#3727 Knowledge Graph of Quantum Computing Algorithms and Use Cases

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#3727 Knowledge Graph of Quantum Computing Algorithms and Use Cases

#3727 Think hard. I want to create a knowledge graph of Quantum Computing algorithms and the problems that can use them. The output should be quantum algorithms and problems as entities, and APPLIED_TO as relationships

Of course. Here is a knowledge graph of quantum computing algorithms, the problems they can be applied to, and the relationships between them.

Foundational & Search Algorithms

Shor's Algorithm

This algorithm is famous for its potential to break modern cryptography. It provides an exponential speedup over the best-known classical algorithms for its target problems.

  • (Shor's Algorithm) -[APPLIED_TO]-> (Integer Factorization)

  • (Shor's Algorithm) -[APPLIED_TO]-> (Discrete Logarithm Problem)

Grover's Algorithm

Grover's algorithm provides a quadratic speedup for searching an unsorted database or any problem that can be framed as a search. 🔎

  • (Grover's Algorithm) -[APPLIED_TO]-> (Unstructured Search)

  • (Grover's Algorithm) -[APPLIED_TO]-> (Database Search)

  • (Grover's Algorithm) -[APPLIED_TO]-> (Satisfiability Problems)

Optimization & Simulation Algorithms

Quantum Annealing / Adiabatic Quantum Computation (AQC)

This is a method used to find the global minimum of a function, making it suitable for complex optimization problems.

  • (Quantum Annealing) -[APPLIED_TO]-> (Optimization Problems)

  • (Quantum Annealing) -[APPLIED_TO]-> (Protein Folding)

  • (Quantum Annealing) -[APPLIED_TO]-> (Logistics and Scheduling)

Variational Quantum Eigensolver (VQE)

VQE is a hybrid quantum-classical algorithm designed for near-term quantum devices to find the energy levels of molecules, a key task in chemistry and materials science. ⚛️

  • (Variational Quantum Eigensolver) -[APPLIED_TO]-> (Quantum Chemistry Simulation)

  • (Variational Quantum Eigensolver) -[APPLIED_TO]-> (Molecular Ground State Calculation)

Quantum Approximate Optimization Algorithm (QAOA)

QAOA is another hybrid algorithm used to find approximate solutions to combinatorial optimization problems.

  • (Quantum Approximate Optimization Algorithm) -[APPLIED_TO]-> (Combinatorial Optimization)

  • (Quantum Approximate Optimization Algorithm) -[APPLIED_TO]-> (Max-Cut Problem)

Specialized & Subroutine Algorithms

Harrow-Hassidim-Lloyd (HHL) Algorithm

The HHL algorithm offers an exponential speedup for solving specific kinds of linear systems of equations, with applications in machine learning and data analysis.

  • (HHL Algorithm) -[APPLIED_TO]-> (Solving Systems of Linear Equations)

  • (HHL Algorithm) -[APPLIED_TO]-> (Quantum Machine Learning)

Quantum Phase Estimation (QPE)

QPE is a crucial subroutine in many other quantum algorithms, including Shor's. It's used to determine the eigenvalues (often corresponding to energy levels) of a quantum system.

  • (Quantum Phase Estimation) -[APPLIED_TO]-> (Finding Eigenvalues of a Unitary Operator)

  • (Quantum Phase Estimation) -[APPLIED_TO]-> (Quantum System Simulation)

Deutsch-Jozsa & Simon's Algorithms

These are early, foundational algorithms that demonstrated the potential for quantum computers to outperform classical ones on specific, tailored problems. While not broadly practical, they were critical proofs of concept.

  • (Deutsch-Jozsa Algorithm) -[APPLIED_TO]-> (Distinguishing Constant vs. Balanced Functions)

  • (Simon's Algorithm) -[APPLIED_TO]-> (Simon's Period-Finding Problem)


Provide Cypher statements for the knowledge graph

Certainly. Here are the Cypher statements to create the quantum computing knowledge graph.

You can run this script in a Neo4j browser or via any Neo4j driver to populate the database. The MERGE command ensures that nodes and relationships are created only if they don't already exist, preventing duplicates.

