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arXiv:2201.06620 · IEEE/ACM International Workshop on Quantum Computing Software (QCS)

RosneT: A Block Tensor Algebra Library for Out-of-Core Quantum Computing Simulation

Sergio Sanchez, Javier Conejero, Francesc Lordan, Anna Queralt, Toni Cortés, Rosa M. Badia, Artur García-Sáez

Published Nov 1, 2021• 4 citations
arXivHTMLPDF

Abstract

With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which we represent Quantum States in tensor factorizations. As the extent of a tensor network increases, so does the size of intermediate tensors requiring HPC tools for their manipulation. Simulations of medium-sized circuits cannot fit on local memory, and solutions for distributed contraction of tensors are scarce. In this work we present RosneT, a library for distributed, out-of-core block tensor algebra. We use the PyCOMPSs programming model to transform tensor operations into a collection of tasks handled by the COMPSs runtime, targeting executions in existing and upcoming Exascale supercomputers. We report results validating our approach showing good scalability in simulations of Quantum circuits of up to 53 qubits.

DOI
10.1109/qcs54837.2021.00004

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With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which we represent Quantum States in tensor factorizations. As the extent of a tensor network increases, so does the size of intermediate tensors requiring HPC tools for their manipulation. Simulations of medium-sized circuits cannot fit on local memory, and solutions for distributed contraction of tensors are scarce. In this work we present RosneT, a library for distributed, out-of-core block tensor algebra. We use the PyCOMPSs programming model to transform tensor operations into a collection of tasks handled by the COMPSs runtime, targeting executions in existing and upcoming Exascale supercomputers. We report results validating our approach showing good scalability in simulations of Quantum circuits of up to 53 qubits.
Abstract We present an efficient tensor-network-based approach for simulating large-scale quantum circuits exemplified by quantum support vector machines (QSVMs). Experimentally, leveraging the cuTensorNet library on multiple GPUs, our method effectively reduces the exponential runtime growth to near-quadratic scaling with respect to the number of qubits in practical scenarios. Traditional state-vector simulations become computationally infeasible beyond approximately 50 qubits; in contrast, our simulator successfully handles QSVMs with up to 784 qubits, executing simulations within seconds on a single high-performance GPU. Furthermore, utilizing the message passing interface for multi-GPU environments, our method demonstrates strong linear scalability, effectively decreasing computation time as dataset sizes increase. We validate our framework using the MNIST and Fashion MNIST datasets, achieving successful multiclass classification and highlighting the potential of QSVMs for high-dimensional data analysis. By integrating tensor-network techniques with advanced high-performance computing resources, this work demonstrates both the feasibility and scalability of simulating large-qubit quantum machine learning models, providing a valuable validation tool within the emerging Quantum-HPC ecosystem.
This paper explores the potential of tensor networks for enabling distributed quantum simulation, a crucial step towards scaling up quantum computations. Traditional quantum simulation faces limitations due to the exponential growth of state vector sizes required for complex systems. Distributed quantum simulation aims to overcome this by partitioning the simulation across multiple quantum processors. However, efficient representation and manipulation of the resulting distributed quantum state remain a significant challenge. This work proposes utilizing tensor networks as a framework for representing and processing these distributed quantum states. Tensor networks offer an inherent structure that facilitates efficient parallel computation and minimizes communication overhead between quantum processors. We outline a theoretical framework, detailing the application of tensor network contractions and disentanglement techniques specifically tailored for distributed quantum simulation scenarios. The core claim of this work is that scaling up quantum simulations requires efficient methods for representing and manipulating quantum states, and tensor networks provide a promising avenue for achieving this goal. We present a method to reduce the computational complexity associated with simulating large quantum systems by leveraging the properties of tensor networks. The approach allows for a more scalable simulation strategy, moving beyond the limitations of traditional state vector representations. Further research will explore specific tensor network architectures and optimization strategies for different simulation problems.
The accurate simulation of quantum circuits remains a significant challenge due to the exponential scaling of computational resources with circuit size. This work explores the application of tensor network methods, specifically Matrix Product States (MPS), to provide a scalable approach for simulating quantum circuits. We demonstrate how tensor networks can efficiently represent and manipulate the states of quantum circuits, reducing the computational burden associated with traditional methods. The core claim of this research is that tensor networks offer a viable path to accurately simulating larger and more complex quantum systems. This research introduces a novel framework for symbolic simulation, leveraging the power of tensor network representations to overcome the limitations of conventional simulation techniques. The effectiveness of this approach is illustrated through theoretical analysis and conceptual examples.
Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.
We present the NVIDIA cuQuantum SDK [1], a state-of-the-art library of composable primitives for GPU-accelerated quantum circuit simulations. As the size of quantum devices continues to increase, making their classical simulation progressively more difficult, the availability of fast and scalable quantum circuit simulators becomes vital for quantum algorithm developers, as well as quantum hardware engineers focused on the validation and optimization of quantum devices. The cuQuantum SDK was created to accelerate and scale up quantum circuit simulators developed by the quantum information science community by enabling them to utilize efficient scalable software building blocks optimized for NVIDIA GPU-based platforms. The functional building blocks provided cover the needs of both state vector- and tensor network- based simulators, including approximate tensor network simulation methods based on matrix product state, projected entangled pair state, and other factorized tensor representations. By leveraging the enormous computing power of the latest NVIDIA GPU architectures, quantum circuit simulators that have adopted the cuQuantum SDK demonstrate significant acceleration, compared to CPU-only execution, for both the state vector and tensor network simulation methods. Furthermore, by utilizing the parallel primitives available in the cuQuantum SDK, one can easily transition to distributed GPU-accelerated platforms, including those furnished by cloud service providers and high-performance computing systems deployed by supercomputing centers, extending the scale of possible quantum circuit simulations. The rich capabilities provided by the cuQuantum SDK are conveniently made available via both Python and C application programming interfaces, where the former is directly targeting a broad Python quantum community and the latter allows tight integration with simulators written in any programming language.
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.