Running cobyla Optimizer (from OpenQAOA) on Hybrid Quantum Computing with NVIDIA CUDA Quantum and IBM Qiskit (on IBM QPUs) - Part 1

This article will be expanded and included as a chapter in my upcoming mid-level Introduction to Quantum Computing book.

Part -1

I. Introduction

A. Overview of Quantum Computing

B. The Emergence of Hybrid Quantum-Classical Systems

C. Purpose of the Article: Exploring an Optimization Use Case

II. Understanding the Technologies

A. NVIDIA CUDA Quantum — H100

1. Architecture and Capabilities

2. Role in Quantum-Classical Hybrid Systems

B. IBM Quantum Computing and Qiskit

1. Qiskit Overview

2. IBM Quantum Computing Capabilities

III. The Optimization Use Case

A. Description of the Problem

B. Relevance and Applications in Various Fields

IV. Designing the Hybrid Quantum-Classical Solution

A. Integrating CUDA Quantum — H100 with IBM Quantum Computing

B. Role of CUDA in Managing Quantum-Classical Interactions

C. Use of Qiskit for Quantum Algorithm Implementation

V. Implementation Details

A. Setting Up the CUDA Quantum — H100 Environment

B. Developing Quantum Circuits Using Qiskit

C. Interfacing Between CUDA Quantum and Qiskit

Part -2

VI. Optimization Algorithm

A. Algorithm Selection and Rationale

B. Quantum Algorithm Adaptation for the Hybrid System

C. Leveraging CUDA Quantum for Enhanced Performance

VII. Results and Analysis

A. Performance Metrics and Results

B. Comparison with Classical and Pure Quantum Approaches

C. Discussion of Results

VIII. Challenges and Limitations

A. Technical Challenges in Hybrid System Integration

B. Limitations of Current Quantum Hardware

C. Potential Solutions and Future Directions

IX. Concluding Remarks

A. Summary of Findings

B. Implications for Future Quantum Computing Developments

C. Final Thoughts on the Potential of Hybrid Quantum-Classical Computing

X. References

A. Academic and Industry Sources

B. Further Reading and Resources

Appendix A

Analysis of the performance metrics and the example code

Appendix B

Benefits of Hybrid Quantum Computing for these optimization use cases.

Details of the use cases specific to Healthcare, Telecommunications, and Financial Service Industries.

I. Introduction

A. Overview of Quantum Computing

Quantum computing represents a significant leap from classical computing, harnessing the peculiar properties of quantum mechanics to process information in fundamentally new ways. Unlike classical bits that represent data as 0s or 1s, quantum computers use quantum bits (qubits), which can exist in multiple states simultaneously due to superposition. Another key principle, entanglement, allows qubits to be interconnected in a way that the state of one qubit can depend on the state of another, no matter the distance between them.

This unique approach enables quantum computers to solve certain complex problems much faster than classical computers. They are particularly adept at tasks like prime factorization, optimization problems, and simulation of quantum systems, which are crucial in fields like cryptography, material science, and drug discovery. However, the technology is still in its nascent stages, with challenges such as qubit stability, error rates, and scalability.

B. The Emergence of Hybrid Quantum-Classical Systems

As the field of quantum computing evolves, a new paradigm is emerging: hybrid quantum-classical systems. These systems combine the strengths of quantum and classical computing to tackle problems that are currently beyond the reach of either technology alone. In a hybrid system, the quantum computer handles specific tasks that leverage its quantum advantages, like executing complex algorithms or processing vast, multidimensional datasets. The classical computer manages tasks better suited to its capabilities, such as data input/output, control operations, and running parts of algorithms, where classical computing is more efficient.

This synergy allows for more practical and immediate applications of quantum computing, as it mitigates some of the current limitations of quantum hardware, such as qubit instability and limited qubit count. Hybrid systems are seen as a crucial step in the evolution of quantum computing, providing a pathway to practical applications even before fully-fledged quantum computers are available.

C. Purpose of the Article: Exploring an Optimization Use Case

The purpose of this article is to delve into a specific use case that demonstrates the power and potential of hybrid quantum-classical systems. We focus on an optimization problem, a class of problems well-suited to quantum computation’s strengths. By leveraging the combined capabilities of NVIDIA’s CUDA Quantum (running on NVIDIA H100 GPUs in Oracle Cloud Infrastructure), a cutting-edge classical computing platform optimized for quantum algorithms, and IBM’s Quantum Computing framework powered by Qiskit, we aim to showcase how these two technologies can be integrated to solve complex optimization problems more efficiently than classical or quantum approaches alone.

This exploration is not just theoretical but also practical, guiding readers through the intricacies of setting up a hybrid system, implementing the optimization algorithm, and analyzing the results. The case study will highlight the unique advantages of hybrid systems, address the challenges faced in integration and execution, and shed light on the future possibilities this collaboration holds for quantum computing applications.

