Applications and Potential of Stacked Chips in Parallel Computing for Quantum Computing Simulation

Abstract

With the rapid development of quantum computing, simulating quantum systems has become an essential tool for verifying quantum algorithms and studying quantum behavior. Stacked chips (such as AI chips using CoWoS 3D stacking technology) demonstrate significant potential in quantum computing simulation due to their high-density interconnects, high-bandwidth memory, and powerful parallel computing capabilities. This report analyzes the application of stacked chips in quantum circuit simulation, tensor network computation, quantum algorithm optimization, and quantum noise simulation. It explores their technical advantages, implementation methods, and limitations while outlining future development directions. The report concludes that stacked chips are currently most suitable for simulating small to medium-scale quantum systems and supporting hybrid quantum-classical computing architectures, with further potential through hardware and algorithmic optimizations.

 Introduction

Quantum computing is based on quantum mechanical principles, utilizing the superposition and entanglement of qubits to achieve computational capabilities beyond classical computing. However, limited by the scale and stability of current quantum hardware, classical computing simulation of quantum systems remains indispensable in quantum research. Stacked chips, especially high-performance AI chips using 3D stacking technologies like CoWoS, have become ideal platforms for simulating quantum computing due to their parallel computing capabilities and heterogeneous integration features. This report explores how stacked chips utilize parallel computing to simulate quantum computing, analyzing their technical implementation, application scenarios, challenges, and providing recommendations for future development.

 Technical Advantages of Stacked Chips

Stacked chips employ 2.5D/3D packaging technologies (such as CoWoS), efficiently integrating multiple chips through silicon interposers and through-silicon vias (TSVs). Their advantages in parallel computing include:

1. High-density interconnects: Low-latency, high-bandwidth chip-to-chip interconnects (such as NVLink) supporting rapid data transfer.

2. High-bandwidth memory (HBM): HBM3 provides bandwidth of several TB/s, meeting the large-scale data access requirements of quantum simulation.

3. Heterogeneous integration: Integration of GPUs, CPUs, and specialized accelerators, adapting to diverse computational tasks.

4. Massive parallelism: Thousands of computing cores (such as NVIDIA H100's CUDA cores) support highly parallel matrix and tensor operations.

5. Low-power design: Shortened interconnect lengths reduce power consumption, suitable for long-duration simulation tasks.

These characteristics enable stacked chips to excel in handling the intensive linear algebra operations and high-dimensional tensor calculations required for quantum simulation.

 Core Tasks in Quantum Computing Simulation

Quantum computing simulation involves the following key tasks:

1. Quantum circuit simulation: Simulating the evolution of quantum gates on quantum states, involving computations of high-dimensional state vectors or density matrices.

2. Quantum state representation: A system of n qubits requires a 2^n dimensional complex vector, with memory requirements growing exponentially with scale.

3. Quantum algorithm verification: Simulating algorithms such as Shor's factorization, Grover's search, or Variational Quantum Eigensolver (VQE).

4. Quantum system simulation: Simulating quantum behaviors of molecular energy levels, quantum field theory, or other physical systems.

5. Noise and error correction simulation: Studying quantum noise models and the performance of error correction codes (such as surface codes).

These tasks require efficient parallel computing and substantial memory, for which stacked chip architecture provides an ideal hardware foundation.

 Implementation Methods for Quantum Computing Simulation with Stacked Chips

Stacked chips utilize parallel computing to simulate quantum computing through the following approaches:

1. Parallelization of quantum circuit simulation

   - Method: Decomposing matrix operations of quantum gates into independent subtasks, distributing them to multiple computing cores for parallel execution. HBM accelerates state vector access, reducing I/O bottlenecks.

   - Example: NVIDIA cuQuantum SDK utilizes CoWoS-packaged GPUs to simulate circuits of 30-40 qubits, achieving efficient parallel processing through state vector partitioning.

2. Distributed simulation

   - Method: Distributing large-scale quantum system simulation tasks across multiple stacked chips, using high-bandwidth interconnects like NVLink to reduce communication overhead.

   - Example: Google TensorFlow Quantum and NVIDIA CUDA-Q platforms use multi-GPU clusters to simulate complex quantum circuits.

3. Tensor network simulation

   - Method: Using Matrix Product States (MPS) or Matrix Product Operators (MPO) to compress quantum state representations, simulating quantum systems through tensor contraction. Tensor Cores in stacked chips accelerate tensor operations.

   - Example: When simulating one-dimensional quantum many-body systems (such as the Ising model), tensor network methods efficiently process high-dimensional tensors using GPU parallel computing capabilities.

4. Quantum algorithm optimization

   - Method: In hybrid quantum-classical algorithms (such as VQE), stacked chips execute gradient calculations and parameter optimization in parallel, accelerating the iteration process.

   - Example: When simulating quantum chemical systems, stacked chips rapidly process Hamiltonian calculations and data preprocessing.

5. Noise and error correction simulation

   - Method: Simulating quantum noise through parallel Monte Carlo methods, or modeling error correction codes using linear algebra operations.