Cypher Script for Quantum Knowledge Graph

// This script creates nodes for Quantum Algorithms and Problems,
// and establishes the APPLIED_TO relationship between them.

// --- Foundational & Search Algorithms ---

// Shor's Algorithm
MERGE (shor:QuantumAlgorithm {name: "Shor's Algorithm"})
MERGE (factorization:Problem {name: "Integer Factorization"})
MERGE (discrete_log:Problem {name: "Discrete Logarithm Problem"})
MERGE (shor)-[:APPLIED_TO]->(factorization)
MERGE (shor)-[:APPLIED_TO]->(discrete_log);

// Grover's Algorithm
MERGE (grover:QuantumAlgorithm {name: "Grover's Algorithm"})
MERGE (search:Problem {name: "Unstructured Search"})
MERGE (db_search:Problem {name: "Database Search"})
MERGE (sat:Problem {name: "Satisfiability Problems"})
MERGE (grover)-[:APPLIED_TO]->(search)
MERGE (grover)-[:APPLIED_TO]->(db_search)
MERGE (grover)-[:APPLIED_TO]->(sat);

// --- Optimization & Simulation Algorithms ---

// Quantum Annealing / AQC
MERGE (annealing:QuantumAlgorithm {name: "Quantum Annealing"})
MERGE (optimization:Problem {name: "Optimization Problems"})
MERGE (protein:Problem {name: "Protein Folding"})
MERGE (logistics:Problem {name: "Logistics and Scheduling"})
MERGE (annealing)-[:APPLIED_TO]->(optimization)
MERGE (annealing)-[:APPLIED_TO]->(protein)
MERGE (annealing)-[:APPLIED_TO]->(logistics);

// Variational Quantum Eigensolver (VQE)
MERGE (vqe:QuantumAlgorithm {name: "Variational Quantum Eigensolver"})
MERGE (chem_sim:Problem {name: "Quantum Chemistry Simulation"})
MERGE (ground_state:Problem {name: "Molecular Ground State Calculation"})
MERGE (vqe)-[:APPLIED_TO]->(chem_sim)
MERGE (vqe)-[:APPLIED_TO]->(ground_state);

// Quantum Approximate Optimization Algorithm (QAOA)
MERGE (qaoa:QuantumAlgorithm {name: "Quantum Approximate Optimization Algorithm"})
MERGE (combo_opt:Problem {name: "Combinatorial Optimization"})
MERGE (maxcut:Problem {name: "Max-Cut Problem"})
MERGE (qaoa)-[:APPLIED_TO]->(combo_opt)
MERGE (qaoa)-[:APPLIED_TO]->(maxcut);

// --- Specialized & Subroutine Algorithms ---

// HHL Algorithm
MERGE (hhl:QuantumAlgorithm {name: "HHL Algorithm"})
MERGE (linear_systems:Problem {name: "Solving Systems of Linear Equations"})
MERGE (qml:Problem {name: "Quantum Machine Learning"})
MERGE (hhl)-[:APPLIED_TO]->(linear_systems)
MERGE (hhl)-[:APPLIED_TO]->(qml);

// Quantum Phase Estimation (QPE)
MERGE (qpe:QuantumAlgorithm {name: "Quantum Phase Estimation"})
MERGE (eigenvalues:Problem {name: "Finding Eigenvalues of a Unitary Operator"})
MERGE (system_sim:Problem {name: "Quantum System Simulation"})
MERGE (qpe)-[:APPLIED_TO]->(eigenvalues)
MERGE (qpe)-[:APPLIED_TO]->(system_sim);

// Deutsch-Jozsa & Simon's Algorithms
MERGE (dj:QuantumAlgorithm {name: "Deutsch-Jozsa Algorithm"})
MERGE (functions:Problem {name: "Distinguishing Constant vs. Balanced Functions"})
MERGE (dj)-[:APPLIED_TO]->(functions);

MERGE (simon:QuantumAlgorithm {name: "Simon's Algorithm"})
MERGE (period_finding:Problem {name: "Simon's Period-Finding Problem"})
MERGE (simon)-[:APPLIED_TO]->(period_finding);

Query to View the Graph

After running the script, you can use the following query to visualize the entire knowledge graph you've created:

MATCH (n) RETURN n;


For each algorithm, identify additional use cases

Of course. Here are additional use cases for each of the quantum algorithms, expanding on their potential applications.