II. Understanding the Technologies

A. NVIDIA CUDA Quantum (on OCI H100 GPU Cloud)

1. Architecture and Capabilities

The NVIDIA CUDA Quantum (on OCI H100 GPU Cloud) represents a significant advancement in the realm of computing, tailored specifically for quantum-classical hybrid systems. This platform is built upon NVIDIA’s robust CUDA (Compute Unified Device Architecture) framework, which has long been at the forefront of parallel computing and GPU acceleration. The NVIDIA H100, part of the Hopper GPU architecture series, is designed to efficiently handle the intensive computational demands typical of quantum computing algorithms. Phenomenal Oracle Cloud Super Clusters back this setup.

Key features of the CUDA Quantum on NVIDIA H100 include:

Enhanced Parallel Processing Capabilities: The H100 leverages thousands of small, efficient cores capable of performing simultaneous operations. This is crucial for quantum simulation, where representing and manipulating qubits requires massive parallelism.

Tensor Cores: These specialized cores are adept at handling the matrix operations and linear algebra that are fundamental to quantum computing algorithms. They offer a significant speedup over traditional CPU-based systems for these tasks.

High Memory Bandwidth: Quantum simulations are memory-intensive. The H100 comes with substantial memory and high bandwidth, reducing bottlenecks in data transfer and enabling more efficient computations.

CUDA Toolkit Enhancements: The platform is supported by a suite of software tools specifically optimized for quantum computing. These include libraries and development tools that ease the implementation of quantum algorithms.

2. Role in Quantum-Classical Hybrid Systems

In a hybrid quantum-classical system, the CUDA Quantum plays a pivotal role. Its primary function is to manage the classical aspects of quantum algorithms and simulations. This involves several key responsibilities:

Algorithm Preprocessing and Postprocessing: Many quantum algorithms require classical preprocessing to set up the problem and postprocessing to interpret the results. The H100 efficiently handles these tasks, ensuring a seamless flow of operations between the quantum and classical components.

Control and Synchronization: In hybrid systems, coordination between the quantum and classical processors is critical. The H100 GPU is responsible for controlling the timing and sequence of operations, ensuring that the quantum processor is fed with the right data at the right time and that its outputs are correctly received and interpreted.

Simulation and Modeling: Before running on actual quantum hardware, quantum algorithms often need to be simulated. The H100 can rapidly simulate quantum circuits, allowing for algorithm testing and refinement. This simulation capability is vital for developing and optimizing quantum algorithms before they are deployed on quantum processors.

Parallel Task Execution: Some hybrid algorithms offload certain computationally intensive tasks to the classical processor. The H100’s parallel processing abilities make it ideal for executing these tasks concurrently with the quantum processor’s operations, thereby enhancing overall system performance.

The NVIDIA CUDA Quantum is not just a powerful classical computing component; it is a critical enabler in the hybrid quantum-classical ecosystem, bridging the gap between the two worlds and maximizing the strengths of each.

B. IBM Quantum Computing and Qiskit

1. Qiskit Overview

Qiskit is an open-source quantum computing software development framework provided by IBM. It’s designed to enable users, ranging from novices to experienced quantum researchers, to develop and run quantum computing programs. Qiskit provides tools for creating quantum algorithms, running them on actual quantum machines or simulators, and analyzing the results. Key features of Qiskit include:

Modular Structure: Qiskit is composed of various modules, each targeting specific aspects of quantum computing. For instance, Qiskit Terra for building quantum circuits, Qiskit Aer for simulation, Qiskit Ignis for quantum error correction, and Qiskit Aqua for quantum algorithms.

Hardware Accessibility: Qiskit seamlessly integrates with IBM’s quantum computing hardware, allowing users to run their quantum programs on real quantum processors hosted on the IBM Quantum cloud service.

Community and Educational Resources: With its extensive documentation, tutorials, and active community, Qiskit is not just a tool but also a learning platform for those interested in quantum computing.

Flexibility and Extensibility: Users can create custom quantum circuits, explore different quantum algorithms, and even contribute to the Qiskit’s development, making it a highly adaptable and evolving tool.

2. IBM Quantum Computing Capabilities

IBM is a pioneer in the field of quantum computing, and its continuous advancements in quantum technology have led to significant developments in quantum hardware and associated services. The capabilities of IBM Quantum Computing include:

Advanced Quantum Processors: IBM has developed a series of quantum processors with increasing qubit counts and quality. These processors are at the core of IBM’s quantum computing offerings, featuring improvements in coherence times, error rates, and connectivity.

Quantum System Integration: IBM has focused not just on qubits but on the entire quantum system, including hardware for qubit control and readout, cryogenic systems to maintain ultra-low temperatures, and software for quantum circuit compilation and optimization.

