Quantum Computing Applications in Stochastic Modeling

Happy to announce a new #quantumcomputing work produced jointly by the Global Technology #appliedresearch and #quantitativeresearch teams at JPMorgan Chase & Co. in collaboration with QC Ware Corp. In this work, we propose two #quantum algorithms for pricing discretely monitored Asian options over T monitoring points where the underlying asset is modeled by an exponentiated Gaussian process. Compared to standard methods based on #montecarlo sampling, which have complexity linear in T, our algorithms have complexity that is at most poly-logarithmic in T. Our first algorithm is built upon a new semi-digital quantum encoding for stochastic processes that combines the advantages of the analog encoding and the digital encoding, allowing speedups in T without restricting the type of operations applicable onto the stochastic process. The other algorithm utilizes a time-domain sub-sampling technique, also proposed in this work, which is inspired by the semi-digital encoding approach. Our algorithms generalize to pricing options where the underlying asset price is modeled by a smooth function of a sub-Gaussian process and the payoff is dependent on the weighted time-average of the underlying asset price. Link to paper: https://lnkd.in/gcAmTpeY Coauthors: QC Ware Corp.: Anupam Prakash, Aditi Dandapani, Iordanis Kerenidis JPMorgan Chase & Co. Quantitative Research: Charlie Che, Ben Wood, JPMorgan Chase & Co. Global Technology Applied Research: Yue Sun, Shouvanik Chakrabarti, Dylan Herman, Niraj Kumar, Shree Hari Sureshbabu, and Marco Pistoia

Many of you will have seen the news about HSBC’s world-first application of quantum computing in algorithmic bond trading. Today, I’d like to highlight the technical paper that explains the research behind this milestone. In collaboration with IBM, our teams investigated how quantum feature maps can enhance statistical learning methods for predicting the likelihood that a trade is filled at a quoted price in the European corporate bond market. Using production-scale, real trading data, we ran quantum circuits on IBM quantum computers to generate transformed data representations. These were then used as inputs to established models including logistic regression, gradient boosting, random forest, and neural networks. The results: • Up to 34% improvement in predictive performance over classical baselines. • Demonstrated on real, production-scale trading data, not synthetic datasets. • Evidence that quantum-enhanced feature representations can capture complex market patterns beyond those typically learned by classical-only methods. This marks the first known application of quantum-enhanced statistical learning in algorithmic trading. For full technical details please see our published paper: 📄 Technical paper: https://lnkd.in/eKBqs3Y7 📰 Press release: https://lnkd.in/euMRbbJG Congratulations to Philip Intallura Ph.D , Joshua Freeland Freeland and all HSBC colleagues involved — and huge thanks to IBM for their partnership.

A More General Quantum Credit Risk Analysis Framework   "..Monte Carlo simulations are computationally expensive due to the rare-event simulation problems inherent in credit risk evaluation. Additionally, Monte Carlo simulations can only generate pseudo-random variables, and the quality of the simulation can be compromised by the appearance of patterns." "To overcome these limitations, researchers have explored new methods, such as those based on quantum computing, which can naturally generate true random samples due to the probabilistic nature of qubits. Moreover, quantum amplitude estimation (QAE) has shown promise in estimating the value at risk and offers a quadratic speedup over classical Monte Carlo methods."   By Emanuele Dri , Antonello Aita , Edoardo Giusto , Davide Ricossa , Davide Corbelletto , Bartolomeo Montrucchio  and Roberto Ugoccioni IBM Italy Intesa Sanpaolo Politecnico di Torino Link https://lnkd.in/dspnyG9v  

Exponential quantum advantage in processing massive classical data by John Preskill https://lnkd.in/eUTvGHaX Abstract Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP = BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

Quantum-Inspired Computing Revolutionizes Turbulence Simulation Breakthrough in Turbulence Modeling • Researchers at the University of Oxford have developed a quantum-inspired approach to simulating turbulence, a historically complex and computationally expensive problem. • Instead of directly modeling the chaotic flow patterns, the team treats turbulence as a probabilistic system, leveraging probability distribution functions (PDFs) to extract critical flow properties such as lift and drag. • This method reduces the computational burden, making turbulence simulations faster and more efficient without losing essential accuracy. Overcoming Computational Barriers • Traditional turbulence simulations require solving high-dimensional Fokker-Planck equations, which are notoriously difficult for classical computing systems. • The Oxford team bypassed these constraints by adopting quantum-inspired algorithms, which are optimized for dealing with probabilistic systems and complex data structures. • Their approach significantly accelerates turbulence modeling across various disciplines, from aerospace engineering to climate science and fluid dynamics. Potential Applications • Aerodynamics: Faster simulations for aircraft wing designs and drag reduction in vehicles. • Weather Prediction: Improved modeling of atmospheric turbulence for more accurate climate forecasting. • Energy Efficiency: Enhancements in wind turbine performance and jet engine optimization. • Quantum Computing Integration: Lays groundwork for future quantum simulations of turbulence, which could further refine computational fluid dynamics (CFD) techniques. Key Takeaways • Quantum-inspired computing is redefining turbulence modeling, offering a probabilistic approach that sidesteps traditional computational bottlenecks. • This breakthrough could revolutionize multiple industries by enabling more accurate and efficient simulations of turbulent systems. • As quantum hardware continues to advance, these methods could serve as a bridge to fully quantum turbulence simulations, unlocking even greater precision in fluid dynamics research.

