arXiv subjects

Gabriela Wójtowicz

Publications and source records attributed to Gabriela Wójtowicz.

7 recordsLinked to original sources

arXiv2026

State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics

The Heisenberg picture can make quantum many-body simulation efficient when evolved observables admit compact operator representation within low-dimensional structures. Conventional Pauli-string propagation and truncation techniques exploit this structure, but in coherent Hamiltonian dynamics their error control is often heuristic and their stability can be poor. We introduce a state-adapted Krylov framework based on geometric generalized mean-field projections of many-body observables onto low-body operator subspaces. The resulting dynamics approximate expectation values, do not extend spatial support beyond that prescribed by Lieb-Robinson bounds, and compress high-body correlations onto their state-relevant low-body representatives rather than simply discarding them. We derive necessary operator-entanglement obstructions to low-body representation and conditional sufficient bounds on representation and dynamical errors involving nonstabilizerness and controlled high-body tails. Numerical benchmarks show improved, stable finite-$m$ hierarchies and simulations on large three-dimensional lattices, establishing a scalable state-adapted alternative to conventional Heisenberg-picture weight-truncation of Pauli strings.

quant-ph↗

arXiv2026

Robustness of spin state superpositions for noisy quantum metrology

Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.

quant-ph↗

arXiv2025

Approaching the scaling limit of transport through lattices with dephasing

We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of these two processes. The resulting equations have a vectorized form related to, but distinct from, Lyapunov's equation. We present an efficient solution that helps to achieve the scaling limit, e.g., of the current decay with lattice length. As an example, we study the super--diffusive--to--diffusive transition in a lattice with long--range hopping and dephasing. The approach enables calculations with up to $10^4$ sites, representing an increase of $10$ to $40$ times over prior studies. This enables a more precise extraction of the diffusion exponent, enhances agreement with theoretical results, and supports the presence of a phase transition. There is a wide range of problems that have Markovian relaxation, noise, and driving. They include quantum networks for machine--learning--based classification and extended reservoir approaches (ERAs) for transport. The results here will be useful for these classes of problems.

quant-ph↗

arXiv2025

Quantum Fisher information from tensor network integration of Lyapunov equation

The Quantum Fisher Information (QFI) is a geometric measure of state deformation calculated along the trajectory parameterizing an ensemble of quantum states. It serves as a key concept in quantum metrology, where it is linked to the fundamental limit on the precision of the parameter that we estimate. However, the QFI is notoriously difficult to calculate due to its non-linear mathematical form. For mixed states, standard numerical procedures based on eigendecomposition quickly become impractical with increasing system size. To overcome this limitation, we introduce a novel numerical approach based on Lyapunov integrals that combines the concept of symmetric logarithmic derivative and tensor networks. Importantly, this approach requires only the elementary matrix product states algorithm for time-evolution, opening a perspective for broad usage and application to many-body systems. We discuss the advantages and limitations of our methodology through an illustrative example in quantum metrology, where the thermal state of the transverse-field Ising model is used to measure magnetic field amplitude.

quant-ph↗

arXiv2024

YASTN: Yet another symmetric tensor networks; A Python library for abelian symmetric tensor network calculations

We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array backend. This serves as the basis for higher-level tensor networks algorithms, operating on matrix product states and projected entangled pair states, implemented here. Using appropriate backend, such as PyTorch, gives direct access to automatic differentiation (AD) for cost-function gradient calculations and execution on GPUs or other supported accelerators. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD, or simulating thermal states of the Hubbard model via imaginary time evolution. We quantify sources of performance gains in those challenging examples allowed by utilizing symmetries.

cond-mat.str-el↗

arXiv2024

The confluence of fractured resonances at points of dynamical, many--body flare

Resonant transport occurs when there is a matching of frequencies across some spatial medium, increasing the efficiency of shuttling particles from one reservoir to another. We demonstrate that in a periodically driven, many--body titled lattice, there are sets of spatially fractured resonances. These ``emanate'' from two essential resonances due to scattering off internal surfaces created when the driving frequency and many--body interaction strength vary, a scattering reminiscent of lens flare. The confluence of these fractured resonances dramatically enhances transport. At one confluence, the interaction strength is finite and the essential resonance arises due to the interplay of interaction with the counter--rotating terms of the periodic drive. We discuss the origin and structure of the fractured resonances, as well as the scaling of the conductance with system parameters. These results furnish a new example of the richness of open, driven, many--body systems.

cond-mat.str-el↗

arXiv2021

Performance of Reservoir Discretizations in Quantum Transport Simulations

Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers' turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that a given reservoir discretization may have little impact on numerical efficiency for certain computational tools. The choice of a relaxation parameter, however, is crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.

cond-mat.mes-hall↗