Quantum Cloud Services: Through IBM Quantum Experience, users can access quantum processors via the cloud, making quantum computing accessible worldwide. This service is integral for researchers, developers, and businesses to experiment with quantum algorithms without needing their quantum hardware.

Collaborative Ecosystem: IBM has fostered a collaborative environment through the IBM Quantum Network, a community of industry, academic, and research institutions. This network aims to advance quantum computing and explore practical applications.

Continued Research and Development: IBM continually invests in research to overcome current challenges in quantum computing, like qubit scalability, error correction, and the development of quantum-safe cryptography.

In the context of the hybrid quantum-classical system described in this article, IBM’s quantum computing capabilities, accessed and managed through Qiskit, provide the quantum backbone. This allows for the exploration of complex optimization problems where quantum computing’s strengths in handling vast solution spaces can be fully leveraged, complemented by the robust classical computational power of the NVIDIA CUDA Quantum on OCI H100 GPU Superclusters.

III. The Optimization Use Case

A. Description of the Problem

The optimization problem we focus on in this use case is a complex, high-dimensional challenge, typical in many real-world scenarios. This particular problem involves finding the optimal solution from a vast set of possibilities, where the number of variables and constraints makes traditional computational methods inefficient or even infeasible.

Key characteristics of this problem include:

B. Relevance and Applications in Various Fields

Optimization problems of this nature are not just theoretical challenges; they have practical implications and applications across various fields:

By applying a hybrid quantum-classical computing approach to such a problem, the goal is to harness the quantum computer’s ability to efficiently navigate vast solution spaces and handle complex, interdependent variables, alongside the classical computer’s strength in managing linear computations, data handling, and real-world interfacing. This symbiosis promises to offer more efficient, accurate, and scalable solutions than what is achievable with either technology alone.

IV. Designing the Hybrid Quantum-Classical Solution

A. Integrating CUDA Quantum with IBM Quantum Computing

The integration of NVIDIA’s CUDA Quantum with IBM’s quantum computing platform, using Qiskit, is a critical step in creating a robust hybrid quantum-classical system. This integration requires a careful orchestration of hardware and software components:

1. Hardware Interfacing: Establishing a reliable and efficient communication channel between the CUDA Quantum — H100 platform and IBM’s quantum hardware is essential. This involves configuring network protocols and ensuring secure data transmission.

2. Software Integration: Leveraging Qiskit’s capabilities to interface with CUDA-enabled devices. The CUDA Toolkit and Qiskit must be harmonized to ensure that quantum algorithms can be seamlessly executed, with CUDA handling the classical computation aspects.

3. Data Transfer Optimization: Optimizing the transfer of data between the classical and quantum systems. This includes minimizing latency and maximizing throughput in the exchange of input parameters, interim computations, and final results.

4. Synchronization and Timing: Ensuring accurate synchronization between quantum and classical computations. This is crucial for algorithms where the output of one computation stage directly influences the next.

B. Role of CUDA in Managing Quantum-Classical Interactions

In a hybrid system, CUDA plays a multifaceted role in managing the interactions between quantum and classical computations:

1. Preprocessing of Data: Before a quantum algorithm is run, CUDA can be used for preparing and structuring data, a process that often requires substantial classical computing power.

2. Parallel Processing of Interim Computations: Quantum algorithms frequently need intermediate classical computation. CUDA’s parallel processing capabilities are well-suited for these tasks, efficiently handling large-scale computations.

3. Real-Time Control and Feedback: CUDA can provide real-time control signals and feedback to the quantum system, based on intermediate results. This is particularly important in adaptive quantum algorithms.

4. Post-Quantum Processing: After quantum computation, CUDA assists in decoding, analyzing, and further processing the results, which often includes handling large datasets and performing complex classical algorithms.

C. Use of Qiskit for Quantum Algorithm Implementation

Qiskit plays a pivotal role in implementing quantum algorithms within this hybrid framework:

1. Quantum Circuit Design: Utilizing Qiskit to design and simulate quantum circuits. This includes setting up the initial states, gates, and measurements required for the quantum computation.

2. Algorithm Adaptation and Optimization: Adapting quantum algorithms to run efficiently on IBM’s quantum hardware, including optimizing them to handle real-world constraints like qubit connectivity and error rates.

3. Execution on Quantum Hardware: Facilitating the execution of these algorithms on IBM’s quantum processors, managed through Qiskit’s interface.

4. Result Retrieval and Analysis: Using Qiskit to retrieve results from quantum computations and perform initial analysis. These results are then passed back to the CUDA platform for further processing.

