Jesús Pérez Expolio’s Post

🌌 Quantum Fourier Transform (QFT) – The Quantum Frequency Lens 🔹 What is QFT? The Quantum Fourier Transform (QFT) is the quantum version of the Discrete Fourier Transform (DFT). It converts quantum states into a phase-encoded superposition, enabling detection of hidden periodicity exponentially faster than classical methods. QFT(|x⟩)=1/sqrt{N}∑k=0N−1 e^2πixk/N |k⟩ 🔹 Working Principle Input State → Start with |x⟩ in qubits. Hadamard Gates → Create superposition. Controlled Phase Rotations (Rk) → Encode phase information. Swap Gates → Correct qubit order. Output → Quantum frequency spectrum representation. 🔹 Circuit Decomposition (3 Qubits) Apply Hadamard → superposition. Controlled R2, R3 rotations → add phase shifts. Repeat for each qubit. Swap qubits → final frequency domain output. 🔹 Example (2 Qubits) Input: |10⟩ Apply H + R2 → encode periodicity. Apply Swap → final state is balanced superposition with encoded phase. 🔹 Applications ✅ Shor’s Algorithm – Efficient factorization. ✅ Quantum Phase Estimation – Physics, eigenvalue problems. ✅ Quantum Chemistry – Energy spectrum simulation. ✅ Quantum Machine Learning (QML) – Frequency-based feature mapping. ✨ New Concept: QFT as a Quantum Frequency Lens Think of QFT as a quantum microscope for hidden patterns. Classical Fourier = Music Equalizer 🎵 → analyzes sound frequencies. Quantum Fourier = Quantum Equalizer 🌌 → reveals hidden periodicities in quantum data. This makes QFT the core of the most powerful quantum algorithms. #QuantumFourierTransform #QFT #QuantumComputing #QML #QuantumAlgorithms #QuantumPhaseEstimation #ShorsAlgorithm #QuantumChemistry #EmergingTech #FutureOfTech #QuantumInnovation #QuantumLens

𝗗𝗶𝘀𝘁𝗿𝗶𝗯𝘂𝘁𝗲𝗱 𝗤𝘂𝗮𝗻𝘁𝘂𝗺 𝗖𝗼𝗺𝗽𝘂𝘁𝗶𝗻𝗴: 𝗠𝗼𝗿𝗲 𝗣𝗼𝘄𝗲𝗿 𝗧𝗵𝗿𝗼𝘂𝗴𝗵 𝗖𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗶𝗼𝗻  How can several smaller quantum computers be connected so that they work together as one powerful system? This idea is called Distributed Quantum Computing (DQC). It could make it possible to run much larger and more powerful algorithms than a single chip could handle on its own. In our new work, we studied how different architectures of variational quantum circuits (VQCs) behave in such a distributed setting, specifically in the context of a classification task from Quantum Machine Learning (QML) within DQC. Using simulations, we tested how circuits perform when multiple quantum processors are linked, and how much entanglement between them is actually required. The results show that circuits with a smart balance of local and global entanglement are more robust to noise than standard approaches. This suggests that well-designed circuit architectures could enable distributed quantum computing to achieve better results in the near future. Our paper "Evaluating Variational Quantum Circuit Architectures for Distributed Quantum Computing" has been accepted at IEEE QAI 2025 and is available as a preprint here:  👉 https://lnkd.in/db8bHuzN  The paper was authored by Leo Sünkel, Jonas Stein, Jonas Nüßlein, Tobias Rohe, and Claudia Linnhoff-Popien.  Supported by the Bavarian Ministry of Economic Affairs (6GQT project) and the German Federal Ministry of Research, Technology and Space (BMFTR).  #QuantumComputing #DistributedSystems #VariationalQuantumCircuits #Research #Innovation 

I have been doing a lot of research on quantum computers lately, and I would love to get my hand one. First I need to replace my hard drive that , but here’s a different way to think about quantum machines: not just as accelerators, but as collapse oracles. Instead of chasing speedups on existing algorithms, we’d use quantum processors to generate collapse signatures — entropy slopes, echo persistence, Binder-style crossings — that reveal how systems stabilize or fail. In our framework, the quantum device becomes an instrument, not just a solver. What I’d like to do: • Use prime-indexed provenance to tag every quantum layer, giving each run a clean, decomposable history. • Filter noisy shot streams by collapse invariants, turning hardware noise into an advantage rather than a limitation. • Record device outputs as symbolic glyphs that can be translated by our chemist, physicist, and mathematician modules into molecules, invariants, or proofs. • Treat universality, collapse stability, and glyph matching as new KPIs for the NISQ era. This isn’t vaporware — the symbolic framework is already in place. The moment funding is secured, this is exactly the kind of experiment we’ll be running on quantum hardware. Not to chase quantum speedups. But to let quantum devices teach us new laws of collapse and coherence. #QuantumComputing #SymbolicAI #CollapseGeometry #DeepTech #NISQ

