Quantum many-body physics boosts QML performance, study shows

Day 07 of Learning Quantum Computing Today’s focus: - Schrödinger Equation😺 - Measurement in Quantum Mechanics - Postulates of QM 🙀 Schrödinger Equation The time-dependent Schrödinger equation describes how a quantum state evolves over time: iħ ∂/∂t |ψ(t)> = H |ψ(t)> |ψ(t)> → the state vector of the system H → the Hamiltonian (energy operator) This guarantees unitary evolution, meaning probability is conserved. 😿 Measurement😸 When measuring a quantum system, the state collapses into one of the eigenstates of the observable A: P(ai) = |<ai | ψ>|² P(ai) → probability of outcome ai After measurement → the system collapses into |ai> with that probability. 🐱Postulates of Quantum Mechanics 1. State Space: Every system is described by a state vector in Hilbert space. 2. Evolution: States evolve according to the Schrödinger equation. 3. Measurement: Outcomes are eigenvalues of the operator; probabilities follow Born’s rule. 4. Composition: Composite systems are described using tensor products (key for qubits). 😼Why this matters for Quantum Computing? The Schrödinger equation governs qubit dynamics. Measurement links math to real-world outcomes on quantum hardware. Postulates form the foundation of quantum algorithms. 😻 Part of my structured learning journey with QuCode. #QuantumComputing #Physics #LearningJourney #QuCode

🌌 Day 5 – The Grammar of Quantum: Tensor Products, Inner/Outer Products & Unitary Operators 🌌 Today’s QuCode 21 Days Challenge took me into the language of quantum computing — and the hidden grammar that governs it. Today's Key Takeaways 🔗 Tensor Products – In classical systems, adding particles means adding states. In quantum, adding qubits multiplies the state space. That’s the magic of the tensor product — weaving simple states into vast, complex fabrics where entanglement naturally emerges. ➕ Inner & Outer Products – The inner product whispers about angles and overlaps, telling us the probability of one state collapsing into another. Flip it around, and the outer product becomes a projector — a way of turning possibilities into outcomes, measurement into meaning. 🔄 Unitary Operators – The guardians of quantum mechanics. They rotate, twist, and evolve states, but never stretch or shrink them. They preserve probabilities, ensuring that while quantum systems transform, they never lose their essence. What struck me most is how these aren’t abstract concepts but the survival rules of quantum mechanics. Without tensor products, we wouldn’t have entanglement. Without inner/outer products, we couldn’t measure. Without unitarity, the entire framework of quantum computing would collapse. Linear algebra isn’t just supporting quantum computing — it defines its reality. It feels like discovering that the alphabet of our universe is not 0 or 1, but the reversible, elegant symphony between them. ✨ In quantum computing, transformation is not destruction — it is preservation. Excited for Day 6: stepping into Dirac Notation & Hilbert Spaces — the notational superpower of quantum mechanics! 🚀 #Day5 #QuCodeChallenge #QuantumComputing #TensorProduct #Unitary #LinearAlgebra #LearningJourney #FutureOfTech

🚀 Day 05 of 21 – Quantum Computing Journey 🚀 Today was all about diving into the mathematics behind quantum mechanics—the real language of quantum computing:QuCode 🔹 Tensor Products – The magic that lets us combine multiple qubits and build larger, more powerful quantum states. 🔹 Inner & Outer Products – Tools to measure relationships between quantum states and construct operators that drive transformations.QuCode 🔹 Unitary Matrices – The foundation of quantum gates, ensuring that quantum operations are reversible and probabilities stay intact. 💡 Reflection: Learning these concepts felt like unlocking the grammar of a new language. Just as grammar gives structure to words, these mathematical tools give structure to quantum computation. Every day, the puzzle pieces are coming together, and the picture of how quantum computers actually “think” is getting sharper. 🌌 #QuantumComputing #QuCode #QuantumMathematics #21DayChallenge #LearningJourney #Innovation

Physicists have developed a quantum-inspired representation of pi by combining ideas from particle scattering and the Euler beta function into a convergent series, enabling accurate pi approximations with far fewer terms and reduced computational complexity, which supports advanced nanoscopic particle work and showcases the evolving, collaborative nature of mathematical theory. https://lnkd.in/gvqS2dHT

🚀 Day 2 of the Quantum Computing Challenge – Cohort 3 (QuCode) Today’s focus was on the mathematical foundations of Probability & Statistics — the invisible framework that supports quantum mechanics and quantum algorithms. 🔑 Key Learnings: Probability theory goes beyond coin tosses — it provides the language to describe uncertainty in quantum systems. Probability distributions help us understand the “shape” of uncertainty, which is critical in predicting quantum outcomes. Bayes’ Theorem highlights how new information reshapes our beliefs — an elegant principle also used in quantum decision-making models. Statistics allows us to interpret experimental quantum data and make sense of inherently probabilistic results. ✨ The takeaway: In quantum computing, randomness isn’t a bug — it’s a feature. Embracing probabilities helps us unlock the true power of quantum algorithms. #QuantumComputing #Probability #Statistics #BayesTheorem #QuCode #21DaysChallenge

