Quantum Physics Concepts

What if three people invented the same theory in completely different languages? In the late 1940s, quantum electrodynamics (QED) our most precise theory of light and matter was taking shape. Three brilliant minds had built its foundations: 🔹 Schwinger with his dense, operator-heavy machinery 🔹 Tomonaga from Japan, with a covariant evolution of states 🔹 Feynman the iconoclast — who introduced a playful visual grammar: wiggly lines, loops, vertices… diagrams! But were they really saying the same thing? Or were these just disconnected ways of calculating? That’s where Freeman Dyson stepped in. In 1949, at just 25, he wrote a paper that didn’t just clarify things — it unified them. He showed that all these distinct approaches - Feynman's intuitive path integrals, Schwinger's rigorous formalism, and Tomonaga's covariant method - were mathematically and physically equivalent. He laid out a term-by-term comparison of how each theory describes quantum processes. He introduced the Dyson series - a structured way to track the time evolution of quantum systems. And perhaps most importantly, he proved that Feynman diagrams weren’t just clever sketches — they emerged logically from the same formal principles as everyone else’s work. By doing so, Dyson gave Feynman’s tools the theoretical license they needed — and helped make them the language of modern particle physics. The impact? Today, every quantum field theory textbook you’ll ever read is written in the dialect Dyson proved was universal. This wasn’t just reconciliation. It was synthesis. And it made QED not only a triumph of calculation, but a triumph of understanding. F. J. Dyson, “The Radiation Theories of Tomonaga, Schwinger, and Feynman,” Phys. Rev. 75, 486–502 (1949).

> Sharing Resource < Great one: "Quantum computation at the edge of chaos" by Tomohiro Hashizume, Zhengjun Wang, Frank Schlawin, Dieter Jaksch Abstract: A key challenge in classical machine learning is to mitigate overparameterization by selecting sparse solutions. We translate this concept to the quantum domain, introducing quantum sparsity as a principle based on minimizing quantum information shared across multiple parties. This allows us to address fundamental issues in quantum data processing and convergence issues such as the barren plateau problem in Variational Quantum Algorithm (VQA). We propose a practical implementation of this principle using the topological Entanglement Entropy (TEE) as a cost function regularizer. A non-negative TEE is associated with states with a sparse structure in a suitable basis, while a negative TEE signals untrainable chaos. The regularizer, therefore, guides the optimization along the critical edge of chaos that separates these regimes. We link the TEE to structural complexity by analyzing quantum states encoding functions of tunable smoothness, deriving a quantum Nyquist-Shannon sampling theorem that bounds the resource requirements and error propagation in VQA. Numerically, our TEE regularizer demonstrates significantly improved convergence and precision for complex data encoding and ground-state search tasks. This work establishes quantum sparsity as a design principle for robust and efficient VQAs. Link: https://lnkd.in/eS_gVZhY #quantummachinelearning #quantumcomputing #research #paper

On this day, Richard Feynman’s landmark paper “Space-Time Approach to Quantum Electrodynamics” was published. In this paper, Feynman relied on results he had initially guessed correctly, and only later proved rigorously using the path integral method. For instance, on page 772, he derives the photon propagator by arguing that only the positive-frequency (energy) part of the photon field is physically meaningful, and that photons can move both forward and backward in time. In this paper, Feynman also introduces renormalization--a technique for extracting finite results from infinities by tying them to experimentally measured parameter values. Feynman discusses the electron’s self-energy problem, how it leads to mass correction, and its role in renormalization. In this paper, Feynman drew on insights he had developed by first treating the electron nonrelativistically, a point he later emphasized in his Nobel lecture: “I just took my guesses from the forms that I had worked out using path integrals for nonrelativistic matter, but relativistic light. It was easy to develop rules of what to substitute to get the relativistic case.” He expressed a similar sentiment in a letter to T. A. Welton: “I am enclosing the reprints of my papers. I gather from your letter that you did not try to read them because if you had I assure you would find them very simple, at least if you don’t try to prove all the things I say are correct. You know how I work so most of it is just a good guess. All the mathematical proofs were later discoveries…" #Physics #quantum #discoveries #math #guess #theories

Richard Feynman was a renowned American physicist known for his groundbreaking contributions to quantum mechanics and his unique ability to explain complex ideas in simple terms. Born in 1918, he played a key role in the development of quantum electrodynamics (QED), a theory that describes how light and matter interact. His work in this field earned him the Nobel Prize in Physics in 1965, making him one of the most influential scientists of the 20th century. Feynman is especially famous for introducing Feynman diagrams, a visual tool that simplifies the understanding of particle interactions. These diagrams revolutionized how physicists perform calculations in quantum field theory by turning complex equations into intuitive graphical representations. He also developed the path integral formulation, a method that describes how particles take every possible path between two points, fundamentally changing how quantum systems are understood. Beyond his scientific achievements, Feynman was admired for his lively personality, curiosity, and passion for teaching. His lectures, especially those compiled in The Feynman Lectures on Physics, remain widely used today. He also contributed to the investigation of the Challenger space shuttle disaster, where he clearly demonstrated the cause of failure. His legacy continues to inspire students and scientists through his creativity, honesty, and love for discovery.

