arXiv subjects

Akib Karim

Publications and source records attributed to Akib Karim.

14 recordsLinked to original sources

arXiv2026

HamQASBench: A Hamiltonian-Informed Diagnostic Benchmark for Evaluating Quantum Architecture Search

Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.

quant-ph↗

arXiv2026

A hardware efficient quantum residual neural network without post-selection

We propose a hardware efficient quantum residual neural network which implements residual connections through a deterministic mixture of the identity operation and variational unitaries, enabling fully differentiable training. In contrast to the previous implementation of residual connections, our architecture avoids post-selection while preserving residual learning. Furthermore, we highlight circuit constructions where barren plateaus could be mitigated, which are considered as a major limitation of variational quantum learning models. In order to show the working of our model, we report its application to image classification tasks by training it for MNIST, CIFAR, and SARFish datasets, achieving accuracies of 99\% and 80\% for binary and multi-class classifications, respectively. These accuracies are comparable to previously achieved from the standard variational models, however our model requires 10x fewer gates making it better suited for resource constraint near-term quantum processors. In addition to high accuracies, the proposed architecture also demonstrates adversarial robustness which is another desirable parameter for quantum machine learning models. Overall our architecture offers a new pathway for developing accurate, robust, trainable and hardware efficient quantum machine learning models.

quant-ph↗

arXiv2026

Fictitious Copy Quantum Error Mitigation

Errors are arguably the most pressing challenge impeding practical applications of quantum computers, which has instigated vigorous research on the development of quantum error mitigation (QEM) techniques. Existing QEM methods suppress errors with a varying degree of efficacy but importantly demand significant additional quantum and classical computational resources. In this work, we present Fictitious Copy Quantum Error Mitigation (FCQEM) method which corrects quantum errors without requiring any additional quantum resources and purely relies on using classical postprocessing of a joint probability distribution to correct expectation values. The joint probability distribution can be measured ``fictitiously'' by sampling one copy of noisy quantum circuit twice, or classically squaring probabilities from simply one copy. We show that FCQEM can recover eigenvalues even if exact eigenstates are not prepared. Furthermore, our technique can benefit other noise mitigation techniques with no additional quantum resources, which is demonstrated by combining FCQEM with the Quantum Computed Moments (QCM) method. FCQEM can compensate for noise that is pathological to QCM, and QCM allows for FCQEM to recover the ground state energy with a larger variety of trial states. We show that our technique can find the exact ground state energy of molecular and spin models under simulated noise models as well as experiments on a Rigetti 84-qubit superconducting quantum processor. The reported FCQEM method is general purpose for the current generation of quantum devices and is applicable to any problem that measures eigenvalues of operators on sharply peaked distributions.

quant-ph↗

arXiv2026

Quantum Jacobi-Davidson Method

Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy eigenstates of a Hamiltonian, which are usually computationally expensive and suffer from convergence issues. In this work, we develop and implement the Quantum Jacobi-Davidson (QJD) method and its quantum diagonalization variant, the Sample-Based Quantum Jacobi-Davidson (SBQJD) method, and demonstrate their fast convergence for ground state energy estimation. We assess the intrinsic algorithmic performance of our methods through exact numerical simulations on a variety of quantum systems, including 8-qubit diagonally dominant matrices, 12-qubit one-dimensional Ising models, and a 10-qubit water molecule (H$_2$O) Hamiltonian. Our results show that both QJD and SBQJD achieve significantly faster convergence and require fewer Pauli measurements compared to the recently reported Quantum Davidson method, with SBQJD further benefiting from optimized reference state preparation. These findings establish the QJD framework as an efficient general-purpose subspace-based technique for solving quantum eigenvalue problems, providing a promising foundation for sparse Hamiltonian calculations on future fault-tolerant quantum hardware.

