arXiv subjects

Arul Rhik Mazumder

Publications and source records attributed to Arul Rhik Mazumder.

9 recordsLinked to original sources

arXiv2026

Exact $T$-counts of CCZ layers from an isotropy bound

The $T$-count is a dominant cost of fault-tolerant Clifford$+T$ computation. We prove that a layer of $m$ disjoint CCZ gates, the diagonal core of a parallel Toffoli layer, needs exactly $6m+1$ $T$ gates in every Hadamard-free Clifford$+T$ circuit with clean ancillas. Campbell and Howard gave the matching construction, and to our knowledge this is the first proof that it is optimal for general $m$. The proof rests on a novel isotropy bound. When a gate's phase polynomial has only cubic terms, the vectors recording which $T$ gates touch each qubit span a self-orthogonal subspace over $\mathbb{F}_2$, and this forces the $T$-count to be at least twice its dimension. This argument gives a lower bound, computable by Gaussian elimination, on the $T$-count of every diagonal gate in the third level of the Clifford hierarchy. It is never below the stabilizer nullity $ν$ and reaches $2ν+1$ on non-Clifford cubic gates. No bound that also holds for circuits with measurement and feedforward can do this, since such circuits implement CCZ ($ν=3$) with four $T$ gates, while the floor gives seven. It also recovers Campbell and Howard's count $4m+3$ for a fan-out of Toffolis. On the output of PyZX's TODD-based optimizer, relative to its Hadamard placement, it certifies $193$ of $311$ phase-polynomial blocks $T$-optimal, against $113$ for nullity, including $37$ of the $72$ blocks too large for exhaustive search.

quant-ph↗

arXiv2026

Benchmarking Zero-Setup Quantum Circuit Simulators

Practitioners increasingly rely on hosted simulation environments, but their performance characteristics remain poorly documented. We present a systematic benchmarking study of GPU-accelerated approximate quantum simulation across two widely used methods: matrix product states (MPS) and Pauli path simulation (PPS), comparing BlueQubit (a hosted tool that handles hardware provisioning, simulator configuration, and job orchestration) against AWS Braket, Quantum Rings, Qiskit pauli-prop, and PauliPropagation (written in Julia). For MPS, we find that GPU runtime yields sub-quadratic scaling with bond dimension, with a growing advantage over CPU at increasing scale. For Pauli path simulation on IBM's 127-qubit kicked Ising benchmark, GPUs deliver up to ${\sim}1{,}700\times$ speedup at fine truncation thresholds ($δ= 2.5 \times 10^{-5}$, 27.6M Pauli terms), and are the only backends that reach accuracy regimes below $δ= 10^{-5}$, which remained inaccessible to the commodity CPU-based implementations and self-contained SDKs evaluated here. We also provide a reproducible characterization of these simulators across regimes, including tradeoffs that isolated evaluations do not show. All benchmarking code and configurations are in a public GitHub repository.

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arXiv2026

An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study

Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($τ\approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7\text{M}$ ESS/s versus $488\text{K}$ ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $χ=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$.

quant-ph↗

arXiv2026

Resource-efficient quantum eigenvalue transform with commutator scaling

We develop quantum algorithms for estimating properties of general matrix functions of Hermitian matrices, with applications to phase estimation, Green's function evaluation, and estimating measurement distributions of time-evolved states. The resulting methods exhibit commutator scaling in matrix parameters similar to that usually found for product formulae, lower circuit depth in other parameters, and require only a single ancillary qubit. Our central primitive consists of classically postprocessing randomly chosen product formulae circuits, which mathematically corresponds to an approximation of a Richardson extrapolation. Within our framework, we introduce a protocol for approximating the measurement distributions of quantum states, extending beyond standard observable estimation. We also provide tightened gate complexity bounds for practically relevant systems, including those with k-local interactions, long-tailed matrix ensembles, and conserved quantities. Finally, numerical experiments confirm that our method can achieve significantly shallower circuit depths than standard product formulae in certain parameter regimes, and highlight the potential of their heuristic application.