Richard Phillips Feynman Richard Feynman was a singular character: a physics genius, eccentric, cheerful and with a rather peculiar character. With his infinite wit, his diabolical intuition and his inexhaustible imagination, he revolutionized physics and laid the foundations of quantum field theory. Feynman's main work is influenced by another physics genius: Paul Dirac. A monstrous physicist whose hobby was writing physical equations in forms compatible with special relativity. Dirac's hero was Einstein and Einstein's inspiration was Maxwell. Feynman learned quantum mechanics from Dirac's book, found that there were too many unknowns and that new ideas were needed. Dirac did everything in his power (which was too much) to find Maxwell's quantum version of classical electrodynamics, but it was still an incomplete theory. This is where Feynman comes in. Deeply influenced by Dirac's work “The Lagrangian in Quantum Mechanics”, Feynman wrote a complete doctoral thesis that would reformulate quantum mechanics. His work entitled “Principles of least action in quantum mechanics” manages to quantize systems from their classical description. That is, with elements of classical mechanics, probability amplitudes between quantum states can be found. The idea behind this is very simple: consider two points A and B in space, and an electron moving from A to B at an initial time t1 and a final time tf. How many real paths exist between points A and B? In classical mechanics there is only one path (the one that satisfies Newton's second law). But what happens in the quantum world? Feynman showed that any path is probable and each one contributes to the probability of finding the electron at point B at time tf starting from point A at time ti. All paths contribute in equal magnitude, but the phase of their contribution is a classical function known as action. In this way, Feynman managed to find probability amplitudes (quantum world) from the classical dynamics of the system (action). It is worth mentioning that both Schrödinger's and Heisenberg's formulations are equivalent to Feynman's work. This would completely change physics and give rise to quantum field theory as we know it today.

⚛️ Minimally Universal Parity Quantum Computing 📜 In parity quantum computing, multi-qubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native gate set. One might then wonder: what is the smallest number of auxiliary qubits that still allows for universal parity computing? Here, we demonstrate that the answer is one, if the number of logical qubits is even, and two otherwise. ℹ️ Smith et al, 2025

Large-scale quantum optimization with fewer qubits Quantum computing has long promised breakthroughs in solving complex optimization tasks, but most approaches require more qubits than current hardware can realistically provide. A recent paper by Sciorilli and coauthors offers an alternative. The authors focus on the MaxCut problem, a classical challenge where you split a graph’s vertices into two sets to maximize the total weight of edges between them. Despite its straightforward formulation, MaxCut is NP-hard, implying no known efficient algorithm can solve all large instances optimally. Their proposed variational solver encodes a problem of size "m" into "n" significantly fewer qubits, using Pauli correlations to achieve polynomial (rather than exponential) space compression. The method combines shallow circuit layers with a final post-processing step, mitigating the risk of “barren plateaus” (where gradient-based training stalls). Numerical simulations show that for problems as large as m=7000, this qubit-efficient approach matches or surpasses advanced classical solvers, yet remains feasible for near-term quantum devices. The results are particularly striking: for a MaxCut instance with m=2000 vertices encoded into only 17 qubits, the solver achieves an approximation ratio above 0.941, surpassing a known hardness threshold. In larger simulations, the method rivals state-of-the-art classical algorithms such as Burer-Monteiro. These findings underscore the promise of qubit-efficient encoding to unlock bigger optimization challenges sooner than expected, potentially offering a tangible path to near-term quantum advantage in both research and industry. Paper: https://lnkd.in/dguKCcEp #QuantumComputing #QuantumOptimization #AIForScience #MachineLearning #Research #Innovation #Qubits #MaxCut #NatureCommunications #DataScience #QuantumAlgorithms #VariationalQuantumAlgorithms #TrappedIon #IndustrialApplications #AcademicResearch

More circuit depth doesn't necessarily mean more power. The same is true in organizations and agentic AI systems: more layers don't necessarily create more value. They can just create more places for the signal to get lost. In Lab 1 of the IBM Qiskit Global Summer School 2026, I built the exact same entangled state two different ways. One took 256 sequential steps. The other took 47. The primary difference is how much noise had a crept in. Here's the setup: I built a GHZ state (a maximally entangled state across many qubits) two different ways: 1. The naive way chains every qubit to the next in a straight line. This is like people, or even agents, working in sequence through layers. 2. A better way maps the actual hardware topology first, then grows the entanglement outward from the best-connected point using a breadth-first search which is like teams being organized around skills without hierarchy. A few things that translate directly to enterprise systems work: 🔹 Your first working version and your production version are rarely the same. The "abstract" circuit that's correct on paper needs to be transpiled, re-mapped, and constrained to the resources you actually have (in this case, IBM's 133-qubit Heron chip). That's not a quantum-only lesson. 🔹 Topology-aware design beats brute force, every time. Starting from a well-chosen center point and working outward is the same instinct behind good distributed systems and organizational design: know your landscape before you build on top of it. 🔹 Depth is a proxy for risk. In quantum circuits, depth roughly maps to accumulated error. In any complex system, the number of sequential dependent steps is a decent proxy for how much can go wrong before you get an answer. Minimizing unnecessary sequential steps is a discipline, not a one-time optimization. After two labs, I've realized that the difficult part of some quantum computing right now isn't the "quantum" part conceptually, it's the engineering discipline of designing for real, constrained systems. Add depth, management layers, headcount, or approval steps without checking whether it maps to how your systems actually work, and you don't get more value. You get more noise. Special thanks for James Weaver for making this lab! #QGSS2026 #QuantumComputing #Qiskit #IBMQuantum #EnterpriseTech #EmergingTech