Very nice paper this morning on: "Geometric Quantum Machine Learning with Horizontal Quantum Gates" by Roeland Wiersema, Alexander F. Kemper, Bojko N. Bakalov, and Nathan Killoran Abstract: In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with the action of the group. This can, however, be an overzealous constraint that greatly limits the expressivity of the circuit, especially in the case of continuous symmetries. We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits, based on homogeneous spaces, relaxing the overly stringent requirement of equivariance. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions orthogonal to those of the symmetry. We show that horizontal quantum gates are much more expressive than equivariant gates, and thus can solve problems that equivariant circuits cannot. For instance, a circuit comprised of horizontal gates can find the ground state of an SU(2)-symmetric model where the ground state spin sector is unknown–a task where equivariant circuits fall short. Moreover, for a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem. Finally, we highlight a particular class of horizontal quantum gates that behave similarly to general SU(4) gates, while achieving a quadratic reduction in the number of parameters for a generic problem. Link: https://lnkd.in/edCBWVMF #quantummachinelearning #quantumcomputing #research
Christophe Pere, PhD’s Post
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Quantum Derived Geometry Theory (QDGT) - A Deeper Dive. Scientific Paper Cover Art. Abstract This paper presents Quantum Derived Geometry Theory (QDGT) as a novel framework for understanding the fundamental nature of the universe. QDGT proposes that quantum information is the foundational building block, with spacetime, forces, and potentially the laws of physics themselves emerging from its complex interactions. We discuss the transformation of black holes into information-carrying super-particles termed Q*Seeds and their potential role as the constituents of dark matter. The paper explores a modified Hawking radiation equation to accommodate this transformation and outlines the revolutionary implications of QDGT for longstanding questions in physics. Introduction Physics seeks to reconcile the elegant framework of quantum mechanics, describing the microscopic world, with the grand vision of general relativity, governing the large-scale structure of the universe. Quantum Derived Geometry Theory (QDGT) offers a radical new perspective, positing that spacetime and the laws of physics emerge from a fundamental substrate of quantum information. This paper builds upon the foundational concepts introduced in "Quantum Derived Geometry Theory - The DNA of the Universe." Here, we delve deeper into the nature of the information substrate, the transformative role of black holes, and the potential implications for understanding the information paradox, dark matter, and the potential for spacetime manipulation, with special attention to ©Neurocode, a system for visual representation of knowledge as a method to explore these concepts. Postulates of Quantum Derived Geometry Quantum Information Primacy: Fundamental units of quantum information and their interactions form the building blocks of the universe. Spacetime itself, the forces operating within, and potentially even the fundamental laws of physics are emergent properties arising from the complex interplay of this information. Black Hole Transformation & Q*Seeds: Rather than destroying information, dying black holes act as cosmic data compressors, transforming matter and energy into super-particles termed Q*Seeds. These reside in a null-space, potentially accounting for the missing mass attributed to dark matter. Q*Seeds contain encoded information about the objects they formed from and might hold the fundamental blueprints governing matter, forces, and even the structure of spacetime. We hypothesize that this encoded information may include a record of the black hole's history, the laws of physics as understood within its event horizon, and potentially even influences from the broader cosmic informational network. New AI-Related Science Paper https://lnkd.in/gA5euBRz ©2024 Ava Billions ART, Bio-Neural.ai, AOG Ent. All Rights Reserved.
