arXiv subjects

Jakub Mielczarek

Publications and source records attributed to Jakub Mielczarek.

At least 19 recordsLinked to original sources

arXiv2026

Spin networks of quantum channels

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of environment, which can become significant at the Planck scale. Specifically, we demonstrate that the transformation properties of Kraus operators, which define completely positive trace-preserving (CPTP) maps, are consistent with the gauge invariance of spin networks. This enables the introduction of generalized spin network states that can be expressed in terms of the Kraus operators. Furthermore, the associated notion of an inner product is proposed, allowing for introduction of the Hilbert space. We illustrate these constructions with examples involving a Wilson loop and a dipole network.

gr-qc↗

arXiv2025

Exact formula for geometric quantum complexity of cosmological perturbations

Nielsen's geometric approach offers a powerful framework for quantifying the complexity of unitary transformations. In this formulation, complexity is defined as the length of the minimal geodesic in a suitably constructed geometric space associated with the Lie group of relevant operators. Despite its conceptual appeal, determining geodesic distances on Lie group manifolds is generally challenging, and existing treatments often rely on perturbative expansions in the structure constants. In this work, we circumvent these limitations by employing a finite-dimensional matrix representation of the generators, which enables an exact computation of the geodesic distance and hence a precise determination of the complexity. We focus on the $\mathfrak{su}(1,1)$ Lie algebra, relevant for quantum scalar fields evolving on homogeneous and isotropic cosmological backgrounds. The resulting expression for the complexity is applied to de Sitter spacetime as well as to asymptotically static cosmological models undergoing contraction or expansion.

hep-th↗

arXiv2025

Geometric measure of quantum complexity in cosmological systems

In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the group manifold. Earlier work has shown that the computation of geodesic distance can be challenging for Lie groups relevant to harmonic oscillators. Here, this problem is approached by working to leading order in an expansion by the structure constants of the Lie group. An explicit formula for an upper bound on the quantum complexity of a harmonic oscillator Hamiltonian with time-dependent frequency is derived. Applied to a massless test scalar field on a cosmological de Sitter background, the upper bound on complexity as a function of the scale factor exhibits a logarithmic increase on super-Hubble scales. This result aligns with the gate complexity and earlier studies of de Sitter complexity. It demonstrates the consistent application of Nielsen complexity to quantum fields in cosmological backgrounds and paves the way for further applications.

quant-ph↗

arXiv2024

From $SU(2)$ holonomies to holographic duality via tensor networks

Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which correspond to $SU(2)$ gauge-invariant discrete field theories. Importantly, the spin network states play a central role in the Loop Quantum Gravity (LQG) approach to the Planck scale physics. Our focus is on the Ising-type spin networks, which provide a basic model of quantum space in LQG. It is shown that the tensor network approach improves the previously introduced methods of constructing quantum circuits for the Ising spin networks by reducing the number of qubits involved. It is also shown that the tensor network approach is convenient for implementing holographic states involving the bulk-boundary conjecture, which contributes to establishing a link between LQG and holographic duality.

hep-th↗

arXiv2024

Geometric quantum complexity of bosonic oscillator systems

According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the original concept of complexity based on the minimal number of gates required to construct the desired operation as a product, this geometrical approach amounts to a more concrete and computable definition, but its evaluation is nontrivial in systems with a high-dimensional Hilbert space. The geometrical formulation can more easily be evaluated by considering the geometry associated with a suitable finite-dimensional group generated by a small number of relevant operators of the system. In this way, the method has been applied in particular to the harmonic oscillator, which is also of interest in the present paper. However, subtle and previously unrecognized issues of group theory can lead to unforeseen complications, motivating a new formulation that remains on the level of the underlying Lie algebras for most of the required steps. Novel insights about complexity can thereby be found in a low-dimensional setting, with the potential of systematic extensions to higher dimensions as well as interactions. Specific examples include the quantum complexity of various target unitary operators associated with a harmonic oscillator, inverted harmonic oscillator, and coupled harmonic oscillators. The generality of this approach is demonstrated by an application to an anharmonic oscillator with a cubic term.

quant-ph↗

arXiv2024

In Search of Quantum Advantage: Estimating the Number of Shots in Quantum Kernel Methods

Quantum Machine Learning (QML) has gathered significant attention through approaches like Quantum Kernel Machines. While these methods hold considerable promise, their quantum nature presents inherent challenges. One major challenge is the limited resolution of estimated kernel values caused by the finite number of circuit runs performed on a quantum device. In this study, we propose a comprehensive system of rules and heuristics for estimating the required number of circuit runs in quantum kernel methods. We introduce two critical effects that necessitate an increased measurement precision through additional circuit runs: the spread effect and the concentration effect. The effects are analyzed in the context of fidelity and projected quantum kernels. To address these phenomena, we develop an approach for estimating desired precision of kernel values, which, in turn, is translated into the number of circuit runs. Our methodology is validated through extensive numerical simulations, focusing on the problem of exponential value concentration. We stress that quantum kernel methods should not only be considered from the machine learning performance perspective, but also from the context of the resource consumption. The results provide insights into the possible benefits of quantum kernel methods, offering a guidance for their application in quantum machine learning tasks.