Foundational & Search Algorithms

Shor's Algorithm

Beyond its well-known applications in breaking RSA and Diffie-Hellman cryptography, Shor's algorithm is fundamentally a period-finding algorithm. This opens it up to other problems where finding a period is the central challenge.

  • Breaking other cryptographic systems: It can be used against other public-key cryptosystems that rely on the difficulty of integer factorization or the discrete logarithm problem, such as Elliptic Curve Cryptography (ECC).

  • Signal processing: In principle, it could be used for analyzing periodic signals, although more specialized and efficient classical algorithms currently exist for these tasks.

Grover's Algorithm

Grover's algorithm's strength lies in its ability to speed up unstructured searches. This has broad implications across many fields.

  • Cryptography: It can be used to perform brute-force attacks on symmetric-key cryptographic algorithms, such as AES, effectively reducing the key size.

  • Collision finding: It can be applied to find collisions in hash functions, which is a critical task in cryptography and data integrity checks.

  • Solving NP-complete problems: For problems where the only known solution is to try all possibilities, Grover's algorithm can provide a quadratic speedup. This includes problems like the Traveling Salesperson Problem and Boolean Satisfiability (SAT).

  • Drug discovery: It can be used to search through large databases of molecular compounds to find candidates with specific properties, accelerating the drug discovery process.

Optimization & Simulation Algorithms

Quantum Annealing / Adiabatic Quantum Computation (AQC)

Quantum annealing is particularly well-suited for a wide range of optimization problems.

  • Financial modeling: It can be used for portfolio optimization, risk analysis, and fraud detection.

  • Machine learning: It can be used to train certain types of machine learning models, such as Boltzmann machines.

  • Materials science: It can be used to design new materials with specific properties by finding the lowest energy configuration of atoms.

Variational Quantum Eigensolver (VQE)

VQE is a versatile algorithm for finding the eigenvalues of a Hamiltonian, with applications beyond quantum chemistry.

  • Drug discovery and development: Simulating molecular interactions to design new drugs and understand their mechanisms of action.

  • Materials science: Designing new catalysts and materials with desired properties.

  • Nuclear physics: Simulating the properties of atomic nuclei.

  • Portfolio optimization: It can be used to find the optimal portfolio of assets that maximizes returns while minimizing risk.

Quantum Approximate Optimization Algorithm (QAOA)

QAOA is another powerful tool for tackling optimization problems, particularly those that can be mapped to a graph structure.

  • Logistics and supply chain management: Optimizing delivery routes, scheduling, and resource allocation.

  • Telecommunications: Optimizing network design and routing.

  • Financial modeling: Finding optimal trading strategies and arbitrage opportunities.

Specialized & Subroutine Algorithms

Harrow-Hassidim-Lloyd (HHL) Algorithm

The HHL algorithm's ability to solve linear systems of equations has applications in various data-intensive fields.

  • Machine learning: It can be used to speed up the training of certain machine learning models, such as support vector machines (SVMs) and principal component analysis (PCA).

  • Data fitting: It can be used to fit data to a model by solving the least-squares problem.

  • Computational fluid dynamics: Solving the systems of linear equations that arise in simulations of fluid flow.

Quantum Phase Estimation (QPE)

QPE is a fundamental building block for many other quantum algorithms, and its applications are correspondingly broad.

  • Factoring: As a subroutine in Shor's algorithm.

  • Quantum simulation: Simulating the time evolution of quantum systems.

  • Calculating reaction rates: Determining the speed of chemical reactions.

Deutsch-Jozsa & Simon's Algorithms

While not having direct practical applications in the same way as the other algorithms, these are crucial for understanding the power of quantum computation.

  • Algorithm development: They serve as a basis and inspiration for the development of more complex and powerful quantum algorithms.

  • Benchmarking quantum hardware: Their relative simplicity makes them useful for testing and benchmarking the performance of quantum computers.

  • Feature selection in machine learning: The Deutsch-Jozsa algorithm can be used to determine if a feature in a dataset is informative or redundant.


Create the additional Cypher statements to support these new use cases

Of course. Here are the additional Cypher statements to expand your knowledge graph with the new use cases.