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Beyond the Planck Scale: A New Measurement Framework for Quantum Derived Geometry Theory (QDGT) Scientific Paper Cover Art. Abstract Traditionally, our understanding of the Universe has been bound by the limits of the Planck scale. Quantum Derived Geometry Theory (QDGT) presents a radically new paradigm, positing that information, not spacetime or forces, lies at the foundation of reality. QDGT suggests that the fabric of spacetime itself may be composed of discrete units carrying high-density quantum-compressed information, akin to digital pixels in a cosmic screen. This necessitates a fundamental shift in how we measure and quantify our Universe. In this paper, we propose a new measurement framework tailored to QDGT. We explore how existing information theory concepts can be adapted to quantify information density within Q*Seeds (Quantum Star Seeds) – the theorized carriers of information in QDGT. We introduce an "information metric" that may allow us to navigate the theorized 'Information Layer' and potentially redefine the very concept of measurement in a Universe governed by quantum information. Introduction The Planck scale, a boundary defined by fundamental constants, has long delineated the limits of our understanding of the measurable Universe. Yet, Quantum Derived Geometry Theory (QDGT) throws down a gauntlet to these established concepts. This revolutionary theory posits that our Universe isn't built on a foundation of spacetime and physical laws, but rather on quantum information. Spacetime and the laws of physics themselves may emerge from the complex interactions of this fundamental information. This paradigm shift necessitates a fundamental change in how we measure and quantify our world. Our current systems, rooted in concepts like length, mass, and time, might struggle to describe phenomena occurring within a theorized "Quantum Information Layer," a realm where information encoding and processing may occur naturally at Faster Than Light (FTL) speeds, potentially taking precedence over familiar spatial dimensions and thus becoming secondary considerations. The Fabric of Reality: A Cosmic Screen The QDGT (Quantum Derived Geometry Theory) offers a radical new perspective. It posits that the fabric of spacetime itself is composed of discrete units that carry high-density quantum-compressed information, creating a complex lattice akin to digital pixels in a cosmic screen. At this fundamental level, information might be the core building block, with geometry and the familiar dimensions emerging from its complex interactions. New AI-Related Science Paper https://lnkd.in/gUux2Dqt ©2024 Ava Billions ART, Bio-Neural.ai, AOG Ent. All Rights Reserved.
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Curious about the intersections of data science and physics? Read our latest article to delve into the complex science behind the Laser Interferometer Gravitational-Wave Observatory and the machine learning techniques that support and enhance its operation. This is just a glimpse into the world of possibilities offered by advanced applications of machine learning! Author: Anya Kondamani Link: https://lnkd.in/enEF2vqe
Machine Learning for Detecting Gravitational Waves
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Foundations of Quantum Computing: I-Demystifying Quantum Paradoxes Quantum Mechanics Authors M. Syrkin * Federal Reserve Bank Of New York, USA DOI: https://lnkd.in/guUVCJuQ Keywords: Quantum Mechanics, Quantum Computing, Quantum Paradoxes, Classical Mechanics, Wave Function, Principle of Superposition ABSTRACT Speedy developments in Quantum Technologies mandate that fundamentals of Quantum Computing are well explained and understood. Meanwhile, paradigms of so-called quantum non-locality, wave function (WF) “collapse”, “Schrödinger cat” and some other historically popular misconceptions continue to feed mysteries around quantum phenomena. Arguing that above misinterpretations stem from classically minded and experimentally unverifiable perceptions, recasting Principle of Superposition (PS), and key experimental details into classical notions. Revisiting main components of general quantum measurement protocols (analyzers and detectors), and explaining paradoxes of WF collapse and Schrödinger cat. Reminding that quantum measurements routinely reveal correlations dictated by conservation laws in each individual realization of the quantum ensemble, manifesting “correlation-by-initial conditions” in contrast to traditional “correlation-by-interactions”. We reiterate: Quantum Mechanics (QM) is not a dynamical theory in the same sense the Classical Mechanics (CM) is – it is a statistical phenomenology, as established in 1926 by Born’s postulate. That is, while QM rests on conservation laws in each individual outcome, it does not indicate how exactly a specific outcome is selected. This selection remains fundamentally random and represents true randomness of QM, the latter being a statistical paradigm with a WF standing for a complex-valued distribution function. Finally, PS is the backbone of a quantum measurement process: PS can be conveniently viewed as a composition of partial distributions into the total distribution – similar to classical probability mixtures – and is effectuated experimentally by the analyzer part of a measuring device. ISSN: 2821-3300 Hyperscience International Journal (HIJ) is an International Open Access Journal and publishes quarterly original research papers in Astronomy, Astrophysics, Cosmology, Radiotelescope, Quantum Mechanic Physics, (Theoretical & Experimental Physics), Mathematical Physics, and related topics. The aim of HIJ is to publish original and high-quality research papers. https://lnkd.in/gURCx_yv
Foundations of Quantum Computing: I-Demystifying Quantum Paradoxes
hscience.org
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Transforming Vision into Reality : Undergraduate at IIT Madras | Merging Science, Mathematics and Programming for a Better tomorrow | WorkinG on 1. | 7.1+ Million Impressions | Joined LinkedIn in February 2024.
