Quantum Speedup Concepts

We are pursuing quantum computing because there’s evidence that quantum can solve certain problems exponentially faster than any classical computer. I’m excited to share a new algorithm from our team with the potential for an exponential speedup in a real-world use case: simulating electric circuits. Circuits built from resistors, inductors, and capacitors — RLC circuits — show up across engineering, from power grids to analog filters to integrated circuit design. Predicting how voltages and currents evolve in these systems is routine. But as circuits grow large and complex, those simulations can become increasingly expensive on classical hardware. What makes RLC circuits so challenging to simulate is that they aren’t described by ordinary differential equations (ODEs), but by differential-algebraic equations (DAEs): systems that combine equations describing time evolution with constraints that must be satisfied at every instant. In the case of RLC circuits, we must solve Kirchhoff’s laws of charge and voltage conservation at every junction, but standard ODE solvers struggle to handle this mixed structure. A new paper authored by Arkopal Dutt, Anirban Chowdhury, Kristan Temme, and Hari Krovi, presents the first quantum algorithm tailored to DAEs of this kind. The approach separates the circuit’s state into two parts: one that evolves dynamically over time, and another that is fixed by the constraints. Each part is then handled with the appropriate technique. The result is an algorithm that prepares a quantum state encoding the circuit’s full time evolution, with a runtime that scales only polylogarithmically in the number of nodes — an exponential improvement over the polynomial worst-case scaling of classical methods. This speedup applies to well-conditioned networks where the circuit can be queried in superposition, meaning its structure is accessed as a function that returns entries on demand, rather than being read out element by element. From the quantum computer’s output state (the state encoding the full solution), physically meaningful quantities, like the energy stored in a set of capacitors or dissipated across a set of resistors, can be extracted directly. Interestingly, the authors also show that this energy-estimation task is as powerful as quantum computation itself: a quantum computer can solve it efficiently, and any problem that admits an efficient quantum solution can be reduced to an instance of it. In complexity-theoretic terms, this implies that, under standard assumptions, no classical algorithm can match a quantum computer on this task. Classical circuit simulation has been a workhorse of electronic design for decades. Demonstrating a provable quantum advantage on a problem this practical is an exciting step, and it lines up closely with IBM Quantum’s broader goal of identifying where quantum computing can deliver real value in engineering and industrial settings.   Full paper: https://lnkd.in/ekTFap64

Entangled Light Delivers a Verified Quantum Advantage in Learning Introduction Quantum advantage has crossed a decisive threshold, not through a quantum computer chip, but via entangled beams of light. A new study demonstrates that quantum resources can reduce a demanding learning task from an estimated 20 million years to just 15 minutes, with a mathematically certified guarantee that no classical method can match the performance under the same conditions. The Core Breakthrough Researchers used entangled light to learn the noise profile of a complex optical process with dramatically fewer measurements. The task focuses on learning, meaning reconstructing the statistical structure of noise to a fixed accuracy, rather than running a general computation. The experiment establishes a genuine quantum advantage, defined as completing a well-specified task faster or with fewer samples than any classical strategy governed by the same rules. How the Quantum Advantage Works The team generated entangled light at telecom wavelengths using an optical parametric oscillator that produces two-mode squeezed states. One beam probed a noisy optical channel while its entangled partner served as a quantum reference memory. A joint continuous-variable Bell measurement extracted correlations inaccessible to classical or unentangled probes. This approach targets high-frequency features of the noise’s characteristic function, the regime where classical methods become exponentially inefficient. Why Classical Methods Fail A 2024 theoretical proof showed that any classical strategy without quantum memory requires exponentially many samples to learn these noise processes. Even adaptive classical measurements cannot overcome this limit. The entangled protocol breaks the barrier by accessing correlations that single-beam measurements cannot reveal. At realistic data rates, the classical equivalent would take over 20 million years to match what the quantum system achieved in minutes. Certification and Practical Relevance The researchers designed a hypothesis-testing framework that formally certifies the quantum speedup, ruling out classical shortcuts. The experiment tolerates ordinary optical loss and noise, demonstrating robustness rather than idealized conditions. Potential applications include precision sensing, optical communications, quantum networks, spectroscopy, and gravitational-wave detection. Why This Matters This result marks a shift from speculative quantum advantage to a measured, certified, and practically relevant one. It shows that quantum technologies can already outperform classical systems by vast margins for specific learning tasks, using realistic hardware. Rather than waiting for large-scale quantum computers, quantum advantage is emerging today in focused domains where information, not brute-force computation, is the bottleneck If this topic resonates, I invite you to connect and continue the conversation. Keith King https://lnkd.in/gHPvUttw

