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.Comment: 17 pages. Matches the version published in PR

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

The higher-order phase transition in toroidal CDT

We investigate the transition between the phases $B$ and $C_b$ observed in four-dimensional Causal Dynamical Triangulations (CDT). We find that the critical properties of CDT with toroidal spatial topology are the same as earlier observed in spherical spatial topology where the $B-C_b$ transition was found to be higher-order. This may have important consequences for the existence of the continuum limit of CDT, describing the perspective UV limit of quantum gravity, which potentially can be investigated in the toroidal model.Comment: 17 pages, 10 figure

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.Comment: Prepared for IGARSS 2023 Proceedings, 4 pages, 2 figure

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.Comment: Prepared for IGARSS 2023 Proceedings, 4 pages, 4 figure

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.Comment: 12 pages, 10 figure

Quantum-Cosmos-Lab/Ising-spin-networks: First release

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Przejścia fazowe w czterowymiarowym modelu CDT na torusie

Sformułowanie poprawnej teorii kwantowej grawitacji, która łączyłaby w sobie ogólną teorię względności oraz mechanikę kwantową wciąż pozostaje nierozwiązanym problemem fizyki. Wobec perturbacyjnej nierenormalizowalności grawitacji traktowanej konwencjonalnymi metodami teorii pola, podejmuje się próby innego skwantowania grawitacji. Jedną z nich są kauzalne dynamiczne triangulacje (CDT), które wykorzystują ideę całek po trajektoriach Feynmana i dyskretyzację czasoprzestrzeni poprzez konstruowanie jej z d-wymiarowych sympleksów. Otrzymany w ten sposób model statystyczny, może być badany w poszukiwaniu przejść fazowych, które mogłyby pomóc w znalezieniu granicy ciągłej teorii i poprawnym sformułowaniu kwantowej grawitacji. Praca zawiera wyniki badań dotyczących przejść fazowych w szczególności pomiędzy tzw. fazami B i Cb.The formulation of the correct quantum theory of gravity, which would combine General Relativity and Quantum Mechanics, remains an unresolved problem in physics. Due to the perturbational nonrenormalizability of gravity treated with conventional methods of field theory, attempts are made to quantize gravity in a different way. One of the methods are Causal Dynamical Triangulations (CDT), which use the idea of Feynman's path integral and discretization of space-time by constructing it from d-dimensional simplices. The statistical model obtained in this way can be examined in the search of phase transitions, which could help to find the continuum limit of the theory and the correct formulation of quantum gravity. The thesis contains results of a research on phase transitions, in particular between the so-called phases B and Cb

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.Comment: 15 page