This script uses MERGE to safely add the new Problem nodes and connect them to the existing QuantumAlgorithm nodes. You can run this script on your existing graph without creating any duplicate data.

Cypher Script for Additional Use Cases

// This script adds new use cases (Problems) and connects them to
// the existing Quantum Algorithm nodes in the graph.

// --- Shor's Algorithm (Additional Use Cases) ---
MERGE (shor:QuantumAlgorithm {name: "Shor's Algorithm"})
MERGE (ecc:Problem {name: "Breaking Elliptic Curve Cryptography"})
MERGE (shor)-[:APPLIED_TO]->(ecc);

// --- Grover's Algorithm (Additional Use Cases) ---
MERGE (grover:QuantumAlgorithm {name: "Grover's Algorithm"})
MERGE (symm_attack:Problem {name: "Symmetric-Key Cryptography Attack"})
MERGE (collision:Problem {name: "Collision Finding in Hash Functions"})
MERGE (tsp:Problem {name: "Traveling Salesperson Problem"})
MERGE (drug_search:Problem {name: "Drug Discovery Candidate Search"})
MERGE (grover)-[:APPLIED_TO]->(symm_attack)
MERGE (grover)-[:APPLIED_TO]->(collision)
MERGE (grover)-[:APPLIED_TO]->(tsp)
MERGE (grover)-[:APPLIED_TO]->(drug_search);

// --- Quantum Annealing (Additional Use Cases) ---
MERGE (annealing:QuantumAlgorithm {name: "Quantum Annealing"})
MERGE (fin_model:Problem {name: "Financial Modeling"})
MERGE (boltzmann:Problem {name: "Training Boltzmann Machines"})
MERGE (mat_design:Problem {name: "Materials Science Design"})
MERGE (annealing)-[:APPLIED_TO]->(fin_model)
MERGE (annealing)-[:APPLIED_TO]->(boltzmann)
MERGE (annealing)-[:APPLIED_TO]->(mat_design);

// --- VQE (Additional Use Cases) ---
MERGE (vqe:QuantumAlgorithm {name: "Variational Quantum Eigensolver"})
MERGE (drug_design:Problem {name: "Drug Design and Development"})
MERGE (catalyst:Problem {name: "Catalyst Design"})
MERGE (nuclear:Problem {name: "Nuclear Physics Simulation"})
MERGE (portfolio:Problem {name: "Portfolio Optimization"})
MERGE (vqe)-[:APPLIED_TO]->(drug_design)
MERGE (vqe)-[:APPLIED_TO]->(catalyst)
MERGE (vqe)-[:APPLIED_TO]->(nuclear)
MERGE (vqe)-[:APPLIED_TO]->(portfolio);

// --- QAOA (Additional Use Cases) ---
MERGE (qaoa:QuantumAlgorithm {name: "Quantum Approximate Optimization Algorithm"})
MERGE (supply_chain:Problem {name: "Supply Chain Management"})
MERGE (telecom:Problem {name: "Telecommunications Network Optimization"})
MERGE (trading:Problem {name: "Financial Trading Strategy Optimization"})
MERGE (qaoa)-[:APPLIED_TO]->(supply_chain)
MERGE (qaoa)-[:APPLIED_TO]->(telecom)
MERGE (qaoa)-[:APPLIED_TO]->(trading);

// --- HHL Algorithm (Additional Use Cases) ---
MERGE (hhl:QuantumAlgorithm {name: "HHL Algorithm"})
MERGE (svm:Problem {name: "Training Support Vector Machines"})
MERGE (data_fit:Problem {name: "Data Fitting"})
MERGE (cfd:Problem {name: "Computational Fluid Dynamics"})
MERGE (hhl)-[:APPLIED_TO]->(svm)
MERGE (hhl)-[:APPLIED_TO]->(data_fit)
MERGE (hhl)-[:APPLIED_TO]->(cfd);

// --- QPE (Additional Use Cases) ---
MERGE (qpe:QuantumAlgorithm {name: "Quantum Phase Estimation"})
MERGE (reaction:Problem {name: "Calculating Chemical Reaction Rates"})
MERGE (qpe)-[:APPLIED_TO]->(reaction);

