, leading to reduced gate fidelities. Here, we experimentally demonstrate a passive design strategy that mitigates these errors by exploiting a stationary geometrical configuration in uniform directional couplers, where first-order variations in the coupling coefficient are intrinsically suppressed. The robust geometry is implemented in a silicon-on-insulator photonic chip hosting two-photon controlled-NOT (CNOT) quantum gates and its performance is directly compared to a non-optimized design. Measurements indicate a mean gate fidelity of $93.30 \pm 0.11\%$, representing a clear improvement over the non-robust implementation mean fidelity of $91.93 \pm 0.17\%$, without any active tuning or footprint increase. This performance approaches the theoretical limit of $93.78\%$, imposed by the imperfect source. Monte Carlo simulations incorporating realistic fabrication noise confirm the observed enhancement and reveal consistent suppression of gate-level error rates. These results demonstrate a compact, fabrication-tolerant building block for scalable, fault-tolerant photonic quantum circuits and highlight the power of passive geometric error mitigation in quantum hardware design.

physics.optics↗

arXiv2025

Accurate Modeling of Directional Couplers with Oxide Cladding: Bridging Simulation and Experiment

Directional couplers are a fundamental building block in integrated photonics, particularly in quantum applications and optimization-based design where precision is critical. Accurate functionality is crucial to ensure reliable operation within classical and quantum circuits. However, discrepancies between simulations and measurements are frequently observed. These inaccuracies can compromise the performance and scalability of integrated photonic systems, underscoring the critical need for advanced, precise simulation methods that bridge the gap between design and implementation. In this work, we show that this discrepancy can be mainly attributed to density changes in the oxide cladding. We conduct a systematic study involving experimental optical measurements, numerical simulations, and direct electron microscopy imaging to investigate this discrepancy in directional couplers. We find that the impact of cladding density variations on performance increases as feature gaps shrink. By incorporating these effects into our simulations using a novel and physically motivated Effective Trench Medium Model (ETMM), we achieve highly accurate reproduction of experimental measurements. We quantify the effects of cladding density variations on the SU(2) symmetry parameters that govern light propagation in directional couplers. This insight is crucial for advancing the precision of compact device fabrication, enabling reliable simulation of photonic integrated devices.

physics.optics↗

arXiv2024

Robust Characterization of Integrated Photonics Directional Couplers

Directional couplers are essential components in integrated photonics. Given their widespread use, accurate characterization of directional couplers is crucial for ensuring optimal performance. However, it is challenging due to the coupling between fibers and waveguides, which is highly sensitive to alignment and fabrication imperfections. To address these challenges, we propose a novel direct measurement technique that offers greater robustness to variations in optical interfaces, while bypassing extinction ratio measurements. Our method enables a broadband and precise characterization of the directional couplers' splitting ratio. We experimentally validate this approach, demonstrate its robustness against intentional errors, and compare it to a naive direct measurement method. Furthermore, our technique is generalized to measure the amplitude of any general 2x2 unitary circuit, providing valuable insights for designing and testing a wide range of photonic integrated devices.

physics.optics↗

arXiv2024

Convergence of the Semi-Discrete WaveHoltz Iteration

In this paper we prove that for stable semi-discretizations of the wave equation for the WaveHoltz iteration is guaranteed to converge to an approximate solution of the corresponding frequency domain problem, if it exists. We show that for certain classes of frequency domain problems, the WaveHoltz iteration without acceleration converges in $O({\omega})$ iterations with the constant factor depending logarithmically on the desired tolerance. We conjecture that the Helmholtz problem in open domains with no trapping waves is one such class of problems and we provide numerical examples in one and two dimensions using finite differences and discontinuous Galerkin discretizations which demonstrate these converge results.

math.NA↗

arXiv2020

Correlated noise in Brownian motion allows for super resolution

Diffusion broadening of spectral lines is the main limitation to frequency resolution in non-polarized liquid state nano-NMR. This problem arises from the limited amount of information that can be extracted from the signal before losing coherence. For liquid state NMR as with most generic sensing experiments, the signal is thought to decay exponentially, severely limiting resolution. However, there is theoretical evidence that predicts a power law decay of the signal's correlations due to diffusion noise in the non-polarized nano-NMR scenario. In this work we show that in the NV based nano-NMR setup such diffusion noise results in high spectral resolution.

quant-ph↗

arXiv2018

Overcoming resolution limits with quantum sensing

The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. An important figure of merit for sensing time dependent signals is the spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.

quant-ph↗

arXiv2018

NV center based nano-NMR enhanced by deep learning

The growing field of nano nuclear magnetic resonance (nano-NMR) seeks to estimate spectra or discriminate between spectra of minuscule amounts of complex molecules. While this field holds great promise, nano-NMR experiments suffer from detrimental inherent noise. This strong noise masks to the weak signal and results in a very low signal-to-noise ratio. Moreover, the noise model is usually complex and unknown, which renders the data processing of the measurement results very complicated. Hence, spectra discrimination is hard to achieve and in particular, it is difficult to reach the optimal discrimination. In this work we present strong indications that this difficulty can be overcome by deep learning (DL) algorithms. The DL algorithms can mitigate the adversarial effects of the noise efficiently by effectively learning the noise model. We show that in the case of frequency discrimination DL algorithms reach the optimal discrimination without having any pre-knowledge of the physical model. Moreover, the DL discrimination scheme outperform Bayesian methods when verified on noisy experimental data obtained by a single Nitrogen-Vacancy (NV) center. In the case of frequency resolution we show that this approach outperforms Bayesian methods even when the latter have full pre-knowledge of the noise model and the former has none. These DL algorithms also emerge as much more efficient in terms of computational resources and run times. Since in many real-world scenarios the noise is complex and difficult to model, we argue that DL is likely to become a dominant tool in the field.

quant-ph↗

arXiv2017

Limits on Spectral Resolution Measurements by Quantum Probes

The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cram\'er-Rao bound of a single frequency estimation.

quant-ph↗

arXiv2017

Fast dynamical decoupling of the Molmer-Sorensen entangling gate

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of $\sqrt{N}$, with $N$ being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of $\frac{\pi}{2}$, independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to $\sigma_z$ noise with ions in a Paul trap.

physics.atom-ph↗

arXiv2016

Refocusing two qubit gate noise for trapped ions by composite pulses

Amplitude noise which inflicts a random two qubit term is one of the main obstacles preventing the implementation of a high fidelity two-body gate below the fault tolerance threshold. This noise is difficult to refocus as any refocusing technique could only tackle noise with frequency below the operation rate. Since the two qubit gate speed is normally the slowest rate in the system, it constitutes the last bottleneck towards an implementation of a gate below the fault tolerant threshold. Here we propose to use composite pulses as a dynamical decoupling approach, in order to reduce two qubit gate noise for trapped ions systems. This is done by refocusing the building blocks of ultrafast entangling gates, where the amplitude noise is reduced to shot-to-shot (STS) noise. We present detailed simulations showing that the fault-tolerance threshold could be achieved with the proposed approach.

quant-ph↗