arXiv subjects

Asif Shakeel

Publications and source records attributed to Asif Shakeel.

13 recordsLinked to original sources

arXiv2026

Mobility Trajectories from Network-Driven Markov Dynamics

We present a generative model of human mobility in which trajectories arise as realizations of a prescribed, time-dependent Markov dynamics defined on a spatial interaction network. The model constructs a hierarchical routing structure with hubs, corridors, feeder paths, and metro links, and specifies transition matrices using gravity-type distance decay combined with externally imposed temporal schedules and directional biases. Population mass evolves as indistinguishable, memoryless movers performing a single transition per time step. When aggregated, the resulting trajectories reproduce structured origin-destination flows that reflect network geometry, temporal modulation, and connectivity constraints. By applying the Perron-Frobenius theorem to the daily evolution operator, we identify a unique periodic invariant population distribution that serves as a natural non-transient reference state. We verify consistency between trajectory-level realizations and multi-step Markov dynamics, showing that discrepancies are entirely attributable to finite-population sampling. The framework provides a network-centric, privacy-preserving approach to generating mobility trajectories and studying time-elapsed flow structure without invoking individual-level behavioral assumptions.

cs.SI↗

arXiv2025

Network-Level Measures of Mobility from Aggregated Origin-Destination Data

We introduce a framework for defining and interpreting collective mobility measures from spatially and temporally aggregated origin--destination (OD) data. Rather than characterizing individual behavior, these measures describe properties of the mobility system itself: how network organization, spatial structure, and routing constraints shape and channel population movement. In this view, aggregate mobility flows reveal aspects of connectivity, functional organization, and large-scale daily activity patterns encoded in the underlying transport and spatial network. To support interpretation and provide a controlled reference for the proposed time-elapsed calculations, we first employ an independent, network-driven synthetic data generator in which trajectories arise from prescribed system structure rather than observed data. This controlled setting provides a concrete reference for understanding how the proposed measures reflect network organization and flow constraints. We then apply the measures to fully anonymized data from the NetMob 2024 Data Challenge, examining their behavior under realistic limitations of spatial and temporal aggregation. While such data constraints restrict dynamical resolution, the resulting metrics still exhibit interpretable large-scale structure and temporal variation at the city scale.

stat.AP↗

arXiv2021

Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing

Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of balancing covariates in randomized trials have efficient randomized algorithms based on the Gram-Schmidt walk (GSW). We frame these problems as quantum Ising models, for which variational quantum algorithms (VQA) are particularly useful. Simulating an example of covariate-balancing on an IBM quantum simulator, we find that the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) yield results comparable to the GSW algorithm.

quant-ph↗

arXiv2020

Efficient and scalable quantum walk algorithms via the quantum Fourier transform

Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a prototype one-dimensional discrete time QW algorithm that economizes resources required in its implementation. Our algorithm needs only a single shift (increment) operation. It also allows complete flexibility in choosing the shift circuit, a resource intensive part of QW implementations. We implement the shift using the quantum Fourier transform (QFT), yielding, to date, the most efficient and scalable, quadratic size, linear depth circuit for the basic QW. This is desirable for Noisy Intermediate-Scale Quantum (NISQ) devices, in which fewer computations implies faster execution and reduced effects of noise and decoherence. As the QFT diagonalizes unitary circulant matrices, we generalize the shift in the basic QW to introduce spatial convolutions in the QW. We demonstrate our basic QW algorithm using the QFT based shift by running it on publicly accessible IBM quantum computers.

quant-ph↗

arXiv2019

The Equivalence of Schrödinger and Heisenberg Pictures in Quantum Cellular Automata

Quantum cellular automata (QCA) are discrete models of space and time homogeneous quantum field theories (QFTs) and regarded as natural candidates for quantum simulation. Description of a QCA over the separable Hilbert space of finite, unbounded configurations (UFC Hilbert space) with unitary state evolution is the {\it Schrödinger template}, and over the incomplete infinite tensor product algebra (ITPA) with evolution by algebra automorphism is the {\it Heisenberg template}. Whether every Heisenberg template admits an equivalent Schrödinger template is a foundational question, and one that has persisted as an open problem. In the present paper we prove that for every Heisenberg template an equivalent Schrödinger template exists. We frame the question from a representation theory standpoint, using constructs and results from the representation theory of finite and countably infinite dimensional vector spaces and from category theory to answer it. With the previously known existence of a Heisenberg template for every Schrödinger template, our result establishes the equivalence of the templates.

quant-ph↗

arXiv2019

Neighborhood-History Quantum Walk

History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhood-history quantum walk (NHQW), in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle's position are interdependent. To demonstrate it, we construct an NHQW on a one-dimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as single-particle sectors of quantum lattice gas automata (QLGA). In contrast, the NHQW constructed in this paper is realized as a single-particle sector of the more general quantum cellular automaton (QCA). The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.

quant-ph↗

arXiv2018

Unentangled Measurements and Frame Functions

Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at least 3. The unentangled frame functions are initially only defined on unentangled (that is, product) states in a multi-partite system. The third author's Unentangled Gleason's Theorem shows that unentangled frame functions determine unique density operators if and only if each subsystem is at least 3-dimensional. In this paper, we determine the structure of unentangled frame functions in general. We first classify them for multi-qubit systems, and then extend the results to factors of varying dimensions including countably infinite dimensions (separable Hilbert spaces). A remarkable combinatorial structure emerges, suggesting possible fundamental interpretations.

quant-ph↗

arXiv2016

Quantum cellular automata without particles

Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are done in terms of Feynman diagrams, which are explicitly interpreted in terms of interacting particles. Similarly, the easiest QCA to construct are quantum lattice gas automata (QLGA). A natural question then is, which QCA are not QLGA? Here we construct a non-trivial example of such a QCA; it provides a simple model in $1+1$ dimensions with no particle interpretation at the scale where the QCA dynamics are homogeneous.

quant-ph↗

arXiv2016

Local Distinguishability of Generic Unentangled Orthonormal Bases

An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an Unentangled Orthogonal Basis (UOB). In general, for $n$ qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of $2^n-1$ two-spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally distinguishable or LOCC distinguishable UOB) are exactly those in the maximum dimensional components. Bennett et al, in their in-depth study of quantum nonlocality without entanglement, include a specific 3 qubit example UOB which is not LOCC distinguishable; we construct certain generalized counterparts of this UOB in $n$ qubits.

quant-ph↗

arXiv2015

Estimating an Activity Driven Hidden Markov Model

We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone records.

stat.ML↗

arXiv2014

History Dependent Quantum Random Walks as Quantum Lattice Gas Automata

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.

math-ph↗

arXiv2014

When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. QLGA have been more deeply analyzed than QCA, whereas general QCA are likely to capture a wider range of quantum behavior. Discriminating between QLGA and QCA is therefore an important question. In spite of much prior work, classifying which QCA are QLGA has remained an open problem. In the present paper we establish necessary and sufficient conditions for unbounded, finite Quantum Cellular Automata (QCA) (finitely many active cells in a quiescent background) to be Quantum Lattice Gas Automata (QLGA). We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA. We use a number of tools from functional analysis of separable Hilbert spaces and representation theory of associative algebras that enable us to treat QCA on finite but unbounded configurations in full detail.

math-ph↗

arXiv2012

An Improved Query for the Hidden Subgroup Problem

An equal superposition query with |0> in the response register is used in the "standard method" of single-query algorithms for the hidden subgroup problem (HSP). Here we introduce a different query, the character query, generalizing the well-known phase kickback trick. This query maximizes the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We then apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.

quant-ph↗