arXiv subjects

Muhammad Faryad

Publications and source records attributed to Muhammad Faryad.

At least 19 recordsLinked to original sources

arXiv2026

Noise Resilience of Quantum Support Vector Machine with Selected Feature Maps

Gate-level noise degrades the classification accuracy of Quantum Support Vector Machines (QSVMs) on Noisy Intermediate-Scale Quantum (NISQ) hardware, and the degree of degradation depends on how classical data is encoded into quantum states. We tested Z, ZZ, a Pauli, and an amplitude-inspired feature maps under depolarizing, bit-flip, and phase-flip noise channels in $52$ controlled experiments with error probabilities $p =0.01, 0.05, 0.10$, and $0.50$. The amplitude-inspired feature map had $100$\% test accuracy up to $p = 0.10$ across all three noise channels, while other feature maps fell to $65$-$90$\% under the same noise level and type. The Z feature map was found to be immune to phase-flip noise to a significantly high error rate, a consequence of the commutation relation $[R_Z, Z] = 0$. Entangled circuit variants produced generalization gaps in train-test sets of up to $17.5$\% under noise, whereas the amplitude variants maintained zero gap throughout. These results give practitioners data-driven criteria for a feature map on near-term quantum hardware.

quant-ph↗

arXiv2026

Quantum Kernel k-Means for Credit-Card Fraud Detection:A Controlled Benchmark on Real Transaction Data

We benchmarked quantum kernel $k$-means against classical clustering for credit-card fraud detection on real transaction data, at up to \MaxQubits{} qubits, under a protocol with separated selection and reporting data and matched search budgets. We find no robust quantum advantage: the sign of the difference depends on register size, all effect sizes are below $0.013$ ARI, and the single significant advantage we observe is fully explained by the number of configurations searched. We further show that ordinary hyperparameter choices move performance by considerably more than the quantum kernel does, that additional qubits degrade rather than improve performance through kernel concentration, and that the clustering framing itself fails at realistic class imbalance though kernel-based anomaly scoring does not. We regard the methodological contribution as the more durable one. The search-budget ablation in particular is inexpensive and, in our case, decisive: it converted a statistically significant advantage into a procedural artefact. We would encourage its routine use.

quant-ph↗

arXiv2026

The Input Problem: A Permanent Bottleneck for Quantum Machine Learning

Quantum algorithms are conventionally presented with their input state supplied for free. When the input is classical data, this convention conceals a cost that is frequently larger than the algorithm it precedes. We review what the three standard encodings, such as basis encoding, amplitude encoding, and Grover--Rudolph distribution loading, actually cost once transpiled to a hardware gate set, and argue that the resulting $\Theta(N)$ bound is a counting theorem rather than an engineering limitation that improved hardware will remove. Measured gate counts for a representative loading task are reported: an optimal library implementation requires $247$ CNOT gates at $n=8$ qubits and doubles with each additional qubit, while the classical preprocessing that produces the rotation angles requires reading the entire input vector. We show how this cost eliminates the quadratic advantage of quantum amplitude estimation for Monte Carlo integration, and argue that the same accounting constrains quantum machine learning more broadly: the strong input models that make quantum algorithms fast on classical data also enable classical dequantization, and quantum kernel methods carry a $\Theta(M^2)$ state-preparation cost for the Gram matrix that does not amortize. We explain that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims. Executable notebooks reproducing every construction and measurement discussed here are available.

