In this paper, we present a groundbreaking largescale system technology that leverages optimization on global, node, and device levels to achieve unprecedented scalability for tensor networks. Our techniques enable accommodating largescale tensor networks with up to tens of terabytes of memory, reaching up to 2304 GPUs with a peak computing power of 561 PFLOPS. Notably, we have achieved a time-to-solution of 14.22 seconds with an energy consumption of 2.39 kWh which achieved a fidelity of 0.002. Our most remarkable result is a time-to-solution of 17.18 seconds, with energy consumption of only 0.29 kWh which achieved a XEB of 0.002 after post-processing. The experiments conducted demonstrate that our research outperforms Google’s quantum processor Sycamore in both speed and energy efficiency, which recorded 600 seconds and 4.3 kWh, respectively. The code is available at https://github.com/DeepLinkorg/OpenTenNet.
In this paper, we present a groundbreaking largescale system technology that leverages optimization on global, node, and device levels to achieve unprecedented scalability for tensor networks. Our techniques enable accommodating largescale tensor networks with up to tens of terabytes of memory, reaching up to 2304 GPUs with a peak computing power of 561 PFLOPS. Notably, we have achieved a time-to-solution of 14.22 seconds with an energy consumption of 2.39 kWh which achieved a fidelity of 0.002. Our most remarkable result is a time-to-solution of 17.18 seconds, with energy consumption of only 0.29 kWh which achieved a XEB of 0.002 after post-processing. The experiments conducted demonstrate that our research outperforms Google’s quantum processor Sycamore in both speed and energy efficiency, which recorded 600 seconds and 4.3 kWh, respectively. The code is available at https://github.com/DeepLinkorg/OpenTenNet.
Quantum Computational Superiority boasts rapid computation and high energy efficiency. Despite recent advances in classical algorithms aimed at refuting the milestone claim of Google's sycamore, challenges remain in generating uncorrelated samples of random quantum circuits. In this paper, we present a groundbreaking large-scale system technology that leverages optimization on global, node, and device levels to achieve unprecedented scalability for tensor networks. This enables the handling of large-scale tensor networks with memory capacities reaching tens of terabytes, surpassing memory space constraints on a single node. Our techniques enable accommodating large-scale tensor networks with up to tens of terabytes of memory, reaching up to 2304 GPUs with a peak computing power of 561 PFLOPS half-precision. Notably, we have achieved a time-to-solution of 14.22 seconds with energy consumption of 2.39 kWh which achieved fidelity of 0.002 and our most remarkable result is a time-to-solution of 17.18 seconds, with energy consumption of only 0.29 kWh which achieved a XEB of 0.002 after post-processing, outperforming Google's quantum processor Sycamore in both speed and energy efficiency, which recorded 600 seconds and 4.3 kWh, respectively.
ABSTRACT Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time to solution and energy consumption, previous classical simulation experiments still underperform the Sycamore processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling that generates uncorrelated samples with a higher linear cross-entropy score and is 7× faster than the Sycamore 53-qubit experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrate state-of-the-art high-performance general-purpose GPUs to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute Sycamore’s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling.
Leapfrogging Sycamore: Harnessing 1432 GPUs for 7× Faster Quantum Random Circuit Sampling
Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of the first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time-to-solution, and energy consumption, previous classical simulation experiments still underperform the \textit{Sycamore} processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling which generates uncorrelated samples with higher linear cross entropy score and is 7 times faster than \textit{Sycamore} 53 qubits experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrated state-of-the-art high-performance general-purpose GPU to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute \textit{Sycamore}'s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling.
We present a framework for effectively simulating the execution of quantum circuits originally designed to demonstrate quantum supremacy using accessible high-performance computing (HPC) infrastructure. Building on prior CPU-only approaches, our pipeline combines a single NVIDIA A100 GPU for quantum state construction, followed by N parallel CPU jobs that perform distributed measurement sampling. We validate the fidelity by simulating the 53-qubit, 14-cycle Sycamore circuit and achieving a linear cross-entropy benchmarking (XEB) score of 0.549, exceeding the published XEB score of 0.002 from Google's reference data. We then evaluate execution time performance with the more complex 53-qubit, 20-cycle circuit, completing the full 2.5 million-shot workload over 100 CPU jobs in 01:15:36, representing a 6.95 x 10^7 speedup compared to Google's original classical estimate. Further, we show that if 1,000 CPU jobs were employed, the estimated duration would be approximately 00:17:35, only 12 minutes slower than the time taken by the original QPU-based experiment. These results illustrate that 'quantum supremacy' is not fixed and continues to be a moving target. In addition, hybrid classical-quantum strategies may provide broader near-term quantum utility than once thought.
We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem of Google's Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries fixed, from the Sycamore circuit with 53 qubits and 20 cycles, with linear cross-entropy benchmark (XEB) fidelity equals 0.739, which is much higher than those in Google's quantum supremacy experiments.
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.