// --- Deutsch-Jozsa & Simon's (Additional Use Cases) ---
MERGE (dj:QuantumAlgorithm {name: "Deutsch-Jozsa Algorithm"})
MERGE (simon:QuantumAlgorithm {name: "Simon's Algorithm"})
MERGE (benchmark:Problem {name: "Quantum Hardware Benchmarking"})
MERGE (feature_sel:Problem {name: "Feature Selection in Machine Learning"})
MERGE (dj)-[:APPLIED_TO]->(benchmark)
MERGE (simon)-[:APPLIED_TO]->(benchmark)
MERGE (dj)-[:APPLIED_TO]->(feature_sel);


Are there more?

Yes, there are many other quantum algorithms, often specializing in particular domains or serving as fundamental building blocks for more complex procedures. Here are a few more notable examples.

Quantum Simulation

Trotter-Suzuki Decomposition

This isn't a single algorithm but a fundamental method for simulating quantum systems. Think of it as a way to create a "stop-motion animation" of a quantum system's evolution. It approximates a complex, continuous process by breaking it down into a sequence of simple, executable quantum gate operations.

  • Applied To:

    • Materials Science: Simulating the behavior of novel materials and superconductors.

    • Drug Discovery: Modeling molecular dynamics to understand how drugs interact with proteins.

    • Fundamental Physics: Simulating particle interactions in high-energy physics.

Quantum Machine Learning 🤖

Quantum Principal Component Analysis (QPCA)

This is the quantum analog of Principal Component Analysis (PCA), a classical machine learning technique used to reduce the complexity of data. QPCA is designed to find the most important features within a quantum state.

  • Applied To:

    • Dimensionality Reduction: Simplifying complex datasets by identifying the most significant patterns.

    • Pattern Recognition: Finding key features in quantum data for tasks like image recognition.

    • State Tomography: Reconstructing an unknown quantum state from measurements.

Quantum Support Vector Machine (QSVM)

This algorithm uses a quantum computer to enhance the Support Vector Machine, a powerful classical method for classifying data. By mapping data into a vast quantum feature space, a QSVM can potentially find patterns that are invisible to classical machines.

  • Applied To:

    • Data Classification: Sophisticated classification tasks in finance, healthcare, and image analysis.

    • Big Data Analysis: Finding subtle correlations in massive datasets.

Advanced Search & Estimation

Quantum Amplitude Estimation (QAE)

This is a powerful generalization of Grover's algorithm. Instead of just finding a solution, QAE estimates the number of solutions or the probability of finding one. This is incredibly useful for problems that involve estimation rather than just searching.

  • Applied To:

    • Financial Risk Analysis: Performing Monte Carlo simulations to estimate financial metrics like "Value at Risk" much faster than classical methods.

    • Numerical Integration: Calculating the value of complex integrals.

Quantum Random Walks

These are the quantum mechanical equivalent of classical "random walks" or "drunkard's walks." Due to quantum interference, they spread much faster and have different statistical properties, which can be harnessed for algorithmic speedups.

  • Applied To:

    • Element Distinctness Problem: Determining if all elements in a list are unique.

    • Graph Traversal Problems: Finding paths or evaluating properties of complex networks.

    • Quantum System Modeling: Simulating energy transport in systems like photosynthesis.


Create the additional Cypher statements

Of course. Here are the Cypher statements to add these new algorithms and their use cases to your knowledge graph.

This script uses the MERGE command to safely add the new nodes and relationships without creating duplicates, making it safe to run on your existing database.

Cypher Script for New Algorithms

// This script adds a new set of quantum algorithms and their applications
// to the existing knowledge graph.