In finance, Monte Carlo simulations help us to measure risks like VaR or price derivatives, but they’re often painfully slow because you need to generate millions of scenarios. Matsakos and Nield suggest something different: they build everything directly into a quantum circuit. Instead of precomputing probability distributions classically, they simulate the future evolution of equity, interest rate, and credit variables inside the quantum computer, including binomial trees for stock prices, models for rates, and credit migration or default models. All that is done within the circuit, and then quantum amplitude estimation is used to extract risk metrics without any offline preprocessing. This means you keep the quadratic speedup of quantum MC while also removing the bottleneck of classical distribution generation. If you want to explore the topic further, here is the paper: https://lnkd.in/dMHeAGnS #physics #markets #physicsinfinance #derivativespricing #quant #montecarlo #simulation #finance #quantitativefinance #financialengineering #modeling #quantum

Computational regimes in matrix-product-state-based quantum trajectory simulations. We explore the subtle regimes for classically simulating and hence “dequantizing” noisy quantum hardware and many-body dynamics. https://lnkd.in/dqa2Z-db In detail, the efficient simulation of open quantum systems is central to modeling noisy quantum hardware and many-body dynamics. In trajectory-based tensor network methods, cost is often associated with trajectory-level quantities such as entanglement growth or bond dimension. However, the total cost of a fixed-accuracy simulation also depends on statistical sampling, and the interplay between per-trajectory complexity and sampling effort remains poorly understood. Here we introduce a cost-resolved framework for #matrixproductstate (MPS)-based quantum trajectory simulations that decomposes total cost into memory per trajectory, runtime per trajectory, and sampling effort. We show that physically equivalent stochastic unravelings of the same Lindblad dynamics do not necessarily reduce total cost, but instead redistribute cost between trajectory complexity and statistical convergence. This trade-off is quantified by two dimensionless inflation factors: a bond dimension inflation α and a sampling inflation κ, which together determine the preferred unraveling under hardware-dependent memory and parallelism constraints. We provide a practical protocol for extracting (α,κ) from modest pilot simulations and demonstrate it using benchmarks across multiple noise channels. The resulting decision maps show that the computationally favorable unraveling can change with noise strength, time-step resolution, system size, and available parallelism. These results establish unraveling choice as a hardware-aware simulation design problem rather than an intrinsic optimization of trajectory entanglement alone. Warm thanks to Aaron Sander, Simon Cichy, Martin Eigel, Maximilian Fröhlich, Tom Peham, and Robert Wille for the once again wonderful collaboration.

> Sharing Resource < Interesting paper this morning: "Provable and scalable quantum Gaussian processes for quantum learning" by Jonas Jäger, Paolo Braccia, Pablo Bermejo, Manuel G. Algaba, Diego García-Martín, Marco Cerezo Abstract: Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning. Link: https://lnkd.in/eqiFk6xD #quantummachinelearning #quantumcomputing #qml #qc #paper #research

People always ask for the papers. Well, we just published one of our data loading results with HSBC in Physical Review Research. If you want to use quantum computers for modeling risk or optimizing portfolios, you first need to load your financial data into quantum circuits (algorithms). The challenge? Typically this process is slow and the number of required operations grows exponentially, making it difficult or impossible to run on today’s quantum computers. Haiqu tackled this bottleneck by building a faster, more scalable method for encoding complex (financial) distributions into quantum circuits. We validated the approach on financial models like heavy-tailed Lévy distributions used to capture extreme market events like crashes and sudden price swings (seems pretty relevant in today’s environment), and executed using the full capacity of IBM’s 156-qubit device. Check ComputerWeekly.com’s coverage here: https://lnkd.in/ek9iyzXS and read the paper in Physical Review here: https://lnkd.in/eJPv4WfK

🚀 The European Securities and Markets Authority (ESMA) has released a detailed analysis about Quantum computing in financial markets. They identified 4 application areas in which quantum could significantly improve market efficiency, risk management and operational resilience. Major institutions are already running proofs of concept to identify where quantum advantage justifies the investment, and ESMA provide an interesting breakdown of public and private investments in which 🇨🇳China is leading the money game with public spending, while 🇺🇸 US startups gets the major share of venture capital attention. Here the 4 high-potential application cases: 1️⃣ Optimization (most promising in near-term) Many financial problems are combinatorial and could be treated with quantum algorithms that use superposition to explore vast solution spaces, and entanglement to model interdependencies. These are highly compatible with quantum annealing and variational algorithms already runnable on current NISQ hardware: - Mean-variance portfolio optimization, risk minimization and hedging  Index tracking - Trade settlement optimization for clearing houses (maximizing settled transactions without breaching credit limits)  - Predicting financial contagion in interconnected networks and identifying FX arbitrage opportunities 2️⃣ Stochastic Modeling Quantum Monte Carlo Integration theoretically needs quadratically fewer sample paths than classical Monte Carlo for the same accuracy. While data-encoding overheads remain a challenge, QMCI is a compelling pathway as hardware matures: - Pricing of derivatives - Risk measurement: VaR, sensitivity analysis of options 3️⃣ Machine Learning Quantum Machine Learning includes algorithms that speed up classical techniques via quantum linear algebra and quantum-native methods suited to near-term devices. Experimental implementations already match classical accuracy while offering better interpretability: - Credit assessment and fraud detection - Quantum Principal Component Analysis for dimensionality reduction in large datasets  - Quantum reinforcement learning and other supervised tasks 4️⃣ Quantum-enabled distributed ledger technologies Quantum computing could enhance blockchain platforms through:  - Proof-of-quantum-work consensus that slashes energy consumption  - Quantum entanglement for instant tamper detection and faster distributed consensus  - Improved scalability, security and interoperability for tokenisation and cross-institution KYC ⚡️ESMA also stresses the urgency of migrating to post-quantum cryptography as a sufficiently powerful quantum computer could break current public-key cryptography threatening financial transaction security. It's an interesting reading about the potential applications of this fast growing technology. Here is they full report, where you can find more datapoints. #quantum #esma #optimization #ibm