Kothar Computing—hardly a household name and yet creating ripples in the arcane corners of Quantum AI. Just now, they've tipped the pot with their latest brainchild–FORGE, tailored to gluttonously devour quantum many-body quandaries. The aim? Replace arduous coding marathons with swift problem-solving sessions—a quantum physicist's gift from the gods, you might say [1][4][6]. FORGE—a hub for collaboration, interactive simulation, and publication—bits into the meat of condensed matter physics, chemistry, and material sciences. Its backbone? Kothar’s own Quantum Symbolic Algebraic Framework. Fancy name or not, it’s tearing down the walls of classical computing limitations with its unwieldy capability to reinterpret, compress, and accelerate computations [1][6]. But the platform isn't just flexing its muscles for tomorrow's quantum computing era—it's got an eye on the academics of today. Their promise is bold: transforming green undergrads into seasoned computational physicists in no time flat [1]. The gates are yet to be flung full wide, but Kothar is sneaking in a select band of academic users for now, eager to lift the veil soon [1][4][6]. Uniting a high-performance computational workshop with an unerringly accessible layout, FORGE is looking to be the quantum Pandora’s box we didn't know we needed [1][6]. Speaking of need—if you've ever wondered how all this quantum hocus-pocus fits into the trading world, do yourself a favour and check out [Quantumai.co](https://dub.sh/qsgr0so) for a peek into how the markets really tick.

--- 🚀 **Geometrical Perspective on Quantum States and Quantum Computation** 📄 A groundbreaking reimagination of quantum computation is here! 🌌 This article introduces a **geometric framework** that fuses the power of differential geometry, linear algebra, and noncommutative geometry to interpret quantum mechanics like never before. Here's the big idea: Quantum states are redefined as **noncommutative connections**, and quantum gates become **gauge transformations**, giving rise to an innovative computational paradigm called **gauge quantum computation**. 🌀 This model encodes information in gauge states and leverages gauge transformations for computational operations, offering fresh solutions to some of quantum computation's key challenges—like handling quantum decoherence. Not only does it simplify computational operations, but it also resonates with efforts in topological quantum computing, opening up exciting new possibilities. 💡 With practical examples like qubits and the Deutsch-Jozsa algorithm, this approach is a promising leap forward in how we design and interpret quantum systems. The future of quantum computing might just look a little more geometric. 🔮 #QuantumComputing #Innovation #AI #Research #NoncommutativeGeometry #MachineLearning #TechUpdates #arXiv ---

🌟 Day 21 – Future of Quantum Computing & Real-world Applications The final day of Qucode Cohort 3 focused on how quantum will transform industries and research in the years ahead. 🔹 Topics Covered: Finance – Portfolio optimization, risk modeling, and faster simulations. Chemistry & Materials – Molecular simulations and drug discovery beyond classical reach. AI & Machine Learning – Quantum-enhanced models and hybrid AI systems. Optimization & Logistics – Supply chain, routing, and large-scale scheduling. The Road Ahead – From today’s NISQ devices to fully fault-tolerant, scalable quantum computers. 📺 Resources: Future Applications (Qiskit) Quantum in Finance (Quantum Sense) 💡 Key Insight: Quantum computing is no longer just academic — it’s steadily becoming a transformative tool for real-world problems. ✨ Hands-On Highlights during the journey: Day 8: Built quantum circuits (X, H, Z, CNOT, Bell state) using Qiskit — a powerful first step in applying theory. Day 15: Implemented quantum algorithms (Deutsch-Jozsa, Bernstein-Vazirani, Grover’s, Shor’s) — seeing abstract concepts come alive in code was incredibly rewarding. 🙏 Grateful to the mentors, peers, and experts for shaping this journey. From linear algebra basics → quantum circuits → algorithms → future applications, these 21 days were both challenging and inspiring. Excited to continue building in the quantum space! #QuantumComputing #QuantumMachineLearning #QuantumAlgorithms #QucodeCohort3 #FutureTech #LearningJourney

> Sharing Resource < Nice paper: "Generative quantum advantage for classical and quantum problems" by Hsin-Yuan Huang, Michael Broughton, Norhan Eassa, Hartmut Neven, Ryan Babbush, Jarrod R. McClean Abstract: Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically intractable distributions, their complexity has thwarted all efforts toward efficient learning. This challenge has hindered demonstrations of generative quantum advantage: the ability of quantum computers to learn and generate desired outputs substantially better than classical computers. We resolve this challenge by introducing families of generative quantum models that are hard to simulate classically, are efficiently trainable, exhibit no barren plateaus or proliferating local minima, and can learn to generate distributions beyond the reach of classical computers. Using a 68-qubit superconducting quantum processor, we demonstrate these capabilities in two scenarios: learning classically intractable probability distributions and learning quantum circuits for accelerated physical simulation. Our results establish that both learning and sampling can be performed efficiently in the beyond-classical regime, opening new possibilities for quantum-enhanced generative models with provable advantage. Link: https://lnkd.in/eSYrY5va #quantummachinelearning #research #paper

Researchers Resolve Identifiability of Classical Stochastic Processes, Enabling Model Comparison and Efficiency Gains Researchers establish a method for determining whether two different computational models produce the same random behaviour, revealing fundamental limits on the complexity needed to accurately represent any natural process #quantum #quantumcomputing #technology https://lnkd.in/dBA76JUQ