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Krzysztof Bieniasz

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cond-mat.str-el cond-mat.mtrl-sci quant-ph Artificial Intelligence

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preprint2026arXiv

Entanglement is Half the Story: Post-Selection vs. Partial Traces

While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum constraints placed on a tensor network manifest a change in capabilities. To this end, we employ a method of inference of classical tensor networks on a quantum computer to define a hybrid architecture. This hybrid tensor network is a practical unified framework for it's classical and quantum tensor network edge cases. We identify post-selection as the important property on which this interpolation hinges. The amount of post-selection corresponds to the level to which quantum constraints are enforced on the tensor network. On this basis, we propose a new hyperparameter which controls the transition between the hybrid and the quantum tensor network. In the comparison of classical and quantum tensor networks it complements the bond dimension. Quantum machine learning is improved by using the hyperparameter to allocate the practically limited post-selection to the quantum model in a trainable manner.

preprint2022arXiv

Tangelo: An Open-source Python Package for End-to-end Chemistry Workflows on Quantum Computers

Tangelo [link: https://github.com/goodchemistryco/Tangelo] is an open-source Python software package for the development of end-to-end chemistry workflows on quantum computers, released under Apache 2.0 license. It aims to support the design of successful experiments on quantum hardware, and to facilitate advances in quantum algorithm development. The software enables quick exploration of different approaches by assembling reusable building blocks and algorithms, with the flexibility to let users introduce their own. Tangelo is backend-agnostic and enables switching between various backends (Braket, Qiskit, Qulacs, Azure Quantum, QDK, Cirq...) with minimal changes in the code. The package can be used to explore quantum computing applications such as open-shell systems, excited states, or more industrially-relevant systems by leveraging problem decomposition at scale. This paper outlines the design choices, philosophy, and main features of Tangelo.

preprint2022arXiv

Theory of dispersive optical phonons in resonant inelastic x-ray scattering experiments

The community currently lacks a complete understanding of how resonant inelastic x-ray scattering (RIXS) experiments probe the electron-phonon ($e$-ph) interaction in solids. For example, most theoretical models of this process have focused on dispersionless Einstein phonons. Using a recently developed momentum average (MA) variational approximation for computing RIXS spectra of band insulators, we examine the influence of both electron and phonon dispersion in the intermediate state of the scattering process. We find that the inclusion of either, and their mutual interplay, introduces significant momentum variations in the RIXS intensity, even for momentum-independent electron-phonon coupling. The phonon dispersion also induces nontrivial changes in the excitation line shapes, which can have a quantitative impact on the data analysis. These results highlight the considerable challenges of interpreting RIXS data in actual materials.

preprint2016arXiv

Green's function variational approach to orbital polarons in KCuF3

We develop an $e_g$ orbital, $t$-$J$-like model of a single charge doped into a two-dimensional plane with ferromagnetic spin order and alternating orbital order, and present its solution by Green's functions in the variational approximation framework. The model is designed to represent the orbital physics within ferromagnetic $(a,b)$ planes of KCuF$_3$ and K$_2$CuF$_4$. The variational approximation (VA) relies on the systematic generation of equations of motion for the Green's function, taking into account the real-space constraints coming from the exclusion of doubly occupied sites. This method is compared to the firmly established self-consistent Born approximation, and to the variational cluster approximation (VCA) which relies on the itinerant regime of the model. We find that the present variational approximation captures the essential aspects of the spectral weight distribution of the coherent quasiparticle state and gives a result similar to the VCA, while also reproducing well the momentum dependence of the spectral moments. In contrast, the spectral function obtained within the self-consistent Born approximation is more incoherent and its quasiparticle is heavier, at strong effective couplings, than observed with VCA and VA.

preprint2016arXiv

The Green function variational approximation: Significance of physical constraints

We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent Dyson expansions and solving the resulting set of equations. This method, dubbed the variational approximation, is both very dependable and flexible, since it is a systematic expansion with precise control over elementary physical processes. It allows for deep insight into the underlying physics of polaron formation as well as for inclusion of many physical constraints, such as excluding crossing diagrams and double occupation constraint, which are not included in the Self-Consistent Born Approximation. Here we examine the role and importance of such constraints by analyzing various spectral functions obtained in second order VA.

preprint2015arXiv

Polaron states in a CuO chain

We introduce a one-dimensional model for a CuO chain, with holes and $S=1/2$ spins localized in $3d_{x^2-y^2}$ orbitals, and $p_σ$ oxygen orbitals without holes in the ground state. We consider a single hole doped at an oxygen site and study its propagation by spin-flip processes. We develop the Green's function method and treat the hole-spin coupling in the self-consistent Born approximation, similar to that successfully used to study polarons in the regular $t$-$J$ model. We present an analytical solution of the problem and investigate whether the numerical integration is a good approximation to this solution.

preprint2014arXiv

Quantum versus classical polarons in a ferromagnetic CuO$_3$-like chain

We present an exact solution for an itinerant hole added into the oxygen orbitals of a CuO$_{3}$-like ferromagnetic chain. Using the Green's function method, the quantum polarons obtained for the Heisenberg SU(2) interaction between localized Cu spins are compared with the polarons in the Ising chain. We find that magnons with large energy are favorable towards quasiparticle existence, even in the case of relatively modest electron-magnon coupling. We observe two quasiparticle states with dispersion $\sim 2t$ each, which emerge from the incoherent continuum when the exchange coupling $J$ increases. Quantum fluctuations in the spin system modify the incoherent part of the spectrum and change the spectral function qualitatively, beyond the bands derived from the perturbation theory.

preprint2013arXiv

Exact spectral function for hole-magnon coupling in the ferromagnetic CuO$_3$-like chain

We present the exact spectral function for a single oxygen hole with spin opposite to ferromagnetic order within a one-dimensional CuO$_{3}$-like spin chain. We find that local Kondo-like exchange interaction generates five different states in the strong coupling regime. It stabilizes a spin polaron which is a bound state of a moving charge dressed by magnon excitations, with essentially the same dispersion as predicted by mean field theory. We then examine in detail the evolution of the spectral function for increasing strength of the hole-magnon interaction. We also demonstrate that the $s$ and $p$ symmetry of orbital states in the conduction band are essentially equivalent to each other and find that the simplified models do not suffice to reproduce subtle aspects of hole-magnon coupling in the charge-transfer model.