Excited to announce a new #QuantumComputing result from JPMorganChase's Global Technology Applied Research, titled “Fast Convex Optimization with Quantum Gradient Descent,” which has just appeared on arXiv! Convex #optimization is a fundamental subroutine in #MachineLearning, engineering, and #DataScience, with many applications in financial engineering. We develop new #QuantumAlgorithms in the “derivative-free” setting where the algorithm only uses the function value and not its gradient. We show that #quantum algorithms without gradient access can match the convergence of classical gradient-descent methods, which do assume gradient access! In the derivative-free setting, this translates to an exponential speedup in terms of the dimension.   Our results also have applications outside the black-box setting. By leveraging a connection between semi-definite programming and eigenvalue optimization, we develop algorithms that exhibit the best known quantum or classical runtimes for semi-definite programming, linear programming, and zero-sum games, which are the three most well-studied classes of structured convex optimization problems. These classes model many practical problems of interest, including portfolio optimization and least-squares regression problems. Coauthors: Brandon Augustino, Dylan Herman, Enrico Fontana, Junhyung Lyle Kim, Jacob Watkins, Shouvanik Chakrabarti, and Marco Pistoia. Link to the article: https://lnkd.in/eMtqXM-r

The Schrödinger Equation Gets Practical: Quantum Algorithm Speeds Up Real-World Simulations Quantum computing has taken a major leap forward with a new algorithm designed to simulate coupled harmonic oscillators, systems that model everything from molecular vibrations to bridges and neural networks. By reformulating the dynamics of these oscillators into the Schrödinger equation and applying Hamiltonian simulation methods, researchers have shown that complex physical systems can be simulated exponentially faster on a quantum computer than with traditional algorithms. This breakthrough demonstrates not only a practical use of the Schrödinger equation but also the deep connection between quantum dynamics and classical mechanics. The study introduces two powerful quantum algorithms that reduce the required resources to only about log(N) qubits for N oscillators, compared to the massive computational demands of classical methods. This exponential speedup could transform fields such as engineering, chemistry, neuroscience, and material science, where coupled oscillators serve as the backbone of real-world modeling. By bridging theory and application, this research underscores how quantum computing is redefining problem-solving in physics and beyond. With proven exponential advantages and the ability to simulate systems once thought computationally impossible, this quantum algorithm marks a milestone in quantum simulation, Hamiltonian dynamics, and real-world physics applications. The findings point toward a future where quantum computers can accelerate scientific discovery, optimize engineering designs, and even open new frontiers in AI and computational neuroscience. #QuantumComputing #SchrodingerEquation #HamiltonianSimulation #QuantumAlgorithm #CoupledOscillators #QuantumPhysics #ComputationalScience #Neuroscience #Chemistry #Engineering

China's Zuchongzhi-3 quantum computer and Google's Willow processor represent two contrasting approaches in the race for quantum supremacy. Both 105-qubit superconducting systems push computational boundaries but prioritize different technical milestones. Zuchongzhi-3, developed by Chinese researchers, demonstrates remarkable raw computational power. In a demanding random circuit sampling task, it processed one million samples using 83 qubits over 32 cycles in just a few hundred seconds—a feat that would take the world’s fastest classical supercomputer billions of years to replicate. This achievement highlights China’s rapid progress in scaling up quantum hardware and achieving unprecedented quantum speedup. In contrast, Google’s Willow chip focuses on improving reliability through advanced quantum error correction. Willow was the first to show that logical, error-corrected qubits can outperform physical qubits in fidelity, reaching a logical qubit error rate below 0.2% per cycle. While Willow’s coherence and gate fidelities are marginally higher, its main contribution is laying the groundwork for scalable, fault-tolerant quantum computing—an essential step for practical real-world applications. https://lnkd.in/dXJwYnxt

