How Quantum Simulations Overcome Classical Limitations

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

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

Google’s 69-Qubit Quantum Simulator Outperforms Supercomputers in Key Calculations Researchers from Google and the PSI Center for Scientific Computing have developed a 69-qubit quantum simulator that can outperform the fastest classical supercomputers in studying complex quantum systems. This breakthrough brings unprecedented accuracy in modeling quantum processes, unlocking new possibilities in materials science, magnetism, and thermodynamics. Key Features of Google’s Quantum Simulator • Combines Digital & Analog Quantum Computing: The simulator supports both universal quantum gates (digital mode) and high-fidelity analog evolution, providing superior performance in cross-entropy benchmarking experiments. • Beyond Classical Computational Limits: This hybrid approach enables calculations that classical supercomputers cannot efficiently simulate, especially in quantum material and energy research. • Specialized for Quantum Simulations: Unlike general-purpose quantum computers, this simulator is optimized for modeling quantum interactions, making it a powerful tool for scientific discovery. Digital vs. Analog Quantum Computing • Digital Quantum Computing: • Uses quantum gates to manipulate qubits, similar to logic gates in classical computing. • Best suited for algorithms, machine learning, and cryptography applications. • Analog Quantum Computing: • Models physical quantum systems directly, simulating real-world interactions with fewer computational steps. • Ideal for studying material science, condensed matter physics, and quantum thermodynamics. Why This Matters • Accelerating Scientific Research: The simulator could help discover new materials, improve energy storage, and refine magnetism-based technologies. • Advancing Quantum Supremacy: By achieving results beyond classical computation, this simulator cements Google’s lead in quantum research. • Potential for Quantum AI Integration: Combining digital and analog approaches may enhance machine learning models and optimize large-scale computations. What’s Next? • Expanding Qubit Count: Google may scale up its hybrid quantum simulations, pushing closer to full-scale quantum supremacy. • Exploring More Applications: Future research could apply these simulations to biophysics, drug discovery, and nuclear physics. • Potential Industry Collaborations: Google’s breakthrough may lead to partnerships in materials engineering and quantum-enhanced AI systems. This 69-qubit quantum simulator represents a major leap in computational power, proving that quantum systems can now surpass supercomputers in specialized scientific tasks, bringing us closer to practical quantum applications.

After 20 years of trying, scientists finally unlocked quantum computing's biggest secret. The process they've been chasing is called "magic state distillation." Here's what makes this discovery so remarkable: Every quantum algorithm that could outperform classical computers needs these "magic states" to function. Think of magic states as premium fuel for quantum computers. Without them, quantum machines can only run basic operations that your laptop could handle just as well. The challenge was creating high-quality magic states in logical qubits. Physical qubits are too noisy and error-prone for serious quantum computing. Logical qubits fix this by using multiple physical qubits to share the same information and automatically correct errors. But until now, nobody could generate the magic states these logical qubits needed. Scientists at QuEra just proved it's possible. They took five imperfect magic states and distilled them into one pristine magic state using logical qubits. This breakthrough means quantum computers can finally run the complex algorithms that will make them more powerful than any supercomputer. We're talking about machines that could revolutionize drug discovery, financial modeling, artificial intelligence, and cryptography. The quantum advantage everyone's been waiting for just became real. As one researcher put it: "We're seeing a shift from asking if quantum computers can be useful to making them truly useful." The next decade of computing is going to be wild. Which breakthrough in quantum computing excites you most? ✍️ Your insights can make a difference! ♻️ Share this post if it speaks to you, and follow me for more.