Quantum Algorithms, from VQE to SQD, Estimate Ground State Energy by Sampling Determinants Researchers have established a precise mathematical formula to calculate the number of measurements needed for quantum algorithms to efficiently estimate ground state energies, paving the way for more practical quantum computation on near-term processors by overcoming limitations of existing methods. #quantum #quantumcomputing #technology https://lnkd.in/eWX6yvhk

Robust Self-testing of Quantum Steering Assemblages Achieves Explicit Lower Bounds Via Operator Inequalities Researchers have developed a new mathematical technique using operator inequalities to rigorously verify the reliability of quantum steering assemblages, surpassing previous methods and offering a pathway towards more dependable quantum technologies. #quantum #quantumcomputing #technology https://lnkd.in/e7sxWkJc

Quantum Optimization with Classical Chaos Enables Effective Parameterization for Hard Maximum Satisfiability Problems Researchers have developed a new method for optimising quantum algorithms, using principles from chaotic systems, that improves performance on complex problems and offers a pathway to more efficient quantum computation. #quantum #quantumcomputing #technology https://lnkd.in/exfayd_q

🚀 Quantum Computation & Quantum Information – Foundational Takeaways From Nielsen & Chuang’s classic text, here are some powerful insights that continue to shape the field of quantum computing 👇 🔑 Foundational Insights 1️⃣ Information is Physical – Landauer’s principle reminds us that information is tied to its medium: atoms, photons, or qubits. Unlike classical bits, qubits can exist in superpositions and cannot be cloned. 2️⃣ No-Cloning Theorem – Born in the 1980s while testing faster-than-light communication, this principle safeguarded relativity and became central to quantum information. 3️⃣ Strong Church–Turing Thesis Under Pressure – Quantum computers, with error correction, survive noise where analog failed, challenging the very limits of computation. ⚙️ Technical Highlights 4️⃣ Quantum Circuits & Gates – Universal quantum computing is possible with just {Hadamard, phase, CNOT, π/8} gates. 5️⃣ Quantum Algorithms – Deutsch–Jozsa, Shor, and Grover remain the three cornerstones demonstrating quantum advantage. 6️⃣ Error Correction – From simple 3-qubit codes to Shor’s code, the Threshold Theorem proves that scalable quantum computing is possible if error rates stay below a limit. 🔮 Deeper Theoretical Notes 7️⃣ Entropy in Quantum Information – Von Neumann entropy and strong subadditivity underpin proofs in quantum cryptography. 8️⃣ Cluster-State Computation – A paradigm shift: computation possible using only measurements on entangled resource states. 9️⃣ Quantum Capacity Surprises – Two zero-capacity channels can combine to transmit quantum info, impossible in classical theory. ✨ Quantum information science isn’t just about new algorithms; it’s about reshaping our understanding of information, computation, and physics itself. 👉 Which of these insights fascinates you most? Let’s discuss in the comments! #Learnamyte #QuantumComputing #QuantumInformation #Upskilling #FutureOfSkills #STEM #EdTech #Qubit #QuantumHardware #QuantumTech #DeepTech #Course #Classes

Experimental Verification Demonstrates Genuine Multipartite Entanglement Activation from Two Copies of Biseparable States Scientists demonstrate that complex quantum correlations, previously thought impossible to create from simple building blocks, can emerge when combining multiple copies of less complex quantum states, opening new avenues for advanced quantum technologies. #quantum #quantumcomputing #technology https://lnkd.in/e6r7BmUx

💡 Quantum Computing & the Role of Complex Numbers A common question: “Where do complex numbers (a + bi) fit into quantum computing?” 🔹 Each qubit’s state is defined by complex amplitudes (α, β). 🔹 Gates manipulate these amplitudes using unitary operations (complex matrices). 🔹 The imaginary part (i) doesn’t directly appear in measurement but drives phase & interference, which are the core of quantum speedup. 🔹 Finally, measurement collapses the state into classical outcomes, with probabilities given by |α|², |β|². ⚡ In short: Complex numbers are the hidden gears of quantum computation — invisible in the final answer, but essential for making quantum advantage possible. #QuantumComputing #QuantumInformation #ComplexNumbers #Qubits #Learning

We are delighted to share our new paper on Nature: Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation https://buff.ly/RM9S3zd In collaboration with Harvard and Yale, QuEra introduces Algorithmic Fault Tolerance (AFT) — a breakthrough framework that cuts error-correction overhead and accelerates the timeline for practical, large-scale quantum computing. Key Highlights • Reduced runtime overhead: AFT slashes the cost of error correction by a factor of d, often ~30×, with neutral-atom architectures enabling 10–100× faster execution of logical algorithms. • New methodology: By combining transversal operations with correlated decoding, AFT maintains exponential error suppression while dramatically speeding up computations. • Practical impact: A companion study (https://buff.ly/x8t8Xs0 ) applies AFT to Shor’s algorithm, illustrating how these advances translate into real-world efficiency gains. At QuEra, we believe this represents a credible, scalable pathway to practical quantum advantage — reinforcing the structural strengths of neutral-atom platforms: reconfigurability, high connectivity, and room-temperature operation. 🔗 Explore the companion resource study here: Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays #QuantumComputing #NeutralAtoms #QuantumErrorCorrection #FaultTolerance #HPC #QuEra #Innovation