⚛️ Hybrid Sequential Quantum Computing 📑 We introduce hybrid sequential quantum computing (HSQC), a paradigm for combinatorial optimization that systematically integrates classical and quantum methods within a structured, stagewise workflow. HSQC may involve an arbitrary sequence of classical and quantum processes, as long as the global result outperforms the standalone components. Our testbed begins with classical optimizers to explore the solution landscape, followed by quantum optimization to refine candidatesolutions, and concludes with classical solvers to recover nearby or exact-optimal states. We demonstrate two instantiations: (i) a pipeline combining simulated annealing (SA), bias-field digitized counterdiabatic quantum optimization (BF-DCQO), and memetic tabu search (MTS); and (ii) a variant combining SA, BF-DCQO, and a second round of SA. This workflow design is motivated by the complementary strengths of each component. Classical heuristics efficiently find low-energy configurations, but often get trapped in local minima. BF-DCQO exploits quantum resources to tunnel through these barriers and improve solution quality. Due to decoherence and approximations, BF-DCQO may not always yield optimal results. Thus, the best quantum-enhanced state is used to continue with a final classical refinement stage. Applied to challenging higher-order unconstrained binary optimization (HUBO) problems on a 156-qubit heavy-hexagonal superconducting quantum processor, we show that HSQC consistently recovers ground-state solutions in just a few seconds. Compared to standalone classical solvers, HSQC achieves a speedup of up to 700× over SA and up to 9× over MTS in estimated runtimes. These results demonstrate that HSQC provides a flexible and scalable framework capable of delivering up to two orders of magnitude improvement at runtime quantum-advantage level on advanced commercial quantum processors. ℹ️ Chandarana et al - 2025

⚛️ Quantum Walk Algorithms: The Foundation of Next-Generation Quantum Search & AI While Shor's Algorithm revolutionized factorization and Grover's Algorithm accelerated search, another powerful paradigm is emerging at the heart of quantum computing: Quantum Walk Algorithms. Quantum Walks are the quantum analog of classical random walks and form a fundamental framework for designing quantum algorithms with provable computational advantages. 🔬 What is a Quantum Walk? A Quantum Walk (QW) describes the evolution of a quantum particle over a graph or network structure according to the laws of quantum mechanics. Unlike a classical random walk, where a walker occupies a single position at any given time, a quantum walker exists in a superposition of multiple states simultaneously. Key quantum phenomena involved: ✅ Superposition – simultaneous exploration of multiple paths ✅ Quantum Interference – constructive and destructive interference amplifies optimal solutions ✅ Entanglement – correlations between quantum states ✅ Unitary Evolution – information-preserving quantum dynamics These properties enable quantum walks to spread across a graph quadratically faster than classical random walks. 🧠 Mathematical Foundation The evolution of a quantum walk is governed by a unitary operator: where: � = Quantum state vector � = Unitary evolution operator For continuous-time quantum walks: where: � = Hamiltonian of the graph � = Evolution time This connects Quantum Walks directly with Hamiltonian Simulation, one of the most important areas in quantum computing. ⚡ Types of Quantum Walks 1️⃣ Discrete-Time Quantum Walk (DTQW) Components: 🔹 Coin Operator 🔹 Shift Operator 🔹 Quantum Interference Applications: Search algorithms Graph traversal Quantum Machine Learning 2️⃣ Continuous-Time Quantum Walk (CTQW) Features: 🔹 No quantum coin required 🔹 Evolution governed directly by the graph Hamiltonian 🔹 Natural framework for quantum simulation Applications: Network analysis Molecular simulation Optimization 🚀 Why Quantum Walks Matter Quantum Walks provide speedups for numerous computational tasks. Graph Search Searching nodes in large graphs exponentially more efficiently than many classical approaches. Element Distinctness Determining whether duplicate elements exist in large datasets. Spatial Search Finding marked locations within large network structures. Optimization Improving combinatorial optimization and routing problems. 🤖 Quantum Walks in AI & Machine Learning Quantum Walks are becoming increasingly important in Quantum Machine Learning (QML). Applications include: 🔹 Quantum Graph Neural Networks (QGNN) 🔹 Quantum Reinforcement Learning (QRL) 🔹 Quantum Recommendation Systems 🔹 Quantum Clustering 🔹 Quantum Pattern Recognition 🔹 Quantum Feature Extraction By leveraging interference effects, Quantum Walks can identify hidden structures within high-dimensional data more efficiently than classical techniques.

