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arXiv:2410.15080

Quantum-Classical Computing via Tensor Networks

Nathaniel Tornow, Christian B. Mendl, Pramod Bhatotia

Published Oct 19, 2024• 0 citations
arXivHTMLPDF

Abstract

Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive overhead due to a naive postprocessing method that neglects potential optimizations in the circuit structure. To overcome this, we introduce qTPU, a framework for scalable hybrid quantum-classical processing using tensor networks. By leveraging our hybrid quantum circuit contraction method, we represent circuit execution as the contraction of a hybrid tensor network (h-TN). The qTPU compiler automates efficient h-TN generation, optimizing the balance between estimated error and postprocessing overhead, while the qTPU runtime supports large-scale h-TN contraction using quantum and classical accelerators. Our evaluation shows orders-of-magnitude reductions in postprocessing overhead, a $10^4\times$ speedup in postprocessing, and a 20.7$\times$ reduction in overall runtime compared to the state-of-the-art Qiskit-Addon-Cutting (QAC).

DOI
10.48550/arxiv.2410.15080

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Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive overhead due to a naive postprocessing method that neglects potential optimizations in the circuit structure. To overcome this, we introduce qTPU, a framework for scalable hybrid quantum-classical processing using tensor networks. By leveraging our hybrid quantum circuit contraction method, we represent circuit execution as the contraction of a hybrid tensor network (h-TN). The qTPU compiler automates efficient h-TN generation, optimizing the balance between estimated error and postprocessing overhead, while the qTPU runtime supports large-scale h-TN contraction using quantum and classical accelerators. Our evaluation shows orders-of-magnitude reductions in postprocessing overhead, a 104×10^4\times104× speedup in postprocessing, and a 20.7×\times× reduction in overall runtime compared to the state-of-the-art Qiskit-Addon-Cutting (QAC).
Quantum circuit compilation is a critical step in realizing quantum computation, aiming to translate high-level quantum algorithms into a sequence of low-level gate operations executable on a quantum hardware. Traditional compilation methods often suffer from exponential scaling in the representation of the quantum state space, leading to prohibitive computational costs. This work introduces a novel approach to quantum circuit compilation utilizing tensor networks. We represent quantum circuits and their resulting states as higher-order tensor networks, enabling efficient manipulation and contraction of these representations. Our algorithm leverages tensor contraction and permutation techniques specifically tailored to the inherent structure of quantum circuits, minimizing the rank of the tensor networks and, consequently, reducing computational overhead. This approach offers the potential for significant speedups compared to conventional compilation techniques, addressing the core challenge of exponential scaling in quantum state representation. The method's effectiveness is demonstrated through theoretical analysis and a novel compilation algorithm.
Quantum processing unit (QPU) has to satisfy highly demanding quantity and quality requirements on its qubits to produce accurate results for problems at useful scales. Furthermore, classical simulations of quantum circuits generally do not scale. Instead, quantum circuit cutting techniques cut and distribute a large quantum circuit into multiple smaller subcircuits feasible for less powerful QPUs. However, the classical post-processing incurred from the cutting introduces runtime and memory bottlenecks. Our tool, called ScaleQC, addresses the bottlenecks by developing novel algorithmic techniques including (1) a quantum states merging framework that quickly locates the solution states of large quantum circuits; (2) an automatic solver that cuts complex quantum circuits to fit on less powerful QPUs; and (3) a tensor network based post-processing that minimizes the classical overhead. Our experiments demonstrate both QPU requirement advantages over the purely quantum platforms, and runtime advantages over the purely classical platforms for benchmarks up to 1000 qubits.
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.
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Quantum computing (QC) is a new paradigm offering the potential of exponential speedups over classical computing for certain computational problems. Each additional qubit doubles the size of the computational state space available to a QC algorithm. This exponential scaling underlies QC’s power, but today’s Noisy Intermediate-Scale Quantum (NISQ) devices face significant engineering challenges in scalability. The set of quantum circuits that can be reliably run on NISQ devices is limited by their noisy operations and low qubit counts. This paper introduces CutQC, a scalable hybrid computing approach that combines classical computers and quantum computers to enable evaluation of quantum circuits that cannot be run on classical or quantum computers alone. CutQC cuts large quantum circuits into smaller subcircuits, allowing them to be executed on smaller quantum devices. Classical postprocessing can then reconstruct the output of the original circuit. This approach offers significant runtime speedup compared with the only viable current alternative—purely classical simulations—and demonstrates evaluation of quantum circuits that are larger than the limit of QC or classical simulation. Furthermore, in real-system runs, CutQC achieves much higher quantum circuit evaluation fidelity using small prototype quantum computers than the state-of-the-art large NISQ devices achieve. Overall, this hybrid approach allows users to leverage classical and quantum computing resources to evaluate quantum programs far beyond the reach of either one alone.
Quantum circuit compilation is a critical step in realizing quantum computation, aiming to translate high-level quantum algorithms into a sequence of gates executable on a specific quantum hardware. However, traditional compilation methods often struggle with the inherent complexities of quantum circuits, including their high dimensionality, susceptibility to noise, and the diverse characteristics of different quantum devices. This work proposes a novel approach to adaptive quantum circuit compilation that leverages the power of tensor networks (TNs) and reinforcement learning (RL). The core idea is to represent quantum circuits as TNs, dynamically adjusting the network's structure to capture the relevant circuit features while minimizing computational overhead and mitigating noise effects. A reinforcement learning agent is trained to iteratively construct and refine these TN representations, guided by feedback signals derived from circuit fidelity metrics and computational cost estimates. This dynamic adaptation allows for a more efficient and robust compilation process, potentially leading to improved performance and reduced error rates in quantum computations. The key contribution lies in the integration of TNs with RL for a self-optimizing compilation pipeline. This approach offers a promising direction for tackling the challenges inherent in quantum hardware limitations and diverse quantum device architectures.