quant-ph↗

arXiv2026

A Systematic Study of Noise Effects in Hybrid Quantum-Classical Machine Learning

Near-term quantum machine learning (QML) models operate in environments wherein noise is unavoidable, arising from both imperfect classical data acquisition and the limitations of noisy intermediate-scale quantum (NISQ) hardware. Although most existing studies have focused primarily on quantum circuit noise in isolation, the combined influence of corrupted classical inputs and quantum hardware noise has received comparatively little attention. In this work, we present a systematic experimental study of the robustness of a variational quantum classifier under realistic multi-level noise conditions. Using the Titanic dataset as a benchmark, a range of dataset-level noise models-including speckle noise, impulse noise, quantization noise, and feature dropout are applied to classical features prior to quantum encoding using a ZZ feature map. In parallel, hardware-inspired quantum noise channels such as depolarizing noise, amplitude damping, phase damping, Pauli errors, and readout errors are incorporated at the circuit level using the Qiskit Aer simulator. The experimental results indicate that noise in classical input data can significantly intensify the effects of quantum decoherence, resulting in less stable training and noticeably lower classification accuracy. Together, these observations emphasize the importance of designing and evaluating quantum machine learning pipelines with noise in mind, and highlight the need to consider classical and quantum noise simultaneously when assessing QML performance in the NISQ era

quant-ph↗

arXiv2026

Hardware-Aware Quantum Support Vector Machines

Deploying quantum machine learning algorithms on near-term quantum hardware requires circuits that respect device-specific gate sets, connectivity constraints, and noise characteristics. We present a hardware-aware Neural Architecture Search (NAS) approach for designing quantum feature maps that are natively executable on IBM quantum processors without transpilation overhead. Using genetic algorithms to evolve circuit architectures constrained to IBM Torino native gates (ECR, RZ, SX, X), we demonstrate that automated architecture search can discover quantum Support Vector Machine (QSVM) feature maps achieving competitive performance while guaranteeing hardware compatibility. Evaluated on the UCI Breast Cancer Wisconsin dataset, our hardware-aware NAS discovers a 12-gate circuit using exclusively IBM native gates (6 ECR, 3 SX, 3 RZ) that achieves 91.23 % accuracy on 10 qubits-matching unconstrained gate search while requiring zero transpilation. This represents a 27 percentage point improvement over hand-crafted quantum feature maps (64 % accuracy) and approaches the classical RBF SVM baseline (93 %). We show that removing architectural constraints (fixed RZ placement) within hardware-aware search yields 3.5 percentage point gains, and that 100 % native gate usage eliminates decomposition errors that plague universal gate compilations. Our work demonstrates that hardware-aware NAS makes quantum kernel methods practically deployable on current noisy intermediate-scale quantum (NISQ) devices, with circuit architectures ready for immediate execution without modification.

quant-ph↗

arXiv2026

Hybrid Quantum--Classical k-Means Clustering via Quantum Feature Maps

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.

quant-ph↗

arXiv2026

Analysis of State Teleportation using Noisy Quantum Gates

Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.

quant-ph↗

arXiv2026

Distribution-Guided and Constrained Quantum Machine Unlearning

Machine unlearning aims to remove the influence of specific training data from a learned model without full retraining. While recent work has begun to explore unlearning in quantum machine learning, existing approaches largely rely on fixed, uniform target distributions and do not explicitly control the trade-off between forgetting and retained model behaviour. In this work, we propose a distribution-guided framework for class-level quantum machine unlearning that treats unlearning as a constrained optimization problem. Our method introduces a tunable target distribution derived from model similarity statistics, decoupling the suppression of forgotten-class confidence from assumptions about redistribution among retained classes. We further incorporate an anchor-based preservation constraint that explicitly maintains predictive behaviour on selected retained data, yielding a controlled optimization trajectory that limits deviation from the original model. We evaluate the approach on variational quantum classifiers trained on the Iris and Covertype datasets. Results demonstrate sharp suppression of forgotten-class confidence, minimal degradation of retained-class performance, and closer alignment with the gold retrained model baselines compared to uniform-target unlearning. These findings highlight the importance of target design and constraint-based formulations for reliable and interpretable quantum machine unlearning.

cs.LG↗

arXiv2025

Geometric Parameterization of Kraus Operators with Applications to Quasi Inverse Channels for Multi Qubit Systems