quant-ph↗

arXiv2025

Symmetry-Checking in Band Structure Calculations on a Noisy Quantum Computer

Band crossings in electronic band structures play an important role in determining the electronic, topological, and transport properties in solid-state systems, making them central to both condensed matter physics and materials science. The emergence of noisy intermediate-scale quantum (NISQ) processors has sparked great interest in developing quantum algorithms to compute band structure properties of materials. While significant research has been reported on computing ground state and excited state energy bands in the presence of noise that breaks the degeneracy, identifying the symmetry at crossing points using quantum computers is still an open question. In this work, we propose a method for identifying the symmetry of bands around crossings and anti-crossings in the band structure of bilayer graphene with two distinct configurations on a NISQ device. The method utilizes eigenstates at neighbouring $\mathbf{k}$ points on either side of the touching point to recover the local symmetry by implementing a character-checking quantum circuit that uses ancilla qubit measurements for a probabilistic test. We then evaluate the performance of our method under a depolarizing noise model, using four distinct matrix representations of symmetry operations to assess its robustness. Finally, we demonstrate the reliability of our method by correctly identifying the correct band crossings of AA-stacked bilayer graphene around $K$ point, using the character-checking circuit implemented on a noisy IBM quantum processor $ibm\_marrakesh$.

quant-ph↗

arXiv2025

Fast and Noise-aware Machine Learning Variational Quantum Eigensolver Optimiser

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for preparing ground states in the current era of noisy devices. The classical component of the algorithm requires a large number of measurements on intermediate parameter values that are typically discarded. However, intermediate steps across many calculations can contain valuable information about the relationship between the quantum circuit parameters, resultant measurements, and noise specific to the device. In this work, we use supervised machine learning on the intermediate parameter and measurement data to predict optimal final parameters. Our technique optimises parameters leading to chemically accurate ground state energies much faster than conventional techniques. It requires significantly fewer iterations and simultaneously shows resilience to coherent errors if trained on noisy devices. We demonstrate this technique on IBM quantum devices by predicting ground state energies of H$_2$ for one and two qubits; H$_3$ for three qubits; and HeH$^+$ for four qubits where it finds optimal angles using only modeled data for training.

quant-ph↗

arXiv2024

Full Band Structure Calculation of Semiconducting Materials on a Noisy Quantum Processor

Quantum chemistry is a promising application in the era of quantum computing since the unique effects of quantum mechanics that take exponential growing resources to simulate classically are controllable on quantum computers. Fermionic degrees of freedom can be encoded efficiently onto qubits and allow for algorithms such as the Quantum Equation-of-Motion method to find the entire energy spectrum of a quantum system. In this paper, we propose the Reduced Quantum Equation-of-Motion method by reducing the dimensionality of its generalized eigenvalue equation, which results in half the measurements required compared to the Quantum Equation-of-Motion method, leading to speed up the algorithm and less noise accumulation on real devices. In particular, we analyse the performance of our method on two noise models and calculate the excitation energies of a bulk Silicon and Gallium Arsenide using our method on an IBM quantum processor. Our method is fully robust to the uniform depolarizing error and we demonstrate that the selection of suitable atomic orbital complexity could increase the robustness of our algorithm under real noise. We also find that taking the average of multiple experiments tends towards the correct energies due to the fluctuations around the exact values. Such noise resilience of our approach could be used on current quantum devices to solve quantum chemistry problems.

quant-ph↗

arXiv2024

Low Depth Virtual Distillation of Quantum Circuits by Deterministic Circuit Decomposition

Virtual distillation (VD) using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for single qubit expectation values however practical calculations require multi-qubit expectation values which cannot be corrected with B gates. We discover low depth circuit decompositions for multi-qubit expectation values by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with number of qubits, but requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states the energy cannot go below the ground state energy. We discover that the variational principle is violated if noise is higher on single expectation values than multi-qubit which renders VQE useless. We show this occurs when using B gates and is preserved if using our low depth decomposition on all expectation values. We perform demonstration on real devices and demonstrate our decomposition can mitigate real experimental noise in VQE for the H$_2$ molecule with a two qubit tapered mapping, H$_3$ with three qubits, and H$_2$ with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables.

quant-ph↗

arXiv2023

All-electron $\mathrm{\textit{ab-initio}}$ hyperfine coupling of Si-, Ge- and Sn-vacancy defects in diamond