Google Unveils Willow: A Leap Forward in Quantum Computing Google Quantum AI has introduced Willow, a cutting-edge quantum chip designed to address two of the field’s most significant challenges: error correction and computational scalability. Willow, fabricated in Google’s Santa Barbara facility, achieves state-of-the-art performance, marking a pivotal step toward realizing a large-scale, commercially viable quantum computer. It gets way geekier from here – but if you’re with me so far… Exponential Error Reduction Julian Kelly, Director of Quantum Hardware at Google, emphasized Willow’s ability to exponentially reduce errors as the system scales. Utilizing a grid of superconducting qubits, Willow demonstrated a historic breakthrough in quantum error correction. By expanding arrays from 3×3 to 5×5 and then 7×7 qubits, researchers cut error rates in half with each iteration. This achievement, referred to as being “below threshold,” signifies that larger quantum systems can now exhibit fewer errors, a challenge pursued since Peter Shor introduced quantum error correction in 1995. The chip also achieved “beyond breakeven” performance, where arrays of qubits outperformed the lifetimes of individual qubits, which is key to ensuring the feasibility of practical quantum computations. Ten Septillion Years in Five Minutes Willow’s computational capabilities were validated using the Random Circuit Sampling (RCS) benchmark, a rigorous test of quantum supremacy. According to Google’s estimates, Willow completed a task in under five minutes that would take a modern supercomputer ten septillion years—a timescale exceeding the age of the universe. This achievement underscores the rapid, double-exponential performance improvements of quantum systems over classical alternatives. While the RCS benchmark lacks direct commercial applications, it remains a critical indicator of quantum computational power. Kelly noted that surpassing classical systems on this benchmark solidifies confidence in the broader potential of quantum technology. Building Toward Practical Applications Google’s roadmap aims to bridge the gap between theoretical quantum advantage and real-world utility. The team is now focused on achieving “useful, beyond-classical” computations that solve practical problems. Applications in drug discovery, battery design, and AI optimization are among the potential breakthroughs quantum computing could unlock. Willow’s advancements in quantum error correction and computational scalability highlight its transformative potential. As Kelly explained, “Quantum algorithms have fundamental scaling laws on their side,” making quantum computing indispensable for tasks beyond the reach of classical systems. Quantum computing is still years away, but this is an exciting milestone. Considering the remarkable rate of technological improvement we’re experiencing right now, practical quantum computing (and quantum AI) may be closer than we think. -s

𝗤𝘂𝗮𝗻𝘁𝘂𝗺 𝗔𝗱𝘃𝗮𝗻𝘁𝗮𝗴𝗲 𝗶𝘀 𝗵𝗲𝗿𝗲! That is the message of today's IBM Quantum blog post - and it marks a milestone the field has been working towards for decades. The pieces are coming together - like in this model of IBM Quantum System Two, built brick by brick by Luca Crippa. 🧱 Quantum advantage occurs when a quantum computer performs a computation beyond what classical computing can achieve alone - and when the result can be rigorously validated. That second part is the hard one: how do you trust an output no classical computer can check? Three new papers answer exactly this, each with a different framework for trusted quantum computation: 🔹 𝗜𝗕𝗠 + 𝗨𝗻𝗶𝘃𝗲𝗿𝘀𝗶𝘁𝘆 𝗼𝗳 𝗖𝗵𝗶𝗰𝗮𝗴𝗼: 70 logical qubits running a classically hard sampling problem, encoded in spacetime codes that detect errors during the computation - the circuit certifies its own fidelity. One of the largest error correction demonstrations to date: ~15 minutes on the quantum computer vs. infeasible classical runtimes. 🔹 𝗜𝗕𝗠 + 𝗤𝗲𝗱𝗺𝗮: Error-mitigated Floquet dynamics at up to 74 qubits revealing persistent oscillations that two state-of-the-art classical methods on RIKEN's supercomputer could not resolve - validated through independent error-mitigation approaches and cross-checked on a second hardware platform. Achieved with commercially available quantum hardware and software. 🔹 𝗜𝗕𝗠 + 𝗔𝗹𝗴𝗼𝗿𝗶𝘁𝗵𝗺𝗶𝗾: 56-qubit experiments tracking how information spreads through heterogeneous quantum systems, in a regime where leading classical methods disagree with each other. The key idea: when you can't verify the answer, verify the process - consistent results across five quantum computers with different noise profiles. And these results don't stand alone. More pieces have clicked into place in recent weeks: 🧱 A clear metrics framework for measuring quantum hardware across scale, quality, and speed 🧱 The announced acquisition of HRL Laboratories, bringing deep research capabilities across various quantum technologies to IBM 🧱 Nighthawk r2, with fast qubit reset delivering ~25x circuit throughput compared to Heron r3 🧱 Qiskit Paulice, embedding post-selected error detection into circuits via spacetime Pauli checks - paving the way for encoded (i.e. "logical") qubits on Nighthawk These demonstrations do not close the case - they open the results to community scrutiny. All three experiments are on the Quantum Advantage Tracker, alongside several other candidates. Quantum advantage is not a single moment but an ongoing process of demonstration and challenge - read the blog, explore the tracker, and try to beat these results classically. Links in the first comment.

