Search

A quantum particle evolving by Schr\"odinger's equation in discrete space constitutes a continuous-time quantum walk on a graph of vertices and edges. When a vertex is marked by an oracle, the quantum walk effects a quantum search algorithm. Previous investigations of this quantum search algorithm on graphs with cliques have shown that the edges between the cliques can be weighted to enhance the movement of probability between the cliques to reach the marked vertex. In this paper, we explore the most restrictive form of this by analyzing search on a weighted barbell graph that consists of two cliques of the same size joined by a single weighted edge/bridge. This graph is generally irregular, so quantum walks governed by the graph Laplacian or by the adjacency matrix can differ. We show that the Laplacian quantum walk's behavior does not change, no matter the weight of the bridge, and so the single bridge is too restrictive to affect the walk. Similarly, the adjacency quantum walk's behavior is unchanged for most weights, but when the weight equals the size of a clique, the probability does collect at the clique containing the marked vertex, and utilizing a two-stage algorithm with different weights for each stage, the success probability is boosted from 0.5 to 0.996, independent of the size of the barbell graph., Comment: 15 pages, 10 figures

The optimal runtime of a quantum computer searching a database is typically cited as the square root of the number of items in the database, which is famously achieved by Grover's algorithm. With parallel oracles, however, it is possible to search faster than this. We consider a many-body quantum system that naturally effects parallel queries, and we show that its parameters can be tuned to search a database in constant time, assuming a sufficient number of interacting particles. In particular, we consider Bose-Einstein condensates with pairwise and three-body interactions in the mean-field limit, which effectively evolve by a nonlinear Schr\"odinger equation with cubic and quintic nonlinearities. We solve the unstructured search problem formulated as a continuous-time quantum walk searching the complete graph in constant time. Depending on the number of marked vertices, however, the success probability can peak sharply, necessitating high precision time measurement to observe the system at this peak. Overcoming this, we prove that the relative coefficients of the cubic and quintic terms can be tuned to eliminate the need for high time-measurement precision by widening the peak in success probability or having it plateau. Finally, we derive a lower bound on the number of atoms needed for the many-body system to evolve by the effective nonlinearity., Comment: 15 pages, 6 figures

This paper presents a non-zoned discrete dielectric lens comprising two or three matching layers to reduce the 50-110 GHz frequency range reflections. Based on Chebyshev and binomial multi-section transformers, the designed models use matching layers at the top and bottom. In addition, the presented designs use pins instead of the conventional slots for the matching layers, thus easing the manufacturing process. The results show that the broadband realized gain obtained using the proposed design is higher for both the two- and three-layer design than the commonly used quarter-wave transformer. A Binomial lens with two matchings layers using 38 unit cells is fabricated and illuminated by an open-ended waveguide to validate the simulation results obtained using CST Microwave Studio. The fabrication process uses stereolithography additive manufacturing.

This paper is a work in progress. We are looking for collaborators to provide us financial datasets in Equity/Futures market to conduct more bench-marking studies. The authors have papers employing similar methods applied on the Numerai dataset, which is freely available but obfuscated. We apply different feature engineering methods for time-series to US market price data. The predictive power of models are tested against Numerai-Signals targets., Comment: arXiv admin note: substantial text overlap with arXiv:2303.07925

We present a robust deep incremental learning framework for regression tasks on financial temporal tabular datasets which is built upon the incremental use of commonly available tabular and time series prediction models to adapt to distributional shifts typical of financial datasets. The framework uses a simple basic building block (decision trees) to build self-similar models of any required complexity to deliver robust performance under adverse situations such as regime changes, fat-tailed distributions, and low signal-to-noise ratios. As a detailed study, we demonstrate our scheme using XGBoost models trained on the Numerai dataset and show that a two layer deep ensemble of XGBoost models over different model snapshots delivers high quality predictions under different market regimes. We also show that the performance of XGBoost models with different number of boosting rounds in three scenarios (small, standard and large) is monotonically increasing with respect to model size and converges towards the generalisation upper bound. We also evaluate the robustness of the model under variability of different hyperparameters, such as model complexity and data sampling settings. Our model has low hardware requirements as no specialised neural architectures are used and each base model can be independently trained in parallel.