   - Example: When simulating the error correction performance of surface codes, parallel cores in stacked chips significantly shorten computation time.

 Application Cases

1. NVIDIA CUDA-Q platform: Using CoWoS-packaged GPUs (such as A100, H100) to simulate quantum circuits, supporting simulation of up to 40 qubits, with efficient data transfer through HBM and NVLink.

2. Quantum chemistry simulation: Stacked chips accelerate molecular energy level calculations using VQE algorithms, supporting drug design and materials science research.

3. Quantum machine learning: Simulating quantum neural networks or quantum support vector machines, with AI cores in stacked chips processing training and simulation tasks in parallel.

 Technical Limitations and Challenges

1. Exponential resource requirements: Simulating n qubits requires 2^n memory and computational resources; stacked chips struggle to simulate systems beyond 50 qubits.

2. Precision limitations: Low-precision computing in AI chips (such as FP16) may affect the high-precision requirements of quantum simulation, requiring specialized optimization.

3. Communication overhead: Data exchange in multi-chip distributed simulation may become a bottleneck, although high-bandwidth interconnects have alleviated some issues.

4. Lack of universality: Stacked chips excel at specific simulation tasks but rely on specialized algorithms for simulating highly entangled systems.

 Future Development Directions

1. Specialized simulation chips: Developing stacked chips specifically for quantum simulation, integrating specialized tensor processing units and higher bandwidth memory.

2. Integration with quantum hardware: Utilizing the heterogeneous integration capabilities of CoWoS to use stacked chips as classical control units for quantum computing, implementing quantum-classical hybrid systems.

3. Algorithm optimization: Combining efficient algorithms such as tensor networks and quantum Monte Carlo to expand the simulation scale of stacked chips.

4. Low-temperature adaptability research: Exploring the application of stacked chips in low-temperature environments to support the packaging requirements of quantum computing hardware.

The announcement of Fujitsu and RIKEN's 256-qubit superconducting quantum computer on April 22, 2025, represents a major milestone in quantum computing hardware development. This achievement, which quadrupled the qubit count from their previous 64-qubit machine announced in October 2023, was made possible through new high-density packaging technology - which aligns perfectly with our discussion of advanced packaging techniques like CoWoS.

This development is particularly relevant to our topic because：

1. Simulation Scaling Challenge: As real quantum computers scale up to 256 qubits, the need for powerful classical simulation becomes even more critical. Directly simulating a 256-qubit system would require 2^256 complex numbers - far beyond any classical computer's capability. This emphasizes the importance of advanced simulation techniques using stacked chips.
2. Hybrid Computing Approach: Fujitsu's plan to offer this quantum computer via their "Fujitsu Hybrid Quantum Computing Platform" in Q1 2025 highlights the growing importance of hybrid quantum-classical computing architectures, where stacked chips can serve as efficient classical partners.
3. Error Correction Development: The mention of error correction algorithm experiments reinforces the need for efficient simulation platforms to develop and test quantum error correction codes before implementing them on actual quantum hardware.
4. NISQ Limitations: The acknowledgment that this system is still in the NISQ (Noisy Intermediate-Scale Quantum) era, requiring about 60,000+ qubits for fully error-corrected quantum computing (FTQC), underlines the continued importance of classical simulation for algorithm development and validation.

This development strengthens the case for investing in advanced classical simulation capabilities using stacked chips, as they will remain essential tools for quantum algorithm development, validation, and optimization even as quantum hardware continues to advance. The high-density packaging techniques pioneered by Fujitsu and RIKEN for their quantum processor may also inform future developments in classical stacked chip architectures optimized for quantum simulation.

 Conclusion

Stacked chips demonstrate significant potential in simulating quantum computing due to their high-density interconnects, high-bandwidth memory, and massive parallel computing capabilities. They are particularly suitable for tasks such as quantum circuit simulation, tensor network computation, quantum algorithm verification, and noise simulation. Currently, stacked chips are most suitable for simulating small to medium-scale quantum systems (fewer than 50 qubits) and serving as classical computing platforms in hybrid quantum-classical systems. Despite limitations from exponential resource requirements and precision issues, the application prospects of stacked chips in quantum simulation will further expand through hardware improvements and algorithmic optimization. In the future, with advancements in quantum computing and packaging technologies, stacked chips are expected to play an increasingly important role in quantum research and applications.

 References

1. NVIDIA cuQuantum SDK Documentation, 

https://developer.nvidia.com/cuquantum-sdk

2. CoWoS Technology Overview, TSMC Official Website, 

https://www.tsmc.com

3. Quantum Computing Simulation Research, Google TensorFlow Quantum,

https://www.tensorflow.org/quantum

4. Tensor Network Simulation Methods, Related Academic Papers, arXiv.

5. Fujitsu and RIKEN develop world-leading 256-qubit superconducting quantum computer ,

https://pr.fujitsu.com/jp/news/2025/04/22.html