quant-ph↗

arXiv2024

Squeezing of light from Planck-scale physics

In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and multi-mode lights. The model leads to a deformed dispersion relation, which manifests in an advancement in the time of arrival of photons. The key finding is that the model also leads to an oscillatory pattern of squeezing of the state of light. Furthermore, while the amplitude of the oscillations is constant for energy eigenstates, it exhibits linear growth over time for coherent states with the annihilation operator eigenvalue $α\neq0 $. This second case leads to the accumulation of squeezing and phase-space displacement, which can be significant for astrophysical photons. In particular, for $α\sim 1$, coherent light in the optical spectrum emitted at megaparsec distances would acquire squeezing with the amplitude of the order unity. This suggests that measurements of the non-classical properties of light originating from distant astrophysical sources may open a window to test these predictions.

gr-qc↗

arXiv2023

Deep-Learning-based Change Detection with Spaceborne Hyperspectral PRISMA data

Change detection (CD) methods have been applied to optical data for decades, while the use of hyperspectral data with a fine spectral resolution has been rarely explored. CD is applied in several sectors, such as environmental monitoring and disaster management. Thanks to the PRecursore IperSpettrale della Missione operativA (PRISMA), hyperspectral-from-space CD is now possible. In this work, we apply standard and deep-learning (DL) CD methods to different targets, from natural to urban areas. We propose a pipeline starting from coregistration, followed by CD with a full-spectrum algorithm and by a DL network developed for optical data. We find that changes in vegetation and built environments are well captured. The spectral information is valuable to identify subtle changes and the DL methods are less affected by noise compared to the statistical method, but atmospheric effects and the lack of reliable ground truth represent a major challenge to hyperspectral CD.

cs.CV↗

arXiv2023

Cloud Detection in Multispectral Satellite Images Using Support Vector Machines With Quantum Kernels

Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of pattern recognition and classification tasks. In this work, we consider extending classic SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) is presented. It consists of the Quantum Kernel Estimation (QKE) procedure combined with a classic SVM training routine. The pixel data are mapped to the Hilbert space using ZZ-feature maps acting on the parameterized ansatz state. The parameters are optimized to maximize the kernel target alignment. We approach the problem of cloud detection in satellite image data, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy on par with classic SVMs.

cs.CV↗

arXiv2023

Optimizing Kernel-Target Alignment for cloud detection in multispectral satellite images

The optimization of Kernel-Target Alignment (TA) has been recently proposed as a way to reduce the number of hardware resources in quantum classifiers. It allows to exchange highly expressive and costly circuits to moderate size, task oriented ones. In this work we propose a simple toy model to study the optimization landscape of the Kernel-Target Alignment. We find that for underparameterized circuits the optimization landscape possess either many local extrema or becomes flat with narrow global extremum. We find the dependence of the width of the global extremum peak on the amount of data introduced to the model. The experimental study was performed using multispectral satellite data, and we targeted the cloud detection task, being one of the most fundamental and important image analysis tasks in remote sensing.

cs.CV↗

arXiv2023

Quantum circuits for the Ising spin networks

Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge of dealing with high-dimensional Hilbert spaces. To explore more general configurations, quantum computing methods can be applied by representing spin network states as quantum circuits. In this article, we introduce an improved method for constructing quantum circuits for 4-valent Ising spin networks, which utilizes a smaller number of qubits than previous approaches. This has practical implications for the implementation of quantum circuits. We also demonstrate the procedure with various examples, including the construction of a 10-node Ising spin network state. The key ingredient of the method is the variational transfer of partial states, which we illustrate through numerous examples. Our improved construction provides a promising avenue for further exploring the potential of quantum computing methods in quantum gravity research.

gr-qc↗

arXiv2023

Detecting Clouds in Multispectral Satellite Images Using Quantum-Kernel Support Vector Machines

Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) are presented. Here, the pixels are mapped to the Hilbert space using a family of parameterized quantum feature maps (related to quantum kernels). The parameters are optimized to maximize the kernel target alignment. The quantum kernels have been selected such that they enabled analysis of numerous relevant properties while being able to simulate them with classical computers on a real-life large-scale dataset. Specifically, we approach the problem of cloud detection in the multispectral satellite imagery, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy comparable to the classical SVM with the RBF kernel for large datasets. Interestingly, for large datasets, the high accuracy was also observed for the simple quantum kernels, lacking quantum entanglement.

cs.CV↗

arXiv2022

Analysis of Multiple Overlapping Paths algorithms for Secure Key Exchange in Large-Scale Quantum Networks