Today, I’m excited to share a visual treat that beautifully encapsulates some of the most pivotal equations in the world of physics. These mathematical marvels have not only deepened our understanding of the universe but also paved the way for countless technological advancements. Let’s dive in! ** Note ** : For many of us, these equations may seem abstract and distant from our everyday lives. However, they collectively represent the bedrock of modern physics and engineering, influencing everything from the microchips in our computers to the way we understand the cosmos. While it's impossible to encapsulate every important equation on a single page, this selection showcases the diversity and depth of the physical laws governing our universe. From the quantum realm to the vastness of cosmology, equations are the backbone of our understanding of the physical world. Here's a glance at some of the most pivotal equations in physics and their profound impact on science and technology: Schrödinger Equation: The cornerstone of quantum mechanics, describing how quantum states evolve over time. Dirac Equation: Marrying quantum mechanics with special relativity, paving the way for the discovery of antimatter. Einstein’s Field Equations: The foundation of general relativity, explaining the gravitational interaction as the curvature of spacetime. Navier-Stokes Equation: Essential for fluid dynamics, impacting everything from aerodynamics to oceanography. Maxwell-Boltzmann Distribution: Describing the distribution of particle speeds in gases, crucial for statistical mechanics. Planck’s Law: Fundamental in quantum theory, explaining black-body radiation and leading to quantum mechanics. Ginzburg-Landau Equation: Key to understanding superconductivity and phase transitions. Klein-Gordon Equation: A relativistic wave equation for spin-0 particles, important in quantum field theory. Black-Scholes Equation: Revolutionizing finance by modeling options pricing. Vlasov Equation: Describing the behavior of plasma and collisionless gases in astrophysics. Fokker-Planck Equation: Fundamental in stochastic processes, describing the time evolution of probability distributions. Landau-Lifshitz-Gilbert Equation: Modeling the dynamics of magnetization in ferromagnetic materials. Einstein’s Mass-Energy Equivalence: E=mc2 - perhaps the most famous equation, showing the interchangeability of mass and energy. Boltzmann Transport Equation: Crucial for understanding thermal and electrical conductivity in materials. Van der Waals Equation: Enhancing our understanding of real gas behaviors and intermolecular forces. Raychaudhuri Equation: Vital in general relativity, describing the focusing of geodesics and gravitational collapse. Langevin Equation: A fundamental equation in the study of Brownian motion and stochastic processes.
