2 Search Results for "Hsieh, Yao-Ching"

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DOI: 10.4230/LIPIcs.SEA.2024.27

Improved Cut Strategy for Tensor Network Contraction Orders

Authors: Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract

In the field of quantum computing, simulating quantum systems on classical computers is crucial. Tensor networks are fundamental in simulating quantum systems. A tensor network is a collection of tensors, that need to be contracted into a result tensor. Tensor contraction is a generalization of matrix multiplication to higher order tensors. The contractions can be performed in different orders, and the order has a significant impact on the number of floating point operations (flops) needed to get the result tensor. It is known that finding an optimal contraction order is NP-hard. The current state-of-the-art approach for finding efficient contraction orders is to combinine graph partitioning with a greedy strategy. Although heavily used in practice, the current approach ignores so-called free indices, chooses node weights without regarding previous computations, and requires numerous hyperparameters that need to be tuned at runtime. In this paper, we address these shortcomings by developing a novel graph cut strategy. The proposed modifications yield contraction orders that significantly reduce the number of flops in the tensor contractions compared to the current state of the art. Moreover, by removing the need for hyperparameter tuning at runtime, our approach converges to an efficient solution faster, which reduces the required optimization time by at least an order of magnitude.

Cite as

Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen. Improved Cut Strategy for Tensor Network Contraction Orders. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{staudt_et_al:LIPIcs.SEA.2024.27,
  author =	{Staudt, Christoph and Blacher, Mark and Klaus, Julien and Lippmann, Farin and Giesen, Joachim},
  title =	{{Improved Cut Strategy for Tensor Network Contraction Orders}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.27},
  URN =		{urn:nbn:de:0030-drops-203924},
  doi =		{10.4230/LIPIcs.SEA.2024.27},
  annote =	{Keywords: tensor network, contraction order, graph partitioniong, quantum simulation}
}

Document

DOI: 10.4230/LIPIcs.CCC.2023.33

On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation

Authors: Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract

Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time T for the simulation greatly affect algorithm runtime as expected. While there are some specific types of Hamiltonians that can be fast-forwarded, i.e., simulated within time o(T), for some large classes of Hamiltonians (e.g., all local/sparse Hamiltonians), existing simulation algorithms require running time at least linear in the evolution time T. On the other hand, while there exist lower bounds of Ω(T) circuit size for some large classes of Hamiltonian, these lower bounds do not rule out the possibilities of Hamiltonian simulation with large but "low-depth" circuits by running things in parallel. As a result, physical systems with system size scaling with T can potentially do a fast-forwarding simulation. Therefore, it is intriguing whether we can achieve fast Hamiltonian simulation with the power of parallelism. In this work, we give a negative result for the above open problem in various settings. In the oracle model, we prove that there are time-independent sparse Hamiltonians that cannot be simulated via an oracle circuit of depth o(T). In the plain model, relying on the random oracle heuristic, we show that there exist time-independent local Hamiltonians and time-dependent geometrically local Hamiltonians on n qubits that cannot be simulated via an oracle circuit of depth o(T/n^c), where the Hamiltonians act on n qubits, and c is a constant. Lastly, we generalize the above results and show that any simulators that are geometrically local Hamiltonians cannot do the simulation much faster than parallel quantum algorithms.

Cite as

Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen. On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 33:1-33:45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chia_et_al:LIPIcs.CCC.2023.33,
  author =	{Chia, Nai-Hui and Chung, Kai-Min and Hsieh, Yao-Ching and Lin, Han-Hsuan and Lin, Yao-Ting and Shen, Yu-Ching},
  title =	{{On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{33:1--33:45},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.33},
  URN =		{urn:nbn:de:0030-drops-183038},
  doi =		{10.4230/LIPIcs.CCC.2023.33},
  annote =	{Keywords: Hamiltonian simulation, Depth lower bound, Parallel query lower bound}
}

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