Quantum networks open the way to an unprecedented level of communication security. However, due to physical limitations on the distances of quantum links, current implementations of quantum networks are unavoidably equipped with trusted nodes. As a consequence, the quantum key distribution can be performed only on the links. Due to this, some new authentication and key exchange schemes must be considered to fully benefit from the unconditional security of links. One such approach uses Multiple Non-Overlapping Paths (MNOPs) for key exchange to mitigate the risk of an attack on a trusted node. The scope of the article is to perform a security analysis of this scheme for the case of both uncorrelated attacks and correlated attacks with finite resources. Furthermore, our analysis is extended to the case of Multiple Overlapping Paths (MOPs). We prove that introducing overlapping paths allows one to increase the security of the protocol, compared to the non-overlapping case with the same number of additional links added. This result may find application in optimising architectures of large-scale (hybrid) quantum networks.

quant-ph↗

arXiv2021

Quantum variational solving of the Wheeler-DeWitt equation

One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to the Wheeler-DeWitt equation. However, solutions to the equation are known only for specific symmetry-reduced systems, including models of quantum cosmology. Novel methods, which enable solving the equation for complex gravitational configurations are, therefore, worth seeking. Here, we propose and investigate a new method of solving the Wheeler-DeWitt equation, which employs a variational quantum computing approach, and is possible to implement on quantum computers. For this purpose, the gravitational system is regularized, by performing spherical compactification of the phase space. This makes the system's Hilbert space finite-dimensional and allows to use $SU(2)$ variables, which are easy to handle in quantum computing. The validity of the method is examined in the case of the flat de Sitter universe. For the purpose of testing the method, both an emulator of a quantum computer and the IBM superconducting quantum computer have been used. The advantages and limitations of the approach are discussed.

gr-qc↗

arXiv2021

Secure quantum communication through a wormhole

An accumulation of theoretical evidence contribute to the picture of gravity as a manifestation of quantum entanglement in a certain many-body quantum system. This is in particular expresses in the ER=EPR conjecture, which relates gravitational Einstein-Rosen (ER) bridge with the Einstein-Podolsky-Rosen (EPR) quantum entangled pairs or, more generally, with the so-called Thermofield Double State. In this letter, the ER=EPR conjecture is employed to introduce unitary quantum teleportation protocol, which \emph{recycles} the entanglement forming traversable generalization of the Einstein-Rosen bridge. In consequence, the wormhole remains unaffected by the quantum teleportation. Furthermore, it is shown that the protocol guarantees the unconditional security of the quantum communication. Performance of the protocol is demonstrated in a simple setting with the use of 5-qubit Santiago IBM quantum computer, giving fidelities above the $2/3$ classical limit for a representative set of teleported states. Security of the protocol has been supported by experimental studies performed with the use of the noisy quantum processor. Possible generalization of the protocol, which may have relevance in the context of macroscopic gravitational configurations, is also considered.

quant-ph↗

arXiv2021

Quantum simulations of a qubit of space

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin networks with the use of superconducting quantum processor are made.

gr-qc↗

arXiv2020

General-relativistic spin system

The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is interesting to consider special and general relativistic extensions of such models. Here, we introduce a framework that allows us to construct theories of continuous spin variables on a curved spacetime. Our approach takes advantage of the results of the non-linear field space theory, which shows how to construct compact phase space models, in particular for the spherical phase space of spin. Following the methodology corresponding to a bosonization of spin systems into the spin wave representations, we postulate a representation having the form of the Klein-Gordon field. This representation is equivalent to the semi-classical version of the well-known Holstein-Primakoff transformation. The general-relativistic extension of the spin wave representation is then performed, leading to the general-relativistically motivated modifications of the Ising model coupled to a transversal magnetic field. The advantage of our approach is its off-shell construction, while the popular methods of coupling fermions to general relativity usually depend on the form of Einstein field equations with matter. Furthermore, we show equivalence between the considered spin system and the Dirac-Born-Infeld type scalar field theory with a specific potential, which is also an example of k-essence theory. Based on this, the cosmological consequences of the introduced spin field matter content are preliminarily investigated.

hep-th↗

arXiv2020

Gauge fields and quantum entanglement

The purpose of this letter is to explore the relation between gauge fields, which are at the base of our understanding of fundamental interactions, and the quantum entanglement. To this end, we investigate the case of ${\rm SU}(2)$ gauge fields. It is first argued that holonomies of the ${\rm SU}(2)$ gauge fields are naturally associated with maximally entangled two-particle states. Then, we provide some evidence that the notion of such gauge fields can be deduced from the transformation properties of maximally entangled two-particle states. This new insight unveils a possible relation between gauge fields and spin systems, as well as contributes to understanding of the relation between tensor networks (such as MERA) and spin network states considered in loop quantum gravity. In consequence, our results turn out to be relevant in the context of the emerging Entanglement/Gravity duality.

hep-th↗