This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse channels, which can be a tedious analytically for complex noise processes and is often achievable only for a limited range of parameters. In this regard, machine learning based algorithms have been employed successfully to find quasi inverse of quantum channels. The space of quantum channels in this scheme is a unit hypersphere, and components of mutually constrained unit vectors residing in this space, are used to construct a physically valid quantum channel. Symplectic constraints, orthogonality, and unit length of the vectors suffice to maintain complete positivity and the trace-preserving property of the channels. By performing gradient descent on this parametric space with a fidelity-based loss function, this approach is found to optimize quasi inverse of a variety of quantum channels, not limited to single-qubits, proving its effectiveness.

quant-ph↗

arXiv2025

Analysis of the Bernstein--Vazirani Algorithm in the presence of Pauli Noise

We analytically investigate the robustness of the Bernstein--Vazirani algorithm in the presence of bit flip, phase flip, and depolarizing noise using the density matrix formalism. We derive the exact expressions for the algorithm's success probability as a function of the error probability $\boldsymbol{p}$ and number of qubits $\boldsymbol{n}$. The analysis compares the three noise models and reveals how performance degrades with increasing system size under standard Pauli noise models. Most importantly, we show that scaling up quantum systems without simultaneously improving qubit quality leads to a sharp decline in ideal quantum speedup.

quant-ph↗

arXiv2025

Enhancement of non-Markovianity due to environment-induced indirect interaction

Non-Markovian effects are often significant when the system-environment coupling is not weak. Indeed, we find that the non-Markovianity is negligible for a single two-level system undergoing pure dephasing via a weak interaction with a harmonic-oscillator environment. In this paper, we show that, within the framework of pure dephasing, the non-Markovianity displayed by a two-level system can, in fact, be far more pronounced. To demonstrate that this is indeed the case, we consider a pure dephasing model where a collection of two-level systems interacts with a common environment. We obtain analytically the dynamics of the collection of the two-level systems, and then take a partial trace over all the two-level systems except one. This remaining single two-level system exhibits markedly non-Markovian dynamics, even when the system-environment coupling is weak. This is due to the indirect interaction between the two-level systems, induced by their interaction with the common environment. In fact, this indirect interaction can not only increase the non-Markovianity by orders of magnitude, but also qualitatively change the characteristics of the non-Markovian behavior. For instance, for a single two-level system undergoing pure dephasing, the dynamics are Markovian for both Ohmic and sub-Ohmic environments. This is markedly not the case when we consider multiple two-level systems. These findings provide insights into controlling decoherence in multi-qubit quantum systems and have implications for quantum technologies where non-Markovianity can be a resource rather than a limitation.

quant-ph↗

arXiv2025

Lecture Notes on Quantum Algorithms

These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states from given initial states, and introduces circuits for building oracles. Chapter 3 presents foundational algorithms such as entanglement creation, quantum teleportation, Deutsch-Jozsa, Bernstein-Vazirani, and Simon's algorithm. Chapters 4 and 5 cover algorithms based on the quantum Fourier transform, including phase estimation, period finding, factoring, and logarithm computation. These chapters also include complexity analysis and detailed quantum circuits suitable for implementation in code. Chapter 6 introduces Grover's algorithm for quantum search and amplitude amplification, including its realization via Hamiltonian simulation and a method for derandomization. Chapter 7 discusses basic techniques for Hamiltonian simulation, such as Lie-Trotter decomposition, sparse Hamiltonians, and the linear combination of unitaries. It also provides example circuits for simulating Hamiltonians expressed as linear combinations of Pauli operators. Chapter 8 introduces variational quantum algorithms, and Chapter 9 presents an algorithm for simulating fermionic many-particle systems, with an emphasis on molecular Hamiltonians. It also outlines the key transformations needed to map a molecular Hamiltonian to a form suitable for simulation on a quantum computer.