Integrating CUDA Quantum with IBM Quantum Computing using Qiskit involves a sophisticated interplay of hardware and software components. CUDA’s role is pivotal in handling the classical aspects of the computations, while Qiskit enables the design, execution, and initial analysis of quantum algorithms, creating a cohesive and efficient hybrid quantum-classical computing system.

V. Implementation Details

A. Setting Up the CUDA Quantum (OCI H100 GPU Environment)

Implementing a hybrid quantum-classical computing system begins with setting up the CUDA Quantum environment. This process involves several critical steps:

1. Hardware Installation and Configuration:

The Terraform code for this reference architecture is available as a sample stack in Oracle Cloud Infrastructure Resource Manager. You can also download the code from GitHub, and customize it to your requirements.

For Oracle Cloud Infrastructure — High Performance Computing with an RDMA cluster network, deploy by using Oracle Cloud Infrastructure Resource Manager: A. Click Deploy to Oracle Cloud If you aren’t already signed in, enter the tenancy and user credentials.

B. Review and accept the terms and conditions. C. Select the region where you want to deploy the stack. D. Follow the on-screen prompts and instructions to create the stack. E. After creating the stack, click Terraform Actions, and select Plan. F. Wait for the job to be completed, and review the plan. To make any changes, return to the Stack Details page, click Edit Stack, and make the required changes. Then, run the Plan action again.

G. If no further changes are necessary, return to the Stack Details page, click Terraform Actions, and select Apply.

→ For Oracle Cloud Infrastructure — High Performance Computing, deploy using the Terraform code in GitHub: 1. Go to GitHub. 2. Clone or download the repository to your local computer. 3. Follow the instructions in the README document.

Follow the link for information on Oracle Supercluster and NVIDIA H100.

2. Software Setup: Install the CUDA Toolkit, which includes the necessary drivers, libraries, and development tools. It’s crucial to use the version of the CUDA Toolkit that is compatible with the H100 GPUs.

Use the build instructions from this GitHub repository.

3. Optimization for Quantum Workloads: Configure the H100 GPUs to optimize their performance for quantum workloads. This involves tuning parameters such as memory usage, processor clocks, and bandwidth settings to align with the specific demands of quantum simulations and computations.

4. Integration with Existing Infrastructure: Ensure that the CUDA environment is integrated with the existing classical computing infrastructure, including data storage, network architecture, and security protocols.

5. Testing and Validation: Conduct comprehensive tests to validate the setup. This includes running benchmark programs to ensure that the GPUs are performing as expected and that there are no issues with the software and hardware integration.

B. Developing Quantum Circuits Using Qiskit

Developing quantum circuits with Qiskit is a key component of implementing hybrid quantum-classical systems:

1. Learning and Using Qiskit: Familiarize with Qiskit’s functionalities and syntax. This involves understanding how to use its various modules for creating quantum circuits, simulation, and interfacing with IBM quantum hardware.

2. Circuit Design and Simulation: Design quantum circuits using Qiskit, tailored to the specific optimization problem. Initially, these circuits can be tested and refined using Qiskit’s simulator, which mimics the behavior of a quantum computer.

3. Algorithm Implementation: Implement the optimization algorithm using quantum circuits. This involves encoding the problem into a quantum framework and ensuring that the algorithm can be efficiently executed on a quantum processor.

4. Testing on Real Quantum Hardware: Once the quantum circuits are ready, use Qiskit to run them on IBM’s quantum computers. Analyze the results to refine the circuits and algorithms as needed.

C. Interfacing Between CUDA Quantum and Qiskit

Creating an effective interface between CUDA Quantum and Qiskit is essential for the successful operation of the hybrid system:

1. Data Exchange Mechanisms: Establish mechanisms for the efficient exchange of data between CUDA and Qiskit. This includes setting up APIs or other communication protocols that allow for the seamless transfer of input data, interim results, and final outputs.

2. Synchronization of Operations: Implement synchronization protocols to ensure that the operations on the CUDA platform and the quantum computations via Qiskit are properly aligned in time. This is crucial for algorithms that require iterative interactions between classical and quantum computations.

3. Error Handling and Correction: Develop error handling mechanisms to manage potential issues in data transfer or computation discrepancies between the classical and quantum computations.

4. Performance Monitoring and Optimization: Continuously monitor the performance of the hybrid system and make necessary adjustments. This could involve optimizing data transfer speeds, computational loads, and balancing tasks between the classical and quantum systems.

Implementing a hybrid quantum-classical computing system entails meticulous setup and configuration of the CUDA Quantum on OCI H100 GPU environment, development of quantum circuits using Qiskit, and establishing a robust and efficient interface between the classical and quantum computing realms. This setup paves the way for tackling complex optimization problems with unprecedented efficiency.

In the next part, I will share the details and Python code around the Optimization Algorithm using Cobyla optimizer from OpenQaOA.