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arXiv:1807.07914 · PLoS ONE

Validating quantum-classical programming models with tensor network simulations

Alexander McCaskey, Eugene Dumitrescu, Mengsu Chen, Dmitry I. Lyakh, Travis S. Humble

Published Dec 10, 2018• 43 citations
arXivHTMLPDF

Abstract

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.

DOI
10.1371/journal.pone.0206704

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The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.
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.
The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.
The Tensor Network Quantum Virtual Machine (TNQVM) is a high-performance classical circuit simulation backend for the eXtreme-scale ACCelerator (XACC) framework that leverages the Intelligent Tensor (ITensor) library for tensor network--based quantum circuit simulation. However, TNQVM's original C++ ITensor backend is tied to an older integrated release, limiting access to newer tensor network algorithms, diagnostics, and performance improvements available in the actively developed Julia-based ITensors ecosystem. We introduce JuliaITensorTNQVM, an interoperability layer that bridges TNQVM's C++ visitor infrastructure and the Julia-ITensors runtime through a C-compatible application binary interface. This design preserves the existing XACC/TNQVM programming model while enabling access to modern tensor network capabilities, including entanglement entropy diagnostics exposed directly to XACC. We evaluate the implementation through two studies: a Page-curve verification protocol using Haar-random states, and QAOA MaxCut simulations on 3-regular graphs. Within these tested regimes, results are consistent with expected entanglement behavior and established scaling trends, supporting JuliaITensorTNQVM as a practical modernization path for tensor network simulation in TNQVM.
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.
Hybrid quantum-classical workflows have become standard methods for executing variational algorithms and other quantum simulation techniques, which are key applications for noisy intermediate scale quantum (NISQ) computers. Validating these simulations is an important task which helps gauge the progress of quantum computer development, and classical simulation can serve as a tool to this end. Both exact and more scalable approximate methods with quantifiable error bounds can be used in validation tasks where the applicable metrics include the distance from a calculable ground truth, the quality of an error model fit to data, etc. Here we present a library extension that includes methods for validation of quantum simulations based on scalable hybrid workflows executable on high performance computers. We provide examples that use approximate methods based on tensor networks and stabilizer simulators to bound the error of quantum simulations on NISQ hardware.
Despite the advantage quantum computers are expected to deliver when performing simulations compared to their classical counterparts, the current noisy intermediate-scale quantum (NISQ) devices remain limited in their capabilities. The training of parameterized quantum circuits (PQCs) remains a significant practical challenge, exacerbated by the requirement of shallow circuit depth necessary for their hardware implementation. Hybrid methods employing classical computers alongside quantum devices, such as the Variational Quantum Eigensolver (VQE), have proven useful for analyzing the capabilities of NISQ devices to solve relevant optimization problems. Still, in the simulation of complex structures involving the many-body problem in quantum mechanics, major issues remain about the representation of the system and obtaining results which clearly outperform classical computational devices. In this research contribution we propose the use of parameterized Tensor Networks (TNs) to attempt an improved performance of the VQE algorithm. A joint approach is presented where the Hamiltonian of a system is encapsulated into a Matrix Product Operator (MPO) within a parameterized unitary TN hereby splitting up the optimization task between the TN and the VQE. We show that the hybrid TN-VQE implementation improves the convergence of the algorithm in comparison to optimizing randomly-initialized quantum circuits via VQE.