quant-ph↗

arXiv2025

Physics-inspired neural networks as quasi inverse of quantum channels

Quantum channels are not invertible in general. A quasi-inverse allows for a partial recovery of the input state, but its analytical results are found only in a restricted space of its parameters. This work explores the potential of neural networks to find the quasi-inverse of qubit channels for any values of the channel parameters while keeping the quasi-inverse as a physically realizable quantum operation. We introduce a physics-inspired loss function based on the mean of the square of the modified trace distance (MSMTD). The scaled trace distance is used so that the neural network does not increase the length of the Bloch vector of the quantum states, which ensures that the network behaves as a completely positive and trace-preserving (CPTP) quantum channel. The Kraus operators of the quasi-inverse channel were obtained by performing quantum process tomography on the trained neural network.

quant-ph↗

arXiv2024

Quasi Inverse of Qubit Channels for Mixed States

We found the quasi inverse of qubit channels as a unitary map, $\mathcal{E}^i$, by minimizing the average trace distance between the input state to the channel and the output of the quasi inverse channel for arbitrary qubit channel $\mathcal{E}$ and for arbitrary input states. The channel $\mathcal{E}$ was assumed completely positive and trace-preserving. To find the quasi inverse for mixed states, we proposed an alternative definition of the quasi inverse based on the mean square of the trace distance (MSTD) of a channel. The definition based on the trace distance allowed easy generalization of the quasi inverse to mixed input states. The quasi inverse of the Pauli, generalized amplitude damping, mixed unitary, and tetrahedron channels calculated based on the MSTD agreed with the one computed using average fidelity in the special case of input states being pure.

quant-ph↗

arXiv2023

Simulation and analysis of quantum phase estimation algorithm in the presence of incoherent quantum noise channels

The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in running QPE and other quantum algorithms is the noise in quantum computers. In the present work, we study the impact of incoherent noise on QPE, modeled as trace-preserving and completely positive quantum channels. Different noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are taken to understand the performance of the QPE in the presence of noise. The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits. However, the standard deviation increases only linearly with the number of qubits for fixed error probability when that error probability is small.

quant-ph↗

arXiv2023

Maximal visualization-enhancement of latent fingermarks on polymer banknotes using columnar thin films

Polymer banknotes are being increasingly adopted to replace older banknotes. Since banknotes are forensically important substrates for fingermark detection and identification, we present a single-step process to enhance the visualization of fingermarks on banknotes using columnar thin films (CTFs) of nickel. This single-step vacuum technique enhances the quality grade of fingermarks maximally, whether the fingermarks are aged for one or seven days before CTF deposition. This work represents progress over currently available sequences of diverse techniques for enhancing fingermarks on polymer banknotes.

physics.optics↗

arXiv2023

Visualization of latent and depleted fingermarks on CDs and DVDs using columnar thin films

CDs and DVDs are forensically important substrates for latent fingermarks. Upright columnar thin films (CTFs) grown conformally over these substrates were shown to significantly enhance the visual quality of fingermarks. Enhancement to maximum possible grade for visual quality occurred, even for the samples that were developed three days after the fingermarks were placed on them. The CTFs were deposited by directing a collimated vapor flux of an evaporant material towards the substrate placed at an angle and made to rotate rapidly.

cond-mat.soft↗

arXiv2019

Surface plasmon-polariton waves obliquely guided along interface containing periodicity direction of one-dimensional photonic crystal

We recently formulated the canonical boundary-value problem of propagation of surface plasmon-polariton (SPP) waves along the direction of periodicity of a one-dimensional photonic crystal. Here we present the general formulation of that canonical problem supporting the oblique propagation of SPP waves in the interface plane. The general dispersion equation has been obtained using the rigorous coupled-wave approach for the oblique propagation and numerically solved using the Muller's method. A periodicity in the wavenumbers of the SPP waves was observed. Furthermore, the regions of high losses for the SPP waves, dubbed as plasmonic bandgaps, were observed in the photonic band diagram of the SPP waves. These plasmonic bandgaps can be used to construct optical filters for the SPP waves.

physics.optics↗