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TetraBox: Advanced Simulation

Simulate Complex Systems with Tensor Network Techniques

TetraBox is Terra Quantum's cutting-edge simulation toolset that harnesses the power of tensor networks, through tensor trains and quantum-inspired algorithms, to solve complex computational problems with unprecedented efficiency.

From quantum chemistry to financial modeling, TetraBox provides the computational power needed to navigate today's most challenging fields.

TetraBox enables you to:

Model intricate physical and financial systems accurately
Explore a vast array of scenarios and parameters quickly
Accelerate research and development across industries
Make data-driven decisions based on precise simulations

Why TetraBox?

Superior Performance


Simulate systems with exponentially faster runtimes compared to traditional methods.

Better Problem Solving


Tackle simulations with coupled variables, revealing intricate correlations in datasets.

Scalability


Physics-driven methods on classical hardware, adapting smoothly to quantum hardware.

Versatility


Address diverse simulation challenges, from molecular dynamics to financial modeling and beyond.

Whether you're simulating molecular interactions, modeling financial markets, or solving complex engineering problems, TetraBox provides the advanced simulation capabilities needed to gain deeper insights and drive innovation in your field.

In the TetraBox Toolset
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TetraOpt

Universal Black-Box Optimization


  • Tensor train-based optimizer for complex, high-dimensional problem-solving
  • Efficiently handles cases with limited function evaluations available
  • Achieves lower cost function values faster than other existing algorithms
  • Designed to be highly parallelizable and user-friendly, making it easy to use for a wide range of applications
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TQOptimaX

Multi-objective Optimization


  • Maximizes hypervolume in solution-space with minimal function evaluations
  • Handles non-linear constraints and provides well-distributed Pareto front solutions
  • Parallelizable for efficient evaluation of multiple solution candidates
  • Leverages TetraOpt for optimizing the acquisition function
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TetraPDE

Physical Design Simulation Tool


  • Solver specialized for partial differential equations with tensor train methods
  • Efficiently handles high-dimensional PDEs in physics and engineering fields
  • Uses adaptive time-stepping and multi-grid techniques for better convergence
  • Supports solving both linear and non-linear PDE systems effectively
Essential Tensor Network Functionality

  • Core tensor train operations for efficient data representation and manipulation
  • Advanced tensor contraction algorithms for high-performance computations
  • Cross-approximation techniques for compact representation of high-dimensional data
  • Tensor rounding and truncation methods for managing computational complexity
Tensor Quantum Programming

  • Framework for mapping tensor network algorithms to quantum circuits
  • Hybrid classical-quantum approach for maximizing computational efficiency
  • Quantum-inspired preprocessing to enhance quantum algorithm performance
  • Seamless integration pathway from classical tensor methods to quantum hardware

Key Features

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Cutting-edge Tensor Network Algorithms

  • Proprietary tensor train methods for efficient high-dimensional data processing
  • Advanced cross-approximation for rapid tensor construction from sparse data
  • Optimized contraction algorithms for high-performance computing
  • Continuous updates based on latest R&D breakthroughs

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Flexible Problem Formulation

  • Support for diverse physical and mathematical models
  • Easy integration of custom equations and boundary conditions
  • Adaptive discretization for optimal accuracy-performance balance
  • Handling of multi-scale and multi-physics simulations

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Scalable Performance

  • Efficient parallelization and GPU acceleration
  • Automatic load balancing for optimal resource use
  • Quantum-ready algorithms for future hardware integration
  • Polynomial scaling with problem size for many applications

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Hardware-Efficient Implementation

  • Designed for execution today on classical hardware and on quantum hardware, as it matures
  • Optimized for current high-performance computing infrastructures
  • Tensor Quantum Programming for seamless classical-quantum transition
  • Leverage of tensor network structures for efficient quantum circuit implementation

How TetraBox Works
TetraBox leverages the power of tensor networks, particularly the tensor train format, to efficiently represent and manipulate high-dimensional data and operators.
Tensor Train Decomposition

  • Represents high-dimensional tensors as a series of lower-dimensional core tensors
  • Enables compact storage and efficient manipulation of complex data structures
  • Reduces computational complexity from exponential to polynomial in many cases
Physics-driven Tensor Train Algorithms

  • Utilizes techniques inspired by quantum computing to enhance classical simulations
  • Employs probabilistic sampling methods to estimate high-dimensional integrals
  • Implements variational approaches for solving eigenvalue problems
Benefits of TetraBox versus Classical Simulation Approaches

  • Enhanced Computational Efficiency

    • Overcome the curse of dimensionality in high-dimensional problems
    • Achieve exponential speedup in many simulation scenarios
    • Handle larger system sizes and longer time scales than classical methods

  • Improved Accuracy in Complex Simulations

    • Capture intricate correlations and interactions in multi-component systems
    • Maintain high precision even for long-time dynamics simulations
    • Provide reliable results in regimes where classical methods break down

  • Superior Handling of Multi-Scale Problems

    • Efficiently represent systems with widely varying spatial or temporal scales
    • Seamlessly integrate microscopic and macroscopic models
    • Capture emergent behaviors in complex systems