Tidal disruption events (TDEs), apart from producing luminous electromagnetic (EM) flares, can generate potentially detectable gravitational wave (GW) burst signals by future space-borne GW detectors. In this Letter, we propose a methodology to constrain the Hubble constant $H_0$ by incorporating the TDE parameters measured by EM observations (e.g., stellar mass, black hole (BH) mass and spin, and other orbital parameters) into the observed TDE GW waveforms. We argue that an accurate knowledge of the BH spin could help constrain the orbital inclination angle, hence alleviating the well-known distance-inclination degeneracy in GW waveform fitting. For individual TDEs, the precise redshift measurement of the host galaxies along with the luminosity distance $D_{\rm L}$ constrained by EM and GW signals would give a self-contained measurement of $H_0$ via Hubble's law, completely independent of any specific cosmological models., Comment: 5 pages, 3 figures, submitted for review

The application of deep learning to non-stationary temporal datasets can lead to overfitted models that underperform under regime changes. In this work, we propose a modular machine learning pipeline for ranking predictions on temporal panel datasets which is robust under regime changes. The modularity of the pipeline allows the use of different models, including Gradient Boosting Decision Trees (GBDTs) and Neural Networks, with and without feature engineering. We evaluate our framework on financial data for stock portfolio prediction, and find that GBDT models with dropout display high performance, robustness and generalisability with reduced complexity and computational cost. We then demonstrate how online learning techniques, which require no retraining of models, can be used post-prediction to enhance the results. First, we show that dynamic feature projection improves robustness by reducing drawdown in regime changes. Second, we demonstrate that dynamical model ensembling based on selection of models with good recent performance leads to improved Sharpe and Calmar ratios of out-of-sample predictions. We also evaluate the robustness of our pipeline across different data splits and random seeds with good reproducibility.

Tidal disruption events (TDEs) are valuable probes of the demographics of supermassive black holes as well as the dynamics and population of stars in the centers of galaxies. In this Letter, we focus on studying how the debris disk formation and circularization processes can impact the possibility of observing prompt flares in TDEs. First, we investigate how the efficiency of disk formation is determined by the key parameters, namely, the black hole mass $M_{BH}$, the stellar mass $m_\star$, and the orbital penetration parameter $\beta$ that quantifies how close the disrupted star would orbit around the black hole. Then we calculate the intrinsic differential TDE rate as a function of these three parameters. Combining these two results, we find that the rates of TDEs with prompt disk formation are significantly suppressed around lighter black holes, which provides a plausible explanation for why the observed TDE host black hole mass distribution peaks between $10^6$ and $10^7M_\odot$. Therefore, the consideration of the disk formation efficiency is crucial for recovering the intrinsic black hole demographics from TDEs. Furthermore, we find that the efficiency of the disk formation process also impacts the distributions of both stellar orbital penetration parameter and stellar mass observed in TDEs., Comment: Accepted to ApJL

The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs, including periodic lattices, strongly regular graphs, Johnson graphs, and the hypercube. In these prior works, the weights of the self-loops preserved the symmetries of the graphs. In this paper, we show that the self-loops can break all the symmetries of vertex-transitive graphs while providing the same computational speedups. Only the weight of the self-loop at the marked vertex matters, and the remaining self-loop weights can be chosen randomly, as long as they are small compared to the degree of the graph., Comment: 15 pages, 8 figures

It is well-known that any quantum gate can be decomposed into the universal gate set {T, H, CNOT}, and recent results have shown that each of these gates can be implemented using a dynamic quantum walk, which is a continuous-time quantum walk on a sequence of graphs. This procedure for converting a quantum gate into a dynamic quantum walk, however, can result in long sequences of graphs. To alleviate this, in this paper, we develop a length-3 dynamic quantum walk that implements any single-qubit gate. Furthermore, we extend this result to give length-3 dynamic quantum walks that implement any single-qubit gate controlled by any number of qubits. Using these, we implement Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a dynamic quantum walk., Comment: 15 pages, 12 figures