⚛️ Sequential Quantum Computing 📑 We propose and experimentally demonstrate sequential quantum computing (SQC), a paradigm that utilizes multiple homogeneous or heterogeneous quantum processors in hybrid classical-quantum workflows. In this manner, we are able to overcome the limitations of each type of quantum computer by combining their complementary strengths. Current quantum devices, including analog quantum annealers and digital quantum processors, offer distinct advantages, yet face significant practical constraints when individually used. SQC addresses this by efficient inter-processor transfer of information through bias fields. Consequently, measurement outcomes from one quantum processor are encoded in the initial-state preparation of the subsequent quantum computer. We experimentally validate SQC by solving a combinatorial optimization problem with interactions up to three-body terms. A D-Wave quantum annealer utilizing 678 qubits approximately solves the problem, and an IBM’s 156-qubit digital quantum processor subsequently refines the obtained solutions. This is possible via the digital introduction of non-stoquastic counterdiabatic terms unavailable to the analog quantum annealer. The experiment shows a substantial reduction in computational resources and improvement in the quality of the solution compared to the standalone operations of the individual quantum processors. These results highlight SQC as a powerful and versatile approach for addressing complex combinatorial optimization problems, with potential applications in quantum simulation of many-body systems, quantum chemistry, among others. ℹ️ Romero et al - 2025

The new manuscript from Oak Ridge National Laboratory, Cleveland Clinic, and IBM, "Quantum Computations on Fusion Blanket Molten Salts," is worth seeing for how it uses quantum computing, not just what it computes. The problem is modeling how tritium binds in FLiBe, a molten salt candidate for fusion reactor blankets. Ensuring adequate supplies of tritium has long been a barrier to realizing the promise of clean and abundant energy from fusion power plants, and solving this issue is a key objective of the U.S. Department of Energy (DOE) Genesis Mission. The electronic interactions that drive tritium's behavior in these salts are strongly correlated and hard for classical methods to capture accurately, so the team split the work. The embedded wavefunction method isolates the chemically active fragment that benefits from quantum computation. The surrounding environment stays on classical HPC. That fragment gets solved with extended sample-based quantum diagonalization (ExtSQD) on IBM Quantum systems, where the quantum processor produces correlated samples and classical compute handles the diagonalization. Fragment energies came out close to full configuration interaction benchmarks, and the team could see exactly where the remaining error sits. This is again quantum-centric supercomputing in practice, and it maps onto the reference architecture we laid out earlier this year (https://lnkd.in/g5Hp9Fce). It also follows the work Cleveland Clinic, RIKEN, and IBM published in May, where the same approach simulated a 12,635-atom protein, the largest biologically relevant system modeled with quantum hardware to date. Proteins then, fusion blanket materials now. Same pattern every time: isolate the fragment that needs quantum, keep the environment on classical, run it as one pipeline where AI, HPC, and quantum each do what they are best at. The workflow is the key thing I want to emphasize but fusion is the proving ground here. This is quantum computing contributing to a real materials problem today, and it points at how we leverage computing in general for the future. Manuscript: https://lnkd.in/gmT2Ey92 Press release: https://lnkd.in/ghpnTcRG #FusionEnergy #NuclearEnergy #Tritium #CleanEnergy #QuantumComputing #QuantumCentricSupercomputing #HPC #GenesisMission

A new paper tackles some of the major roadblocks in quantum machine learning, proposing innovative solutions for data loading, model training, and initialization. I wanted to share some key findings from the research paper "Bit-bit encoding, optimizer-free training and sub-net initialization: techniques for scalable quantum machine learning" by Sonika Johri. Here are some of the most important outcomes: * Bit-bit encoding: The authors introduce a novel "bit-bit" encoding scheme where both input and output data are represented as binary strings. This method allows for universal approximation of any function between input and output bits, overcoming limitations of other encoding methods like amplitude or angle encoding. A classical binary encoding scheme is used to extract the most predictive bits from real-valued datasets. * Optimizer-free training: The paper demonstrates a method to train variational quantum circuits without using a classical optimizer. This is achieved by updating one parameter at a time using an analytical expression for its minimum, which guarantees convergence to a local minimum. This approach bypasses the need to tune hyperparameters like the learning rate, which is a major challenge in traditional quantum machine learning. * Sub-net initialization: To address the issue of barren plateaus, the authors propose a "sub-net initialization" strategy. This involves training smaller models on more compressed data and using these models to initialize larger models that utilize more qubits. This technique allows for incremental training of quantum models as more quantum resources become available. * Scalability: The combined performance of these techniques is demonstrated on subsets of the MNIST dataset for models with an all-to-all connected architecture using up to 16 qubits in simulation. The results show that the loss function consistently decreases as the model's capability increases, which is maintained for datasets of varying complexity. The study also argues that near-term quantum computers can be utilized to build large quantum models by incrementally expanding the encoded bit string, training models until convergence, and reusing smaller models for the training of larger ones. Here the article: https://lnkd.in/dCzwaCSd #quantumcomputing #machinelearning #qml #ai #research #innovation #ml #datascience