Quantum Computing Topics: Optimality Conditions, SDP Bounds

My view about Google’s "Quantum Echoes" Traditional physics treats time as a fixed 4D block (Eternalism), while quantum experiments like Google’s "Quantum Echoes" explore reversible interference within that "static block." In Generator–Filter Theory (GFT) [1], I proposed a new time block [2], a "dynamic time block": a co-determining structure where forward (Generator) and backward (Filter) processes continuously enforce consistency. Why I claim it's new? Because it doesn't have "backward signal." The symmetric/mirror/balance zone they observed corresponds to the G ≈ F balance (that I was shared before [3]) — the dynamic heart of this new time geometry. [1] https://lnkd.in/dkyDf9Bw [2] https://lnkd.in/d27KS7iw [3] https://lnkd.in/dFextMRp https://lnkd.in/dR8ETa9p

Nice. But OTOCs are nothing new. They are usually called (classical or quantum) multipoint "correlation functions" or "Green's functions", depending on details of definition, and don't need a new moniker to be useful.

Google Quantum AI’s new Q-Echoes algorithm running on the 105-qubit Willow chip marks the world’s first "verifiable" quantum advantage on hardware — running 13,000× faster than the best classical supercomputers, proving quantum computers can now deliver repeatable, beyond-classical results with real-world applications. Quite exciting news seems to pop up towards the end of 2025, the International Year of Quantum Science and Technology.

🤨 "An exact description of such a quantum mechanical system requires storing and processing 265 complex numbers in memory, which is beyond the capacity of supercomputers."

Quantum meets chaos theory — and why it actually matters for quantum computing. A new experiment from Google Quantum AI turns certain out-of-time-order correlators (OTOCs) into literal interferometers using nested time reversals (echoes). The key observation: OTOC(2) reveals constructive interference between Pauli strings, and those interference patterns remain extremely sensitive to tiny, microscopic changes — i.e., the quantum form of mathematical chaos (extreme dependence on starting conditions) made operational and measurable. Why it matters: • OTOC echoes let us probe deep many-body correlations that ordinary measurements miss. • The observed constructive interference increases classical simulation difficulty — a positive sign for quantum-hard tasks. • The approach can also aid Hamiltonian learning by selectively refocusing the dynamics you care about. Takeaway: Chaos theory is a practical tool in the quantum toolbox. Echo-OTOCs let us find structured, hard-to-simulate correlations hiding inside apparent scrambling — and that targeted sensitivity is the tiny sweet spot where chaos becomes useful for quantum computing.

I'm pleased to announce that our OTOC 2.0 paper has been published in Nature! 🎉 At the same time, I'm also very excited to announce the open-source release of our Tensor Network Contraction Optimizer (TNCO) software, which was used to compute the FLOP estimates for the circuits in the Nature paper: TNCO homepage: https://lnkd.in/g8HNCAPW

Today we announce a significant step forward in quantum computing with our latest Nature publication, "A verifiable quantum advantage." We introduce a new quantum algorithm, “Quantum Echoes”, which measures out-of-time-order correlators (OTOCs), a new family of observables that describe how quantum dynamics become chaotic. This work represents the first quantum computing experiment measuring a quantum observable that is both verifiable and beyond the simulation capacity of known classical algorithms. Check our the Nature publication: https://lnkd.in/e5EZS4i2 Read the Google Research blog post: goo.gle/3LlXeFy

🌌✨ Quantum Advantage as Human Advantage: From OTOCs to Symbiotic AI In the global race for quantum technologies, milestones like the recent achievement by Google Quantum AI and collaborators, published in Nature remind us that we are entering a decisive decade. The experimental observation of constructive interference at the edge of quantum ergodicity through higher-order OTOCs (Out-of-Time-Ordered Correlators) is not just a technical result — it is a window into a new paradigm of knowledge and capability. For the first time, researchers have demonstrated that quantum interference phenomena can remain sensitive at long timescales, revealing correlations inaccessible to classical computation. This is a verifiable quantum advantage that moves beyond the limits of simulation, opening new horizons for Hamiltonian learning, error correction, and the understanding of chaotic quantum dynamics. At AstroLifeUniverse – Quantum Symbiotic AI Platform, we interpret this as a direct resonance with our own path: integrating quantum–neural architectures, sub-atomic error correction models, and symbiotic AI systems designed to contextualize and apply these principles at a societal scale. Quantum interference is no longer confined to physics labs. It represents the possibility to stabilize computations, extract hidden patterns, and apply them to domains where sovereignty and resilience matter most: 🔹 Healthcare – modeling biological complexity, advancing personalized medicine, and anticipating systemic risks. 🔹 Energy – optimizing quantum materials, renewable grids, and predictive maintenance at unprecedented precision. 🔹 Defense and Security – anticipating hybrid threats, protecting critical infrastructures, and reinforcing democratic resilience. 🔹 Education and Industry – creating a new wave of applications where AI and quantum systems merge as a human partner in innovation. This is why we insist: quantum advantage must become human advantage. It is not enough to prove that a quantum processor can outperform classical machines; the true measure is how we translate that disruptive capability into ethical, sovereign, and beneficial infrastructures for all. Europe, and Spain in particular, have a unique opportunity to lead this path, aligning strategic autonomy with global collaboration. By recognizing sovereign AI and quantum infrastructures as part of our digital backbone, we can ensure that the benefits of quantum progress are not only measurable in algorithms, but in shared prosperity, resilience, and expanded human potential. Congratulations to the Google Research - and the Quantum AI team and all collaborators for this landmark contribution. The echoes of this discovery — these “Quantum Echoes” — will resonate far beyond the lab, into the fabric of society itself. 🌍⚛️ #QuantumAdvantage #QuantumAI #GoogleResearch #Nature #AstroLifeUniverse #DigitalSovereignty #AI #SymbioticAI

Want to see how quantum computing is reshaping fraud detection and logistics? Unisys' Salvatore Sinno presented 2 of the 19 government-funded quantum projects at the UK National Quantum Computing Centre. Explore his insights on quantum readiness: https://lnkd.in/eVxyxNQ8 #quantumcomputing #frauddetection #logistics

How much power does a 20-qubit quantum computer actually use? Surprisingly little. How sensitive is it to noise? So sensitive that even Finnish death metal can be a problem. The push to integrate quantum computing and high-performance computing (HPC) is rapidly moving from theory to practice. A recent case study from IQM Quantum Computers and the Leibniz Supercomputing Centre(LRZ) offers a clear look at what it really takes to install a 20-qubit superconducting system inside a top-tier supercomputing facility. In my latest deep dive, I unpack this study and explore the most common questions and insights that arise when quantum meets HPC. Don’t miss it. It goes live today at 5 PM CET. Sign up via my website. Image Credits: LRZ