Colour centres in diamond are attractive candidates for numerous quantum applications due to their good optical properties and long spin coherence times. They also provide access to the even longer coherence of hyperfine coupled nuclear spins in their environment. While the NV centre is well studied, both in experiment and theory, the hyperfine couplings in the more novel centres (SiV, GeV, and SnV) are still largely unknown. Here we report on the first all-electron \textit{ab-initio} calculations of the hyperfine constants for SiV, GeV, and SnV defects in diamond, both for the respective defect atoms ($^{29}$Si, $^{73}$Ge, $^{117}$Sn, $^{119}$Sn), as well as for the surrounding $^{13}$C atoms. Furthermore, we calculate the nuclear quadrupole moments of the GeV defect. We vary the Hartree-Fock mixing parameter for Perdew-Burke-Ernzerhof (PBE) exchange correlation functional and show that the hyperfine couplings of the defect atoms have a linear dependence on the mixing percentage. We calculate the inverse dielectric constant to predict an \textit{ab-initio} mixing percentage. The final hyperfine coupling predictions are close to the experimental values available in the literature. Our results will help to guide future novel experiments on these defects.

cond-mat.mes-hall↗

arXiv2021

Bright $\mathrm{\textit{ab-initio}}$ photoluminescence of NV+ in diamond

The positively charged nitrogen vacancy (NV+) centre in diamond has been traditionally treated as a dark state due to the experimental lack of an optical signature. Recent computational studies have shown that it is possible for the NV+ defect to have an excited state transition equivalent to that of the negatively charged (NV-) centre, but no PL predictions have been reported so far. We report the first $\mathrm{\textit{ab-initio}}$ calculation showing that the NV+ center presents quantum emission, with zero phonon line at 765 nm and a non-zero transition dipole moment, approximately 4x smaller than the transition dipole moment of NV-. We calculate the energy levels of the multielectron states under time-dependent density functional theory (singlet and triplet E states), and using our recently developed frequency cutoff method, we predict the full PL spectrum. Our results suggest that this state cannot be considered intrinsically 'dark' and charge specific quenching mechanisms should be investigated as the cause of the lack of optical activity in experimental characterizations.

cond-mat.mes-hall↗

arXiv2020

An $\mathrm{\textit{ab-initio}}$ effective solid state photoluminescence by frequency constraint of cluster calculation

Measuring the photoluminescence of defects in crystals is a common experimental technique for analysis and identification. However, current theoretical simulations typically require the simulation of a large number of atoms to eliminate finite size effects, which discourages computationally expensive excited state methods. We show how to extract the room-temperature photoluminescence spectra of defect centres in bulk from an $\mathrm{\textit{ab-initio}}$ simulation of a defect in small clusters. The finite size effect of small clusters manifests as strong coupling to low frequency vibrational modes. We find that removing vibrations below a cutoff frequency determined by constrained optimization returns the main features of the solid state photoluminescence spectrum. This strategy is illustrated for an NV$^{-}$ defect in diamond, presenting a connection between defects in solid state and clusters; the first vibrationally resolved $\mathrm{\textit{ab-initio}}$ photoluminescence spectrum of an NV$^{-}$ defect in a nanodiamond; and an alternative technique for simulating photoluminescence for solid state defects utilizing more accurate excited state methods.

cond-mat.mes-hall↗

arXiv2018

Beating the Classical Limits of Information Transmission using a Quantum Decoder

Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states, however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per bit and a single entangling gate at the decoder. By simulating the channel using a photonic interferometric setup, we experimentally increase the reliability of transmitting a data bit by greater than 20% for a certain damping range over classically sending the message twice. We show how our methodology can be extended to larger systems by simulating the transmission of a single bit with up to eight uses of the channel and a two-bit message with three uses of the channel, predicting a quantum enhancement in all cases.

quant-ph↗

arXiv2016

High-dimensional entanglement certification

Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell's inequality, and entanglement witness. The method we developed works for arbitrarily large system dimension $d$ and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to $32$ composed of polarisation-entangled photon pairs.

quant-ph↗

arXiv2014

Near orthogonal launch of SPR modes in Au films

We report the excitation of a surface plasmon resonance (SPR) close to the orthogonal axis of a gold (Au) film on borosilicate glass. Direct spectroscopic measurement of SPR shifts using different liquids are made at ~5° incidence within a reflection spectrophotometer. Scattering of light that is able to penetrate across the film at the interfaces is the proposed mechanism by which coupling, and plasmon localization, is established.

physics.optics↗