Fresh off the press in APL Quantum: Reimagining Magnetic Material Design with Quantum-Inspired Logic. 🔬 In my previous posts, I talked about the "#Quantum On-Ramp" and our new #MATLAB integration. Today, I want to share the rigorous scientific validation behind it. Our latest research, "Design of magnetic lattices with a quantum-inspired evolutionary optimization algorithm," has just been published in APL Quantum journal. This work was a fantastic collaboration between Prof. Pınar Acar and her talented students (Zekeriya Ender Eger and Waris Khan) at Virginia Tech, alongside the dedicated team at BQP, led by Rut Lineswala, with Dr. Eswara Sai Kumar Kandula, Udbhav Sharma, & Priyo. 🤝 The Challenge: Designing magnetic #materials at the lattice level is a massive computational bottleneck. Using the Ising model to find the #magnetic equilibrium under uncertainty (like fluctuating temperature and external fields) results in a high-dimensional, non-convex optimization landscape with countless local minima. The Breakthrough: We utilized the Quantum-Inspired Evolutionary Optimization (QIEO) algorithm, one of our core capabilities in QuantumNOW™ solver, to tackle this. Key Findings: 1. Large-Scale Success: While traditional methods like Genetic Algorithms (GA) and Simulated Annealing (SA) struggle as dimensionality grows, our QIEO solver successfully optimized 50x50 lattices systems where conventional classical methods often become computationally impractical. We reported 20X+ speedup vs SA in that case. 2. Handling Uncertainty: The algorithm remained robust even when accounting for stochastic variables in temperature and magnetic fields, proving that quantum logic can solve real-world "noise" problems today. 3. HPC Efficiency: This entire study was conducted on existing high-performance computing (#HPC) infrastructure, creating the foundation for hybrid QC + HPC environments. Why this matters for your R&D team? The exact algorithms validated in this paper are available right now in the #BQPhy Toolbox for MATLAB. Whether you are working on magnetic materials, satellite trajectories, or complex design optimization, you can leverage this "Quantum On-Ramp" today. You can read the full paper here:

🧬 Quantum Supremacy? Google’s New Quantum Algorithm Could Transform Molecular Simulation Google recently published a Nature paper describing a new quantum algorithm called Quantum Echoes — a technique purpose-built for quantum computers that may become the foundation for faster, more accurate molecular simulations. In simple terms, this algorithm lets researchers simulate how a small change in one part of a molecule (like a protein, RNA, or DNA segment) affects distant regions of the same molecule — something that’s computationally brutal on classical machines. The breakthrough is in scaling: - 🧮 Traditional simulations slow down exponentially as the number of atoms increases. - ⚛️ Quantum Echoes, running on Google’s new Willow quantum chip, scales linearly — achieving roughly a 13,000× speed-up compared to the world’s fastest classical supercomputer. What makes this especially exciting is that few quantum algorithms have ever shown verified speed-ups over classical methods — and most well-known examples (like Shor’s algorithm, which breaks encryption, or Grover’s algorithm, used for database searches) are primarily computer science milestones. Quantum Echoes is one of the first algorithms with direct scientific relevance — with potential applications in biology, chemistry, and drug discovery. It could help refine molecular structures by filling in gaps where experimental techniques struggle: - 🧱 X-ray crystallography gives high-resolution geometry but only in crystal form. - ❄️ Cryo-EM captures large complexes, but flexible regions often go blurry. - 🔬 NMR detects local interactions, but long-range couplings are weak and hard to measure. By simulating the missing connections between distant parts of a molecule, this algorithm could provide extra structural constraints in ambiguous regions, improving model accuracy and bridging the gap between experimental biology and computational modelling. The future of molecular simulation might just be quantum-powered. ⚛️ 🔗 Links to the paper and Google’s announcement are in the comments. #QuantumComputing #MolecularSimulation #Bioinformatics #StructuralBiology #ComputationalBiology #DrugDiscovery #QuantumBiology #NMR #CryoEM #GoogleQuantumAI #WillowChip #NaturePaper #ScienceInnovation #FutureOfBiotech #QuantumAdvantage