High-performance classical simulator for quantum circuits, in particular the tensor network contraction algorithm, has become an important tool for the validation of noisy quantum computing. In order to address the memory limitations, the slicing technique is used to reduce the tensor dimensions, but it could also lead to additional computation overhead that greatly slows down the overall performance. This paper proposes novel lifetime-based methods to reduce the slicing overhead and improve the computing efficiency, including, an interpretation method to deal with slicing overhead, an inplace slicing strategy to find the smallest slicing set and an adaptive tensor network contraction path refiner customized for Sunway architecture. Experiments show that in most cases the slicing overhead with our inplace slicing strategy would be less than the Cotengra, which is the most used graph path optimization software at present. Finally, the resulting simulation time is reduced to 96.1s for the Sycamore quantum processor RQC, with a sustainable single-precision performance of 308.6Pflops using over 41M cores to generate 1M correlated samples, which is more than 5 times performance improvement compared to 60.4 Pflops in 2021 Gordon Bell Prize work.
High-performance classical simulator for quantum circuits, in particular the tensor network contraction algorithm, has become an important tool for the validation of noisy quantum computing. In order to address the memory limitations, the slicing technique is used to reduce the tensor dimensions, but it could also lead to additional computation overhead that greatly slows down the overall performance. This paper proposes novel lifetime-based methods to reduce the slicing overhead and improve the computing efficiency, including, an interpretation method to deal with slicing overhead, an inplace slicing strategy to find the smallest slicing set and an adaptive tensor network contraction path refiner customized for Sunway architecture. Experiments show that in most cases the slicing overhead with our inplace slicing strategy would be less than the Cotengra, which is the most used graph path optimization software at present. Finally, the resulting simulation time is reduced to 96.1s for the Sycamore quantum processor RQC, with a sustainable single-precision performance of 308.6Pflops using over 41M cores to generate 1M correlated samples, which is more than 5 times performance improvement compared to 60.4 Pflops in 2021 Gordon Bell Prize work.
We develop a high-performance tensor-based simulator for random quantum circuits(RQCs) on the new Sunway supercomputer. Our major innovations include: (1) a near-optimal slicing scheme, and a path-optimization strategy that considers both complexity and compute density; (2) a three-level parallelization scheme that scales to about 42 million cores; (3) a fused permutation and multiplication design that improves the compute efficiency for a wide range of tensor contraction scenarios; and (4) a mixed-precision scheme to further improve the performance. Our simulator effectively expands the scope of simulatable RQCs to include the 10X10(qubits)X(1+40+1)(depth) circuit, with a sustained performance of 1.2 Eflops (single-precision), or 4.4 Eflops (mixed-precision)as a new milestone for classical simulation of quantum circuits; and reduces the simulation sampling time of Google Sycamore to 304 seconds, from the previously claimed 10,000 years.
Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and extended. In this work, we propose novel strategies for tensor network contraction based simulator on Sunway architecture. Our approach addresses three main aspects: complexity, computational paradigms and fine-grained optimization. Data reuse schemes are designed to reduce floating-point operations, and memory organization techniques are employed to eliminate slicing overhead while maintaining parallelism. Step fusion strategy is extended by multi-core cooperation to improve the data locality and computation intensity. Fine-grained optimizations, such as in-kernel vectorized permutations, and split-K operators, are developed as well to address the challenges in new hotspot distribution and topological structure. These innovations can accelerate the simulation of the Zuchongzhi-60-24 by more than 10 times, using more than 1024 Sunway nodes (399,360 cores). Our work demonstrates the potential for enabling efficient classical simulation of increasingly complex quantum circuits.
A major milestone in the era of noisy intermediate scale quantum computers is \textit{quantum supremacy} [Nature \textbf{574}, 505 (2019)] claimed on the Sycamore quantum processor of 53 qubits, which can perform a random circuit sampling task within 200 seconds while the same task is estimated to require a runtime of 10,000 years on Summit. This record has been renewed with two recent experiments on the Zuchongzhi 2.0 (56 qubits) and Zuchongzhi 2.1 (60 qubits) quantum processors. On the other front of quantum supremacy comparison, there has also been continuous improvements on both the classical simulation algorithm as well as the underlying hardware. And a fair justification of the computational advantages for those quantum supremacy experiments would require to practically simulate the same problems on current top supercomputers, which is still in lack. Here we report the full-scale simulations of these problems on new generation Sunway supercomputer, based on a customized tensor network contraction algorithm. Our benchmark shows that the most challenging sampling task performed on Sycamore can be accomplished within 1 week, thus collapsing the quantum supremacy claim of Sycamore. Additionally, we show that the XEB fidelities of the \textit{quantum supremacy circuits} with up to 14 cycles can be verified in minutes, which also provides strong consistency check for quantum supremacy experiments. Our results redefine quantum supremacy baseline using the new generation Sunway supercomputer.
Classical simulation of quantum computation plays a critical role in numerical studies of quantum algorithms and the validation of quantum devices. Here, we introduce SW_Qsim, a tensor-network-based quantum simulator, which is designed with a two-level parallel structure for efficient implementation on the many-core New Sunway Supercomputer. We propose a minimize-memory contraction path algorithm for rectangular quantum grids to reduce the memory overhead, and provide the memory-limited simulation capacity of SW26010pro. Moreover, tensor operations are carefully optimized on the SW processor to achieve high performance. We design a fault tolerance mechanism to improve the extreme-scale parallel stability. We benchmark SW_Qsim's simulation of RQCs up to 400-qubits, achieving near-linear strong and weak scaling with up to 28.75 million cores, far beyond the previous state of the art. Our work sheds light on the development of efficient quantum algorithms for use in the physical, chemical, and engineering science fields.
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.
Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation. For a nontrivial subset of these quantum circuits, 50 to 100 qubits can easily be simulated on a single compute node.