The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems, however, the Hamiltonian is proportional to the adjacency matrix instead. It is well-known that these quantum walks are equivalent when the graph is regular, i.e., when each vertex has the same number of neighbors. If the graph is irregular, however, the quantum walks evolve differently. In this paper, we show that for some irregular graphs, if the particle is initially localized at a certain vertex, the probability distributions of the two quantum walks are identical, even though the amplitudes differ. We analytically prove this for a graph with five vertices and a graph with six vertices. By simulating the walks on all 1,018,689,568 simple, connected, irregular graphs with eleven vertices or less, we found sixty-four graphs with this notion of equivalence. We also give eight infinite families of graphs supporting these equivalent walks., Comment: 23 pages, 15 figures

A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that implements a quantum circuit can be quite complicated. In this paper, we give six scenarios under which a dynamic graph can be simplified, and they exploit commuting graphs, identical graphs, perfect state transfer, complementary graphs, isolated vertices, and uniform mixing on the hypercube. As examples, we simplify dynamic graphs, in some instances allowing single-qubit gates to be implemented in parallel.

We evaluate the micromagnetic energy of a domain wall contained in a thin, horn-shaped nanostructure and propose a method to extract the strength of the interfacial Dzyaloshinskii-Moriya interaction based on the equilibrium position of the wall. An inplane magnetic field coupled with the interfacial DMI balances a competing driving force related to the "nanohorn" tapering and consequent variation in length. It is evident that the strength of the the DMI is directly correlated to the equilibrium position of the DW. Moreover, the range of measurable DMI values can be controlled by varying the degree of tapering in the nanohorn. Numerical and semi-analytical calculations were separately performed and show broad agreement. The calculations provided here offer an alternative framework for future measurement of DMI, which has been notoriously difficult to do experimentally., Comment: 3 pages, 3 figures, submitted to IEEE Transactions on Magnetics

We estimate the rate of tidal disruption events (TDEs) that will be detectable with future gravitational wave detectors as well as the most probable properties of these events and their possible electromagnetic counterpart. To this purpose we combine standard gravitational waves and electromagnetic results with detailed rates estimates. We find that the \emph{Laser Interferometer Space Antenna} (LISA) should not detect any TDEs, unless black holes (BHs) are typically embedded by a young stellar population which, in this situation, could lead up to few 10 events during the duration of the mission. If there are gravitational wave observations, these events should also be observable in the X-ray or the optical/UV part of the electromagnetic spectrum, which may open up the multi-messenger era for TDEs. The generation of detectors following LISA will at least yearly observe $10^4$ TDEs at cosmological distances, allowing to do population studies and constrain the black hole mass function. In all cases, most probable events should be around black holes with a mass such that the Keplerian frequency at the Schwarzschild radius is similar to the optimal frequency of the detector and with a large penetration factor., Comment: accepted to MNRAS

We use a combination of observational data in order to reconstruct the free function of f(T) gravity in a model-independent manner. Starting from the data-driven determined dark-energy equation-of-state parameter we are able to reconstruct the f(T) form. The obtained function is consistent with the standard {\Lambda}CDM cosmology within 1{\sigma} confidence level, however the best-fit value experiences oscillatory features. We parametrise it with a sinusoidal function with only one extra parameter comparing to {\Lambda}CDM paradigm, which is a small oscillatory deviation from it, close to the best-fit curve, and inside the 1{\sigma} reconstructed region. Similar oscillatory dark-energy scenarios are known to be in good agreement with observational data, nevertheless this is the first time that such a behavior is proposed for f(T) gravity. Finally, since the reconstruction procedure is completely model-independent, the obtained data-driven reconstructed f(T) form could release the tensions between {\Lambda}CDM estimations and local measurements, such as the H0 and {\sigma}8 ones., Comment: 8 pages, 5 figures

The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search problem, this corresponds to searching the complete graph, or all-to-all network, for a marked vertex by querying an oracle. In this tutorial, we derive how discrete- and continuous-time (classical) random walks and quantum walks solve this problem in a thorough and pedagogical manner, providing an accessible introduction to how random and quantum walks can be used to search spatial regions. Some of the results are already known, but many are new. For large $N$, the random walks converge to the same evolution, both taking $N \ln(1/\epsilon)$ time to reach a success probability of $1-\epsilon$. In contrast, the discrete-time quantum walk asymptotically takes $\pi\sqrt{N}/2\sqrt{2}$ timesteps to reach a success probability of $1/2$, while the continuous-time quantum walk takes $\pi\sqrt{N}/2$ time to reach a success probability of $1$., Comment: 33 pages, 11 figures