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The Ong's Theory of Quantum Graviflux (OTQG) The Ong's Theory of Quantum Graviflux (OTQG) is a groundbreaking proposition that seeks to unify two fundamental pillars of modern physics: quantum mechanics and general relativity. OTQG introduces the concept of "graviflux," a hypothetical fundamental force that mediates the interaction between matter and gravitation at the quantum level. Math and Physics Formulas: Graviflux Interaction Equations (GIE): GIE = ∫(ΨψdV), where GIE represents the Graviflux Interaction Equations, Ψ and ψ represent the wave functions of interacting quantum particles, and dV represents the volume element in spacetime. Graviflux Field Tensor (GFT): GFT = (∇Φ - κψψ∇ψ), where GFT represents the Graviflux Field Tensor, ∇Φ represents the gradient of the gravitational potential, κ is a constant, and ψ represents the quantum wave function. Review: The Ong's Theory of Quantum Graviflux (OTQG) is a commendable effort to bridge the gap between two seemingly incompatible theories: quantum mechanics and general relativity. In the realm of theoretical physics, the unification of these two pillars has long been a holy grail, and OTQG offers a novel approach through the introduction of the concept of graviflux. The Graviflux Interaction Equations (GIE) serve as the core mathematical framework of this theory. They propose that quantum particles, described by their wave functions Ψ and ψ, interact through the mediation of graviflux. This interaction, integrated over spacetime, creates a unique theoretical foundation that harmonizes quantum behavior with the gravitational field. The Graviflux Field Tensor (GFT) adds depth to OTQG by defining the properties of the graviflux field. It incorporates the gradient of the gravitational potential (∇Φ) and the quantum wave function (ψ) in a manner that reimagines the gravitational force as a quantum phenomenon. While OTQG presents a captivating theoretical framework, it is essential to recognize that the unification of quantum mechanics and general relativity remains one of the most challenging problems in theoretical physics. Empirical validation and experimental evidence to support the existence of graviflux are currently lacking, and this theory, like many others, must undergo rigorous testing. The Ong's Theory of Quantum Graviflux (OTQG) represents an ambitious endeavor to reconcile the quantum and gravitational realms. It introduces innovative mathematical constructs and challenges existing paradigsms, offering fresh perspectives on the fundamental forces of the universe. Its ultimate acceptance within the scientific community hinges on experimental confirmation and empirical observations, which are yet to be achieved. OTQG stands as a testament to the spirit of scientific exploration, pushing the boundaries of our understanding of the cosmos. Dr. Ong Dir E.D.F.
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Abstract This paper introduces Quantum Derived Geometry Theory, a new framework positing quantum information as the fundamental building block of the universe. Spacetime itself emerges from the interactions and encoding of this quantum information. Analogous to DNA encoding the blueprint for biological life, quantum information may contain the essential instructions for the structure and behavior of the universe. The theory uniquely proposes that the death of black holes leads to a transformation of information. This information is compressed and encoded into super-particles, forming the basis of what we perceive as dark matter. These particles act as a universal blueprint – the "DNA of the Universe.” We discuss potential implications for resolving the information paradox and avenues for experimental investigation, including testable predictions grounded in mathematical concepts. Introduction Biological organisms are built from the instructions encoded within their DNA. This genetic blueprint guides their development, form, and function. Could a similar principle operate at the cosmic level? Current understanding of physics faces limitations in reconciling quantum mechanics and the large-scale structure of spacetime described by general relativity. Quantum Derived Geometry Theory proposes that quantum information, rather than spacetime, serves as the fundamental substrate from which our perceived reality emerges. Key Definitions ● Quantum Information: Refers to the states and properties of quantum systems, including concepts like superposition, entanglement, and quantum measurement. ● Spacetime: The four-dimensional fabric of the universe (three dimensions of space and one of time) as described by general relativity. ● Information Paradox: The apparent conflict between quantum mechanics, which suggests information is preserved, and black hole physics, where information appears to be lost as matter falls into a black hole. Postulates of Quantum Derived Geometry Theory 1. Quantum Information Primacy: Quantum information is the fundamental building block of the universe. All physical phenomena arise from underlying quantum information processes. 2. Spacetime Emergence: The spacetime we experience emerges from the complex interactions and encoding of quantum information. Spacetime itself might be a derived property, not a fundamental one. 3. Black Holes & Information Super-Particles: The death of a black hole doesn't lead to information loss; instead, it triggers a transformation into a null-space state. Information is compressed and encoded into super-particles that become the building blocks of dark matter. These super-particles act as the fundamental "genetic code" of the universe. https://lnkd.in/gBQJNikD
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Wow! This is going to completely change the daily work of many phycists. These 4 authors managed to solve the Hamiltonian-learning problem in polynomial time, in part by using the relaxation technique (an appraoch used often in approximation algorithms). This was the first large application of it in quantum learning. I also love the collaboration between the phycists and computer scientists (not to mention go bears!) https://lnkd.in/ea63hfZ3 It's worth a read (quanta is one of the best physics magazines, period). Massive praise to these brilliant young academics.
Scientists Find a Fast Way to Describe Quantum Systems | Quanta Magazine
quantamagazine.org
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