// --- Quantum Simulation ---
MERGE (tsd:QuantumAlgorithm {name: "Trotter-Suzuki Decomposition"})
MERGE (mats_sci:Problem {name: "Materials Science Simulation"})
MERGE (mol_dyn:Problem {name: "Molecular Dynamics Simulation"})
MERGE (physics_sim:Problem {name: "Fundamental Physics Simulation"})
MERGE (tsd)-[:APPLIED_TO]->(mats_sci)
MERGE (tsd)-[:APPLIED_TO]->(mol_dyn)
MERGE (tsd)-[:APPLIED_TO]->(physics_sim);

// --- Quantum Machine Learning ---
MERGE (qpca:QuantumAlgorithm {name: "Quantum Principal Component Analysis"})
MERGE (dim_red:Problem {name: "Dimensionality Reduction"})
MERGE (patt_rec:Problem {name: "Pattern Recognition"})
MERGE (tomo:Problem {name: "State Tomography"})
MERGE (qpca)-[:APPLIED_TO]->(dim_red)
MERGE (qpca)-[:APPLIED_TO]->(patt_rec)
MERGE (qpca)-[:APPLIED_TO]->(tomo);

MERGE (qsvm:QuantumAlgorithm {name: "Quantum Support Vector Machine"})
MERGE (data_class:Problem {name: "Data Classification"})
MERGE (big_data:Problem {name: "Big Data Analysis"})
MERGE (qsvm)-[:APPLIED_TO]->(data_class)
MERGE (qsvm)-[:APPLIED_TO]->(big_data);

// --- Advanced Search & Estimation ---
MERGE (qae:QuantumAlgorithm {name: "Quantum Amplitude Estimation"})
MERGE (risk:Problem {name: "Financial Risk Analysis"})
MERGE (integral:Problem {name: "Numerical Integration"})
MERGE (qae)-[:APPLIED_TO]->(risk)
MERGE (qae)-[:APPLIED_TO]->(integral);

MERGE (qrw:QuantumAlgorithm {name: "Quantum Random Walks"})
MERGE (element:Problem {name: "Element Distinctness Problem"})
MERGE (graph:Problem {name: "Graph Traversal Problems"})
MERGE (model:Problem {name: "Quantum System Modeling"})
MERGE (qrw)-[:APPLIED_TO]->(element)
MERGE (qrw)-[:APPLIED_TO]->(graph)
MERGE (qrw)-[:APPLIED_TO]->(model);


From <https://gemini.google.com/app>  Google Gemini 2.5 Pro



Neo4j Knowledge Graph of Quantum Computing Algorithms and Use Cases


Variational Quantum Eigensolver


Relationships CSV:

(:QuantumAlgorithm {name: Shor's Algorithm})-[:APPLIED_TO]->(:Problem {name: Integer Factorization})

(:QuantumAlgorithm {name: Shor's Algorithm})-[:APPLIED_TO]->(:Problem {name: Discrete Logarithm Problem})

(:QuantumAlgorithm {name: Shor's Algorithm})-[:APPLIED_TO]->(:Problem {name: Breaking Elliptic Curve Cryptography})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Unstructured Search})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Database Search})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Satisfiability Problems})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Symmetric-Key Cryptography Attack})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Collision Finding in Hash Functions})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Traveling Salesperson Problem})

(:QuantumAlgorithm {name: Grover's Algorithm})-[:APPLIED_TO]->(:Problem {name: Drug Discovery Candidate Search})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Optimization Problems})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Protein Folding})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Logistics and Scheduling})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Financial Modeling})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Training Boltzmann Machines})

(:QuantumAlgorithm {name: Quantum Annealing})-[:APPLIED_TO]->(:Problem {name: Materials Science Design})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Quantum Chemistry Simulation})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Molecular Ground State Calculation})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Drug Design and Development})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Catalyst Design})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Nuclear Physics Simulation})

(:QuantumAlgorithm {name: Variational Quantum Eigensolver})-[:APPLIED_TO]->(:Problem {name: Portfolio Optimization})

(:QuantumAlgorithm {name: Quantum Approximate Optimization Algorithm})-[:APPLIED_TO]->(:Problem {name: Combinatorial Optimization})

(:QuantumAlgorithm {name: Quantum Approximate Optimization Algorithm})-[:APPLIED_TO]->(:Problem {name: Max-Cut Problem})

(:QuantumAlgorithm {name: Quantum Approximate Optimization Algorithm})-[:APPLIED_TO]->(:Problem {name: Supply Chain Management})

(:QuantumAlgorithm {name: Quantum Approximate Optimization Algorithm})-[:APPLIED_TO]->(:Problem {name: Telecommunications Network Optimization})