  • Adaptive Problem Reformulation

    • Automatically identify and exploit low-rank structures in data and operators
    • Dynamically adjust tensor ranks for optimal accuracy-to-performance trade-off
    • Seamlessly switch between different tensor network formats as needed

  • Quantum Readiness

    • Benefit from physics-driven speedups today on classical hardware
    • Easily transition to quantum hardware as it becomes available
    • Future-proof your simulation workflows with quantum-compatible algorithms
Example Problem Types and Applications
TetraBox excels in solving complex, high-dimensional simulation problems across various domains. Here are examples of key problem types:

  • Quantum Chemistry Simulations

    • Speed up molecular design by up to 50x, accelerating drug and material design
    • Efficient modeling of complex molecular structures and electronic properties
    • Accurate calculation of quantum many-body systems for advanced material science

  • Advanced Material Simulation

    • High-fidelity simulations of complex fluid flows
    • Efficient handling of turbulence and multi-phase systems
    • Accelerated design optimization for aerospace andautomotive applications



  • Risk and Financial Modeling

    • Fast and accurate pricing of complex financial instruments
    • Efficient Monte Carlo simulations for risk assessment
    • High-dimensional portfolio optimization

    Read CaseStudy

  • Physical Design Simulation

    • Solving multi-dimensional PDEs in physics and engineering
    • Efficient handling of coupled systems of equations
    • Accurate long-time simulations for complex dynamical systems

    Read Case Study

• Speed up molecular design by up to 50x, accelerating drug and material design
• Efficient modeling of complex molecular structures and electronic properties
• Accurate calculation of quantum many-body systems for advanced material science

• High-fidelity simulations of complex fluid flows
• Efficient handling of turbulence and multi-phase systems
• Accelerated design optimization for aerospace andautomotive applications



• Fast and accurate pricing of complex financial instruments
• Efficient Monte Carlo simulations for risk assessment
• High-dimensional portfolio optimization

Read CaseStudy

• Solving multi-dimensional PDEs in physics and engineering
• Efficient handling of coupled systems of equations
• Accurate long-time simulations for complex dynamical systems

Read Case Study

Case Study

Accelerating Exotic Options Pricing
Using TetraBox
Challenge
Cirdan Capital, a London-based investment bank, needed to optimize the pricing of exotic options, such as multi-asset autocallable options. Traditional Monte Carlo methods were computationally expensive and time-consuming, limiting their ability to assess risks and identify market imbalances quickly.
Solution
Terra Quantum implemented a cutting-edge tensor network-based approach using TetraBox. We developed an innovative algorithm that could:
  • Efficiently handle high-dimensional financial models
  • Leverage tensor train decomposition for compact representation of complex financial data
  • Accelerate Monte Carlo-like simulations using quantum-inspired techniques
Results
  • 75% improvement in pricing speed for exotic options and related Greeks
  • 75% reduction in computing power required for pricing calculations
  • Potential savings of millions in compute costs annually for large trading banks
  • Ability for traders and risk managers to understand risk positions faster
Impact
The TetraBox-powered solution significantly enhanced Cirdan Capital's capabilities to:
  • Respond more quickly to volatile market conditions
  • Assess risks more frequently by valuing their books more often during the day
  • Identify intra-day market imbalances more effectively
  • Reduce operational costs through more efficient use of computational resources

Dive Deeper with Our Research Publications

Quantum Physics-informed Neural Networks for Simulating Computational Fluid Dynamics in Complex Shapes

May 2024

Alternating minimal energy methods for linear systems in higher dimensions

Aug 2023

Low‐rank solution of an optimal control problem constrained by random Navier‐ Stokes equations

Aug 2023

Quantum physics informed neural networks for simulating computational fluid dynamics in complex shapes

May 2023

Tensor Train Optimization for Conformational Sampling of Organic Molecules

Oct 2024

Dr. Michael Perelshtein

Dr. Michael Perelshtein

Global Director of Advanced Technologies

At Terra Quantum, we're challenging the existing illusion of complexity that simulating nature must always be exponentially hard. Our tensor networks framework, utilising tensor trains, tackles intricate numerical challenges in chemistry, finance, and logistics through innovative approaches to function approximation, data compression, black-box optimization, and linear equation solving. It's rewarding to see our clients integrate our physics-driven solutions, which do not immediately require quantum hardware, already gaining significant performance improvements today while preparing for the mature QPUs to come.

Accessing TetraBox

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Work with Our Experts for Custom Development Services

• Collaborate with our simulation specialists to address your specific challenges

 • Benefit from tailored solutions that integrate seamlessly with your existing processes

 • Receive ongoing support and optimization as your simulation needs evolve

TQ42 Interface

Access TetraOpt in TQ42

• Access our blackbox optimiser in TQ42, via CLI or Python SDK

• Benefit from the scalability and security of our cloud-based platform

Academy BG

Take the Tensor Networks course in TQ Academy

• Access a specialized platform for hands-on experience with Tensor Networks capabilities

• Participate in guided tutorials and workshops led by our simulation experts

• Explore real-world use cases and benchmark your problems against TetraBox performance

Explore TQ Academy

Ready to Transform Your Simulation Capabilities?

Let's discuss your specific challenges.