IP Library Granted Patent US 12,481,907
Granted Patent B2
US 12,481,907 · App. 17/238,870 · Granted Nov 25, 2025

Methods and systems for tensor network contraction based on hypergraph decomposition and parameter optimization

Inventors: Jiachen Huang (Hangzhou, CN); Jianxin Chen (Hangzhou, CN)
Assignee: Alibaba Group Holding Limited
G06N10/60G06F18/214G06F18/2323G06N10/80
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Quick Facts
Patent No.
US 12,481,907
App. No.
17/238,870
Granted
Nov 25, 2025
Kind
B2
Abstract

Methods and systems for tensor network contraction are provided. A method implemented by a computing host includes obtaining a plurality of tensor nodes associated with a tensor network and a plurality of indices respectively associated with the plurality of tensor nodes; generating a graph associated with the tensor network, wherein the plurality of tensor nodes correspond to a plurality of vertices of the graph and the plurality of indices correspond to a plurality of edges of the graph, respectively; decomposing the graph into a plurality of sub-graphs; and for each sub-graph of the plurality of sub-graphs, iteratively decomposing a current sub-graph into a plurality of next-tier sub-graphs until a size of each of the plurality of next-tier sub-graphs is less than a pre-set threshold.

Claims (81)

1 . A method implemented by a computing host, the method comprising:

obtaining a plurality of tensor nodes associated with a tensor network that is defined according to states of a quantum circuit and a plurality of indices respectively associated with the plurality of tensor nodes;

generating a graph associated with the tensor network, wherein the plurality of tensor nodes correspond to a plurality of vertices of the graph and the plurality of indices correspond to a plurality of edges of the graph, respectively;

decomposing the graph into a plurality of sub-graphs using a multi-partite decomposition algorithm associated with a first set of parameters;

for each sub-graph of the plurality of sub-graphs, iteratively decomposing a current sub-graph into a plurality of next-tier sub-graphs until a size of each of the plurality of next-tier sub-graphs is less than a pre-set threshold using a bipartition decomposition algorithm associated with a second set of parameters, the iteratively decomposing including:

determining that a first index of one or more first indices associated with a first node has a same dimension as a second index of one or more second indices associated with a second node in at least one of the plurality of next-tier sub-graphs;

contracting the first node and the second node to form a third node;

computing a count of nodes in the at least one of the plurality of next-tier sub-graphs; and

determining the count of nodes is less than the pre-set threshold;

dynamically optimizing the first set of parameters and/or the second set of parameters to generate a plurality of contraction trees associated with the tensor network that simulates the quantum circuit in a quantum computing simulation platform based on the plurality of next-tier sub-graphs; and

finding an optimal contraction tree from the plurality of contraction trees that reduces computation time and/or storage space to enable a simulation of quantum computations without fully simulating a full dimensional space of the quantum computations.

2 . The method of claim 1 , wherein individual contraction tree includes a set of vertices being traversed in a respective next-tier sub-graph and indices associated with the set of vertices.

3 . The method of claim 1 , further comprising:

decomposing the graph into the plurality of sub-graphs using a multi-partite decomposition algorithm.

4 . The method of claim 3 , further comprising:

optimizing one or more first parameters associated with the multi-partite decomposition algorithm.

5 . The method of claim 1 , further comprising:

iteratively decomposing the current sub-graph into a plurality of next-tier sub-graphs using a bipartition decomposition algorithm.

6 . The method of claim 5 , further comprising:

optimizing one or more second parameters associated with the bipartition decomposition algorithm.

7 . The method of claim 1 , further comprising:

generating one or more third indices associated with the third node based on the one or more first indices and the one or more second indices.

8 . The method of claim 2 , further comprising:

computing costs associated with the plurality of contraction trees;

determining whether a cost associated with at least one contraction tree satisfies a pre-set condition; and

in response to determining that the cost associated with at least one contraction tree satisfies the pre-set condition, outputting the at least one contraction tree as an optimal contraction tree; or

in response to determining that the cost associated with at least one contraction tree does not satisfy the pre-set condition,

adjusting one or more parameters associated with decomposing the graph into a plurality of sub-graphs;

iteratively decomposing the graph to generate at least one updated contraction tree until the pre-set condition is satisfied, and

outputting the at least one updated contraction tree as the optimal contraction tree.

9 . The method of claim 8 , wherein the one or more parameters are associated with at least one of a multi-partite decomposition algorithm and a bipartition decomposition algorithm.

10 . A system comprising:

one or more processors, and

memory communicatively coupled to the one or more processors, the memory storing computer-executable modules executable by the one or more processors that, when executed by the one or more processors, cause the one or more processors to perform actions including:

obtaining a plurality of tensor nodes associated with a tensor network that is defined according to states of a quantum circuit and a plurality of indices respectively associated with the plurality of tensor nodes;

generating a graph associated with the tensor network, wherein the plurality of tensor nodes correspond to a plurality of vertices of the graph and the plurality of indices correspond to a plurality of edges of the graph, respectively;

decomposing the graph into a plurality of sub-graphs using a first set of parameters;

for each sub-graph of the plurality of sub-graphs, iteratively decomposing a current sub-graph into a plurality of next-tier sub-graphs until a size of each of the plurality of next-tier sub-graphs is less than a pre-set threshold using a bipartition decomposition algorithm associated with a second set of parameters;

