Physicists create new pi representation for nanoscale work

Physicists are now using principles from quantum mechanics to build a new model of the abstract concept of pi. Or, more accurately, they built a new model that happens to include a great new representation of pi. #quantum #mathematics https://lnkd.in/g3giMw_N

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

🔍 *Day 5 of QuCode’s 21-Day Quantum Computing Challenge: Cohort 3* Today’s deep dive: *Tensor Products, Inner & Outer Products, and Unitary Matrices* ⚛🧠 We’re getting into the mathematical foundations that power *quantum mechanics* and *quantum circuits*. 📌 *Key Takeaways:* 🔗 *Tensor Products* The building block of multi-qubit systems! Tensor products allow us to describe composite quantum states — when two qubits combine, their state space expands exponentially. From a simple |0⟩ ⊗ |1⟩ to full quantum entanglement, this concept is core to scalability in quantum computing. 🔄 *Inner vs. Outer Products* * *Inner Product* = a measure of similarity between quantum states (like ⟨ψ|φ⟩). * *Outer Product* = used to construct operators (like |ψ⟩⟨φ|).  These operations form the mathematical backbone of measurement, projection, and quantum gates. 🌀 *Unitary Matrices* All quantum gates must be unitary! Because quantum evolution is *reversible and preserves probability amplitudes*. Unitary matrices satisfy: U†U = I, ensuring no information is lost during quantum computation. 💡 It’s fascinating to see how linear algebra concepts we once saw as abstract now directly map to real-world quantum phenomena. 👩💻 The journey continues, and the math is getting beautifully intense. Let’s keep pushing the limits of what we understand and can build! \#QuantumComputing #TensorProduct #UnitaryMatrix #InnerProduct #OuterProduct #QuantumChallenge #QubitByQubit #LinearAlgebra #21DayChallenge #QuantumCohort #STEMLearning  

🌌 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

General Dynamics and the Next Era of Computing For decades, computing has advanced by scaling hardware and refining classical algorithms. Quantum computing promised a leap forward, but it has remained constrained by the same assumptions: probabilistic frameworks stacked on top of fragile approximations. General Dynamics changes this. By redefining physics in terms of flux, curvature, and spin, GD provides a foundation where computation itself is not limited by ad-hoc constants or probabilistic guesswork. Instead, information processing emerges as a direct consequence of geometry and coherence. What does this mean for computing? • Quantum algorithms become geometric: probability distributions collapse into predictable flux trajectories, opening the door to deterministic quantum logic. • Operating systems become physical: instead of patching abstractions onto silicon, we can design systems that flow with curvature-driven coherence at the hardware level. • AGI becomes attainable: because intelligence is not just software, it is coherence across scales. GD provides the framework where scale relativity is preserved, allowing machines to learn, adapt, and reason without breaking the laws of physics they run on. The age of approximations has carried us far. But the next leap—true AGI—requires a physics that unifies quantum mechanics with macroscopic logic. That is what General Dynamics delivers. This is not just new physics. It is the foundation of a new computing era. #GeneralDynamics #Computing #Quantum #AGI #Physics #Innovatio

Back in Theory of Computation, I learned that a Turing machine is essentially a finite state machine with memory. Each state determines whether you read, write, or move the tape left or right. 📼 Fast forward to 2025: with graph-based agentic systems, I see a similar paradigm. But instead of a tape, we now have states augmented as each node is visited. And instead of strict rules, state transitions are influenced by stochastic LLM outputs, more probabilistic than deterministic. 🤖 Of course, agentic systems are still Turing machines at their core. But it’s an interesting thought experiment: how the abstractions evolve, while the foundations remain the same. 🔧 ☕

GM-QAOA Avoids Barren Plateaus, Demonstrating Dynamical Lie Algebra Isomorphism to Or, Maximizing Conserved Quantities Researchers demonstrate that a specific quantum algorithm, utilising a particular mixing technique, possesses a mathematical structure linked to maximal conservation laws and, crucially, avoids a common problem hindering quantum computation known as barren plateaus for a wide range of optimisation challenges #quantum #quantumcomputing #technology https://lnkd.in/eZEcG8QP

Day 5: The Mathematical Machinery of Quantum States and Operations The #21DaysOfQuantum journey with QuCode continues by diving deeper into the essential mathematical tools that form the language of quantum mechanics. Today's focus was on the operators and products that describe how quantum systems evolve and interact. Today's Focus: Tensor Products, Inner/Outer Products, and Unitary Matrices. These are not abstract mathematical curiosities; they are the fundamental components for describing multi-qubit systems, quantum measurements, and quantum logic. - Tensor Products: This operation is how we describe the state of multiple qubits. While a single qubit lives in a 2D space, two qubits live in a 4D space, formed by the tensor product of their individual spaces. This is the mathematical foundation for quantum entanglement and the exponential growth of state space that gives quantum computing its potential power. - Inner & Outer Products: These operations are two sides of the same coin and are crucial for understanding quantum measurement and operators. The Inner Product (⟨φ|ψ⟩) measures the overlap between two states. Its magnitude squared gives the probability that a system in state |ψ⟩ will be measured in state |φ⟩. The Outer Product (|ψ⟩⟨φ|) is used to build operators, most notably projection operators, which are essential for describing the effect of measurement on a quantum state. - Unitary Matrices: These matrices represent reversible quantum gates (like the Pauli-X, Hadamard, or CNOT gate). The key property of a unitary matrix is that its inverse is equal to its conjugate transpose (U†U = I). This unitarity ensures that the evolution of a closed quantum system is always reversible and preserves the total probability—a fundamental postulate of quantum mechanics. Grasping these concepts is critical because they translate directly into the code we write. A quantum circuit is, at its core, a series of unitary matrices (gates) applied via tensor products to multi-qubit state vectors, with measurements defined by inner products. The journey from mathematical definition to quantum algorithm is becoming clearer. On to Day 6. #QuantumComputing #LinearAlgebra #Mathematics #QuantumMechanics #Qubits #TensorProduct #Unitary #STEM #LearnInPublic

How does quantum many-body physics affect quantum machine learning results? One might jump to entanglement and non-linearity. In fact, disorder drives QML performance and entanglement plays a necessary yet limited role. Check out Dr. Payal Solanki and Anh Pham's paper on Quantum Extreme Learning for simulated Rydberg Hamiltonians where they discover that Anderson disorder in a many-body system contributes to the best model outcome. At Deloitte Quantum we intersect fundamental physics with industrial applications to move #quantumcomputing forward. More to come 😉 Paper 🔗 https://lnkd.in/gvUs_RF4

Free-fermion Findability Advances Via Twin-Collapse Algorithm for Simplified Many-Body Hamiltonians Researchers have developed a new mathematical technique that simplifies complex physical models by systematically reducing their complexity while accurately preserving their essential energy characteristics, thereby expanding the range of solvable problems in areas like materials science and quantum computing #quantum #quantumcomputing #technology https://lnkd.in/eveTYH_C