arXiv subjects

Ibsal Assi

Publications and source records attributed to Ibsal Assi.

7 recordsLinked to original sources

arXiv2026

Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection

In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS--Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.

quant-ph↗

arXiv2026

A Variational Framework for Time-Dependent Quantum Systems with Applications to Floquet Hamiltonians

We introduce a variational framework for approximating the time-evolution operator $\hat{U}(t)$ within a physically motivated operator manifold, reformulating quantum dynamics as a tractable problem in operator space using stationary action principle. For periodically driven systems, the resulting approximate evolution operator directly yields an effective Floquet Hamiltonian, offering a non-perturbative alternative to conventional expansion-based methods. The framework is systematically improvable by enlarging the operator pool and naturally incorporates symmetries and physical constraints. When the operator manifold is chosen from the terms of a truncated Magnus expansion, the variational procedure effectively resums the Magnus series within the restricted space, significantly enhancing accuracy. We benchmark the approach on the driven Rabi model, the driven Lipkin-Meshkov-Glick model, and the one-dimensional driven Ising chain, yielding effective Floquet Hamiltonians that are systematically more accurate than low-order Magnus expansions, particularly in regimes where the latter converge poorly, and illustrating applicability to systems with exponentially large Hilbert spaces. Although we focus here on Floquet systems, the formalism applies equally to generic time-dependent Hamiltonians, providing a versatile tool for non-equilibrium quantum dynamics.

quant-ph↗

arXiv2026

Majorana Fermions in spin up and down electronic complexes in spin-orbit coupled array of semiconductor quantum dots in proximity to $s$-type superconductor and in magnetic field

Semiconductor-s-type superconductor nanowires host spinful fermions and cannot be reduced to a single spinless Kitaev chain hosting single Majorana zero mode. Instead, such systems can be converted into two coupled p-wave Kitaev-like chains associated with different spin sectors. Using the bond Fermion transformation and exact diagonalization, we analyze parity resolved spectra and local spectral functions, demonstrating that zero-energy modes strongly localized at the system boundaries emerge only in one effective chain. Inter-chain coupling lifts parity degeneracy and redistributes the low-energy spectral weight, providing a controlled framework to assess the stability of Majorana-like modes in the finite spinful nanowires.

cond-mat.mes-hall↗

arXiv2025

Beyond Trotterization: Variational Product Formulas for Quantum Simulation

We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global action principle, where Euler-Lagrange equations govern their optimal dynamics. Unlike conventional wavefunction-based variational methods, our approach specifically targets the time evolution operation and this allows a single set of optimized parameters to be applied to any initial state for a fixed Hamiltonian avoiding costly optimization procedures. Our method outperforms the standard Trotter-Suzuki formulas, typically achieving higher accuracy than higher-order Suzuki schemes. This translates directly to quantum computing applications, where it enables the design of quantum circuits with fewer gates which reduces noise and improves precision. Although we focus on quantum dynamics, the method is broadly applicable to problems involving general time-evolution operators. Applied to various model Hamiltonians, our approach reduces errors by factors of 2 to 5 compared to Trotter-Suzuki decompositions, demonstrating its promise for accurate quantum simulation with improved efficiency. In certain cases, the variational ansatz achieves higher accuracy than more complex higher-order Suzuki formulas while reducing the gate count by nearly half within a single circuit layer. Furthermore, we derive approximate analytical expressions for the variational parameters up to cubic order in time, valid for generic Hamiltonians. These approximations enable long-time quantum simulations with improved accuracy over equivalent Suzuki decompositions, providing ready-to-use evolution formulas that match Suzuki's gate complexity while delivering better performance.

quant-ph↗

arXiv2025

NonHermitian Topological Phases in a Hermitian Modified Bosonic Kitaev Chain

We present a modification to the bosonic Kitaev chain that, despite being Hermitian, supports both nonHermitian skin effect and nontrivial topological edge modes in its excitation Hamiltonian. We establish an exact mapping between the excitation Hamiltonian of our system and a nonHermitian Su-Schrieffer-Heeger (SSH) model, which allows for a completely analytical characterization of its topology. In particular, topological phase transition points separating a topologically trivial and nontrivial regime were identified analytically by the appropriate winding number invariant and the presence of zero energy modes. Similarly to the regular bosonic Kitaev chain, the nonHermitian skin effect and some (but not all) topological edge modes are quickly destroyed at nonzero bosonic onsite potential (harmonic oscillator frequency). Remarkably, however, disorder partially recovers some of these features. This work thus demonstrates the potential of a modified bosonic Kitaev chain as a platform to generate rich nonHermitian topological phenomena from a completely Hermitian system's perspective. Lastly, we suggest a possible experimental realization of the model, which could allow for total control over the parameter space.

quant-ph↗

arXiv2024

Designing Majorana Quasiparticles in InAsP Quantum Dots in InP Nanowires with Variational Quantum Eigenvalue Solver

This work presents steps toward the design of Majorana zero modes (MZM) in InAsP quantum dots (QD) embedded in an InP semiconducting nanowire in contact with a p-type superconductor described by the Kitaev Hamiltonian. The single particle spectrum is obtained from million atom atomistic calculations with QNANO and many-electron spectra using exact diagonalization (ED) and the hybrid Variational Quantum Eigensolver (VQE) method. A variational ansatz is constructed to capture the ground state of the system by utilizing a generalized form of the analytical solution for a particular set of parameters. By systematically deviating from the analytically solvable regime while maintaining the system in the topological phase (TP), the effectiveness of the variational function in reproducing the correct ground state and topological properties of the system is evaluated. This is done through a quantum algorithm for a many-body state containing MZM. The results are compared with exact solution in topological phase and demonstrate the capability of VQE, along with classical simulations, to accurately model the many-body spectra in topologically nontrivial state.

quant-ph↗

arXiv2023

Symbolic determinant construction of perturbative expansions

We present a symbolic algorithm for treating perturbative expansions of Hamiltonians with general two-body interactions. The method, formally equivalent to determinant Monte Carlo methods, merges well-known analytics with the recently developed symbolic integration tool, algorithmic Matsubara integration (AMI) that allows for the evaluation of the imaginary frequency/time integrals. By explicitly performing Wick contractions at each order of the perturbative expansion we order-by-order construct the fully analytic solution of the Green's function and self energy expansions. A key component of this process is the assignment of momentum/frequency conserving labels for each contraction that motivates us to present a fully symbolic Fourier transform procedure which accomplishes this feat. These solutions can be applied to a broad class of quantum chemistry problems and are valid at arbitrary temperatures and on both the real- and Matsubara-frequency axis. To demonstrate the utility of this approach, we present results for simple molecular systems as well as model lattice Hamiltonians. We highlight the case of molecular problems where our results at each order are numerically exact with no stochastic uncertainty.

cond-mat.str-el↗