arXiv subjects

Krzysztof Bieniasz

Publications and source records attributed to Krzysztof Bieniasz.

13 recordsLinked to original sources

arXiv2026

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.

quant-ph↗

arXiv2024

Iterative Qubit Coupled Cluster using only Clifford circuits

The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An ideal state preparation protocol can be characterized by being easily generated classically and can be transformed to a quantum circuit with minimal overhead while having a significant overlap with the targeted eigenstate of a given Hamiltonian. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) approach, which exclusively uses Clifford circuits. These circuits can be efficiently simulated on a classical computer, with polynomial scaling according to the Gottesman-Knill theorem. Since the iQCC method has been developed as a quantum algorithm firstly, our variant can be mapped naturally to quantum hardware. We additionally implemented several optimizations to the algorithm enhancing its scalability. We demonstrate the algorithm's correctness in ground-state simulations for small molecules such as H2, LiH, and H2O, and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space, requiring 40 qubits. Results show that the convergence of the algorithm is well-behaved, and the ground state can be represented accurately. Moreover, we show an automated workflow for restricting the qubit active space, thus relieving computational resources by considering only qubits affected by non-trivial operations.

quant-ph↗

arXiv2022

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.

quant-ph↗

arXiv2022

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.

cond-mat.str-el↗

arXiv2021

Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra

Resonant inelastic X-ray scattering (RIXS) is used increasingly for characterizing low-energy collective excitations in materials. RIXS is a powerful probe, which often requires sophisticated theoretical descriptions to interpret the data. In particular, the need for accurate theories describing the influence of electron-phonon ($e$-p) coupling on RIXS spectra is becoming timely, as instrument resolution improves and this energy regime is rapidly becoming accessible. To date, only rather exploratory theoretical work has been carried out for such problems. We begin to bridge this gap by proposing a versatile variational approximation for calculating RIXS spectra in weakly doped materials, for a variety of models with diverse $e$-p couplings. Here, we illustrate some of its potential by studying the role of electron mobility, which is completely neglected in the widely used local approximation based on Lang-Firsov theory. Assuming that the electron-phonon coupling is of the simplest, Holstein type, we discuss the regimes where the local approximation fails, and demonstrate that its improper use may grossly \textit{underestimate} the $e$-p coupling strength.

cond-mat.str-el↗

arXiv2019

From "Weak" to "Strong" Hole Confinement in a Mott Insulator

We study the problem of a single hole in an Ising antiferromagnet and, using the magnon expansion and analytical methods, determine the expansion coefficients of its wave function in the magnon basis. In the 1D case, the hole is "weakly" confined in a potential well and the magnon coefficients decay exponentially in the absence of a string potential. This behavior is in sharp contrast to the 2D square plane where the hole is "strongly" confined by a string potential and the magnon coefficients decay superexponentially. The latter is identified here to be a fingerprint of the strings in doped antiferromagnets that can be recognized in the numerical or cold atom simulations of the 2D doped Hubbard model. Finally, we attribute the differences between the 1D and 2D cases to the magnon-magnon interactions being crucially important in a 1D spin system.

cond-mat.str-el↗

arXiv2019

Spectral properties of spin-orbital polarons as a fingerprint of orbital order

Transition metal oxides are a rich group of materials with very interesting physical properties that arise from the interplay of the charge, spin, orbital, and lattice degrees of freedom. One interesting consequence of this, encountered in systems with orbital degeneracy, is the coexistence of long range magnetic and orbital order, and the coupling between them. In this paper we develop and study an effective spin-orbital superexchange model for $e_g^3$ systems and use it to investigate the spectral properties of a charge (hole) injected into the system, which is relevant for photoemission spectroscopy. Using an accurate, semi-analytical, magnon expansion method, we gain insight into various physical aspects of these systems and demonstrate a number of subtle effects, such as orbital to magnetic polaron crossover, the coupling between orbital and magnetic order, as well as the orbital order driving the system towards one-dimensional quantum spin liquid behavior. Our calculations also suggest a potentially simple experimental verification of the character of the orbital order in the system, something that is not easily accessible through most experimental techniques.

cond-mat.str-el↗

arXiv2017

Orbiton-magnon interplay in the spin-orbital polarons of KCuF3 and LaMnO3

We present a quasi-analytical solution of a spin-orbital model of KCuF$_{3}$, using the variational method for Green's functions. By analyzing the spectra for different partial bosonic compositions as well as the full solution, we show that hole propagation needs both orbiton and magnon excitations to develop, but the orbitons dominate the picture. We further elucidate the role of the different bosons by analyzing the self-energies for simplified models, establishing that because of the nature of the spin-orbital ground state, magnons alone do not produce a full quasiparticle band, in contrast to orbitons. Finally, using the electron-hole transformation between the $e_g$ states of KCuF$_3$ and LaMnO$_3$ we suggest the qualitative scenario for photoemission experiments in LaMnO$_3$.

cond-mat.str-el↗

arXiv2016

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.

cond-mat.str-el↗

arXiv2016

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.

cond-mat.str-el↗

arXiv2015

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.

cond-mat.str-el↗

arXiv2014

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.

cond-mat.str-el↗

arXiv2013

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.

cond-mat.str-el↗