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arXiv2026

Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress

We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris--Rips filtration of S&P~500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding $n_k$ simplex indices into $O(n_k^{1/κ})$ qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of~\cite{Sciorilli25} does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over $n=4$--$12$ qubits. The classical stage matches ripser~\cite{bauer2021ripser} on all 190 sliding windows (2007-2009). On the real market Laplacians ($β_1=1$--$22$), warm-starting from a classical null-space surrogate allows PCE-VQE to recover $β_1$ exactly at every scale, placing the obstacle in the optimisation landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC $0.818$, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC $0.009$, $0.515$) shows the calibration does not generalize across crisis regimes.

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arXiv2025

Quantum Annealing Approaches to Solving the Shipment Rerouting Problems

In this paper, we study a shipment rerouting problem (SRP) which generalizes many NP-hard sequencing and packing problems. A SRP's solution has ample practical applications in vehicle scheduling and transportation logistics. Given a network of hubs, a set of goods must be delivered by trucks from their source-hubs to their respective destination-hubs. The objective is to select a set of trucks and to schedule these trucks' routes so that the total cost is minimized. The problem SRP is NP-hard; only classical approximation algorithms have been known for some of its NP-hard variants. In this work, we design classical algorithms and quantum annealing algorithms for this problem with various capacitated trucks. The algorithms that we design use novel mathematical programming formulations and new insights into solving sequencing and packing problems simultaneously. Such formulations take advantage of network infrastructure, shipments, and truck capacities. We conduct extensive experiments showing that in various scenarios, the quantum annealing solver generates near-optimal or optimal solutions much faster than the classical algorithm solver.

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arXiv2024

Differential Evolution Algorithm based Hyper-Parameters Selection of Transformer Neural Network Model for Load Forecasting

Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.

cs.NE↗

arXiv2024

Benchmarking Metaheuristic-Integrated QAOA against Quantum Annealing

The Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising Noisy Intermediate Quantum Algorithms (NISQ) in solving combinatorial optimizations and displays potential over classical heuristic techniques. Unfortunately, QAOA performance depends on the choice of parameters and standard optimizers often fail to identify key parameters due to the complexity and mystery of these optimization functions. In this paper, we benchmark QAOA circuits modified with metaheuristic optimizers against classical and quantum heuristics to identify QAOA parameters. The experimental results reveal insights into the strengths and limitations of both Quantum Annealing and metaheuristic-integrated QAOA across different problem domains. The findings suggest that the hybrid approach can leverage classical optimization strategies to enhance the solution quality and convergence speed of QAOA, particularly for problems with rugged landscapes and limited quantum resources. Furthermore, the study provides guidelines for selecting the most appropriate approach based on the specific characteristics of the optimization problem at hand.

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arXiv2023

Comparative Evaluation of Metaheuristic Algorithms for Hyperparameter Selection in Short-Term Weather Forecasting

Weather forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of weather systems remains a challenge for traditional statistical models. Apart from Auto Regressive time forecasting models like ARIMA, deep learning techniques (Vanilla ANNs, LSTM and GRU networks), have shown promise in improving forecasting accuracy by capturing temporal dependencies. This paper explores the application of metaheuristic algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), to automate the search for optimal hyperparameters in these model architectures. Metaheuristic algorithms excel in global optimization, offering robustness, versatility, and scalability in handling non-linear problems. We present a comparative analysis of different model architectures integrated with metaheuristic optimization, evaluating their performance in weather forecasting based on metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The results demonstrate the potential of metaheuristic algorithms in enhancing weather forecasting accuracy \& helps in determining the optimal set of hyper-parameters for each model. The paper underscores the importance of harnessing advanced optimization techniques to select the most suitable metaheuristic algorithm for the given weather forecasting task.

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