dynamically optimizing the first set of parameters and/or the second set of parameters to generate a plurality of contraction trees associated with the tensor network that simulates the quantum circuit in a quantum computing simulation platform based on the plurality of next-tier sub-graphs, a respective contraction tree including a set of vertices being traversed in a respective next-tier sub-graph and indices associated with the set of vertices;

computing costs associated with the plurality of contraction trees;

determining whether a cost associated with at least one contraction tree satisfies a pre-set condition; and

in response to determining that the cost associated with the at least one contraction tree satisfies the pre-set condition, outputting the at least one contraction tree as an optimal contraction tree; or

in response to determining that the cost associated with at least one contraction tree does not satisfy the pre-set condition,

adjusting one or more parameters associated with decomposing the graph into a plurality of sub-graphs,

iteratively decomposing the graph to generate at least one updated contraction tree until the pre-set condition is satisfied, and

outputting the at least one updated contraction tree as the optimal contraction tree.

11 . The system of claim 10 , wherein the one or more parameters are associated with at least one of a multi-partite decomposition algorithm and a bipartition decomposition algorithm.

12 . The system of claim 10 , wherein the actions further comprise:

decomposing the graph into the plurality of sub-graphs using a multi-partite decomposition algorithm; and

iteratively decomposing the current sub-graph into a plurality of next-tier sub- graphs using a bipartition decomposition algorithm.

13 . A computer-readable storage medium storing computer-readable instructions executable by one or more processors of a video compression system, that when executed by the one or more processors, cause the one or more processors to perform actions comprising:

obtaining a plurality of tensor nodes associated with a tensor network that is defined according to states of a quantum circuit and a plurality of indices respectively associated with the plurality of tensor nodes;

generating a graph associated with the tensor network, wherein the plurality of tensor nodes correspond to a plurality of vertices of the graph and the plurality of indices correspond to a plurality of edges of the graph, respectively;

decomposing the graph into a plurality of sub-graphs using a multi-partite decomposition algorithm associated with a first set of parameters;

for each sub-graph of the plurality of sub-graphs, iteratively decomposing a current sub-graph into a plurality of next-tier sub-graphs until a size of each of the plurality of next-tier sub-graphs is less than a pre-set threshold using a bipartition decomposition algorithm associated with a second set of parameters, the iteratively decomposing including:

determining that a first index of one or more first indices associated with a first node has a same dimension as a second index of one or more second indices associated with a second node in at least one of the plurality of next-tier sub-graphs;

contracting the first node and the second node to form a third node;

computing a count of nodes in the at least one of the plurality of next-tier sub-graphs; and

determining the count of nodes is less than the pre-set threshold; and

dynamically optimizing the first set of parameters and/or the second set of parameters to generate a plurality of contraction trees associated with the tensor network that simulates the quantum circuit in a quantum computing simulation platform based on the plurality of next-tier sub-graphs.

14 . The computer-readable storage medium of claim 13 , wherein individual contraction tree includes a set of vertices being traversed in a respective next-tier sub-graph and indices associated with the set of vertices.

15 . The computer-readable storage medium of claim 14 , wherein the actions further comprise:

computing costs associated with the plurality of contraction trees;

determining that a cost associated with at least one contraction tree does not satisfy a pre-set condition;

adjusting one or more parameters associated with decomposing the graph into a plurality of sub-graphs;

iteratively decomposing the graph to generate at least one updated contraction tree until the pre-set condition is satisfied, and

outputting the at least one updated contraction tree as an optimal contraction tree.

16 . The computer-readable storage medium of claim 15 , wherein the one or more parameters are associated with at least one of a multi-partite decomposition algorithm and a bipartition decomposition algorithm.

17 . The computer-readable storage medium of claim 13 , wherein the actions further comprise:

decomposing the graph into the plurality of sub-graphs using a multi-partite decomposition algorithm; and

iteratively decomposing the current sub-graph into a plurality of next-tier sub-graphs using a bipartition decomposition algorithm.

18 . The computer-readable storage medium of claim 14 , wherein the actions further comprise:

computing costs associated with the plurality of contraction trees;

determining that a cost associated with at least one contraction tree does satisfies a pre-set condition; and

outputting the at least one contraction tree as an optimal contraction tree.

19 . The system of claim 10 , wherein the iteratively decomposing includes:

determining that a first index of one or more first indices associated with a first node has a same dimension as a second index of one or more second indices associated with a second node in at least one of the plurality of next-tier sub-graphs;

contracting the first node and the second node to form a third node;

computing a count of nodes in the at least one of the plurality of next-tier sub-graphs; and

determining the count of nodes is less than the pre-set threshold.

20 . The system of claim 10 , wherein the actions further comprise decomposing the graph into the plurality of sub-graphs using a multi-partite decomposition algorithm.

Assignments (2)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Jul 7, 2026
From: ALIBABA GROUP HOLDING LIMITED
To: Z-AXIS PTE. LTD.
Reel/Frame 075934/0205 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 30, 2021
From: HUANG, JIACHEN; CHEN, JIANXIN
To: ALIBABA GROUP HOLDING LIMITED
Reel/Frame 056104/0653 →
Continuity (2)
Provisional Application 63015116 · Apr 24, 2020
Related Publication 20210334690A1 · Oct 28, 2021
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