(:QuantumAlgorithm {name: Quantum Approximate Optimization Algorithm})-[:APPLIED_TO]->(:Problem {name: Financial Trading Strategy Optimization})

(:QuantumAlgorithm {name: HHL Algorithm})-[:APPLIED_TO]->(:Problem {name: Solving Systems of Linear Equations})

(:QuantumAlgorithm {name: HHL Algorithm})-[:APPLIED_TO]->(:Problem {name: Quantum Machine Learning})

(:QuantumAlgorithm {name: HHL Algorithm})-[:APPLIED_TO]->(:Problem {name: Training Support Vector Machines})

(:QuantumAlgorithm {name: HHL Algorithm})-[:APPLIED_TO]->(:Problem {name: Data Fitting})

(:QuantumAlgorithm {name: HHL Algorithm})-[:APPLIED_TO]->(:Problem {name: Computational Fluid Dynamics})

(:QuantumAlgorithm {name: Quantum Phase Estimation})-[:APPLIED_TO]->(:Problem {name: Finding Eigenvalues of a Unitary Operator})

(:QuantumAlgorithm {name: Quantum Phase Estimation})-[:APPLIED_TO]->(:Problem {name: Quantum System Simulation})

(:QuantumAlgorithm {name: Quantum Phase Estimation})-[:APPLIED_TO]->(:Problem {name: Calculating Chemical Reaction Rates})

(:QuantumAlgorithm {name: Deutsch-Jozsa Algorithm})-[:APPLIED_TO]->(:Problem {name: Distinguishing Constant vs. Balanced Functions})

(:QuantumAlgorithm {name: Deutsch-Jozsa Algorithm})-[:APPLIED_TO]->(:Problem {name: Quantum Hardware Benchmarking})

(:QuantumAlgorithm {name: Deutsch-Jozsa Algorithm})-[:APPLIED_TO]->(:Problem {name: Feature Selection in Machine Learning})

(:QuantumAlgorithm {name: Simon's Algorithm})-[:APPLIED_TO]->(:Problem {name: Simon's Period-Finding Problem})

(:QuantumAlgorithm {name: Simon's Algorithm})-[:APPLIED_TO]->(:Problem {name: Quantum Hardware Benchmarking})

(:QuantumAlgorithm {name: Trotter-Suzuki Decomposition})-[:APPLIED_TO]->(:Problem {name: Materials Science Simulation})

(:QuantumAlgorithm {name: Trotter-Suzuki Decomposition})-[:APPLIED_TO]->(:Problem {name: Molecular Dynamics Simulation})

(:QuantumAlgorithm {name: Trotter-Suzuki Decomposition})-[:APPLIED_TO]->(:Problem {name: Fundamental Physics Simulation})

(:QuantumAlgorithm {name: Quantum Principal Component Analysis})-[:APPLIED_TO]->(:Problem {name: Dimensionality Reduction})

(:QuantumAlgorithm {name: Quantum Principal Component Analysis})-[:APPLIED_TO]->(:Problem {name: Pattern Recognition})

(:QuantumAlgorithm {name: Quantum Principal Component Analysis})-[:APPLIED_TO]->(:Problem {name: State Tomography})

(:QuantumAlgorithm {name: Quantum Support Vector Machine})-[:APPLIED_TO]->(:Problem {name: Data Classification})

(:QuantumAlgorithm {name: Quantum Support Vector Machine})-[:APPLIED_TO]->(:Problem {name: Big Data Analysis})

(:QuantumAlgorithm {name: Quantum Amplitude Estimation})-[:APPLIED_TO]->(:Problem {name: Financial Risk Analysis})

(:QuantumAlgorithm {name: Quantum Amplitude Estimation})-[:APPLIED_TO]->(:Problem {name: Numerical Integration})

(:QuantumAlgorithm {name: Quantum Random Walks})-[:APPLIED_TO]->(:Problem {name: Element Distinctness Problem})

(:QuantumAlgorithm {name: Quantum Random Walks})-[:APPLIED_TO]->(:Problem {name: Graph Traversal Problems})

(:QuantumAlgorithm {name: Quantum Random Walks})-[:APPLIED_TO]->(:Problem {name: Quantum System Modeling})


From <Neo4j: quantum-computing database>

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