The lackadaisical quantum walk is a discrete-time, coined quantum walk on a graph with a weighted self-loop at each vertex. It uses a generalized Grover coin and the flip-flop shift, which makes it equivalent to Szegedy's quantum Markov chain. It has been shown that a lackadaisical quantum walk can improve spatial search on the complete graph, discrete torus, cycle, and regular complete bipartite graph. In this paper, we observe that these are all vertex-transitive graphs, and when there is a unique marked vertex, the optimal weight of the self-loop equals the degree of the loopless graph divided by the total number of vertices. We propose that this holds for all vertex-transitive graphs with a unique marked vertex. We present a number of numerical simulations supporting this hypothesis, including search on periodic cubic lattices of arbitrary dimension, strongly regular graphs, Johnson graphs, and the hypercube., Comment: 17 pages, 5 figures

We study a model of a semiflexible long chain polymer confined to a two-dimensional slit of width $w$, and interacting with the walls of the slit. The interactions with the walls are controlled by Boltzmann weights $a$ and $b$, and the flexibility of the polymer is controlled by another Boltzmann weight $c$. This is a simple model of the steric stabilisation of colloidal dispersions by polymers in solution. We solve the model exactly and compute various quantities in $(a,b,c)$-space, including the free energy and the force exerted by the polymer on the walls of the slit. In some cases these quantities can be computed exactly for all $w$, while for others only asymptotic expressions can be found. Of particular interest is the zero-force surface -- the manifold in $(a,b,c)$-space where the free energy is independent of $w$, and the loss of entropy due to confinement in the slit is exactly balanced by the energy gained from interactions with the walls., Comment: 25 pages, 10 figures

It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, $T$, and CNOT gates, and these gates are easily extended to multi-qubit systems. For example, the $T$ gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of four. We also construct a generalized phase gate, of which $Z$, $S$, and $T$ are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- and two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk., Comment: 10 pages, 6 figures

The lackadaisical quantum walk, which is a quantum walk with a weighted self-loop at each vertex, has been shown to speed up dispersion on the line and improve spatial search on the complete graph and periodic square lattice. In these investigations, each self-loop had the same weight, owing to each graph's vertex-transitivity. In this paper, we propose lackadaisical quantum walks where the self-loops have different weights. We investigate spatial search on the complete bipartite graph, which can be irregular with $N_1$ and $N_2$ vertices in each partite set, and this naturally leads to self-loops in each partite set having different weights $l_1$ and $l_2$, respectively. We analytically prove that for large $N_1$ and $N_2$, if the $k$ marked vertices are confined to, say, the first partite set, then with the typical initial uniform state over the vertices, the success probability is improved from its non-lackadaisical value when $l_1 = kN_2/2N_1$ and $N_2 > (3 - 2\sqrt{2}) N_1$, regardless of $l_2$. When the initial state is stationary under the quantum walk, however, then the success probability is improved when $l_1 = kN_2/2N_1$, now without a constraint on the ratio of $N_1$ and $N_2$, and again independent of $l_2$. Next, when marked vertices lie in both partite sets, then for either initial state, there are many configurations for which the self-loops yield no improvement in quantum search, no matter what weights they take., Comment: 18 pages, 12 figures

The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$ marked vertices with different initial states. We prove intriguing dependence on the number of marked and unmarked vertices in each partite set. For example, when the graph is irregular and the initial state is the typical uniform superposition over the vertices, then the success probability can vary greatly from one timestep to the next, even alternating between 0 and 1, so the precise time at which measurement occurs is crucial. When the initial state is a uniform superposition over the edges, however, the success probability evolves smoothly. As another example, if the complete bipartite graph is regular, then the two initial states are equivalent. Then if two marked vertices are in the same partite set, the success probability reaches 1/2, but if they are in different partite sets, it instead reaches $1$. This differs from the complete graph, which is the quantum walk formulation of Grover's algorithm, where the success probability with two marked vertices is 8/9. This reveals a contrast to the continuous-time quantum walk, whose evolution is governed by Schr\"odinger's equation, which asymptotically searches the regular complete bipartite graph with any arrangement of marked vertices in the same manner as the complete graph., Comment: 13 pages, 7 figures