Tensor Network Contraction Ordering for Quantum Circuit Simulation
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Solution Overview
Problem
Current classical computers are limited by binary code, leading to increased computation time and resources when processing complex data, and simulating quantum circuits on these systems requires significant time and resources, hindering the development of quantum algorithms.
Innovation Solution
A method and system for simulating quantum computation on a classical computer by optimizing tensor networks through efficient input contraction using algorithms and processors to eliminate indices, employing techniques like diagonal and ZZ gates, line graph processing, and parallelization across multiple processors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum circuits are simulated on classical computers using traditional methods, then the simulation can be performed, but the computation time and resource requirements increase significantly
Solution Approach 1:
The patent segments the quantum circuit simulation into tensor network components, representing the quantum state as a product of smaller tensors rather than a single large matrix. This segmentation allows the simulation to be performed in manageable chunks, reducing the computational burden and time required while maintaining accuracy.
Solution Approach 2:
The patent changes the parameter representation from traditional binary state vectors to tensor network parameters. By representing quantum states using tensor decompositions with controllable bond dimensions, the system can adjust the precision-parameter tradeoff, achieving accurate simulations with reduced computational resources and time.
2Reliability
If quantum circuits are simulated on classical computers using traditional methods, then the simulation can be performed, but the memory requirements increase significantly
Solution Approach 1:
The patent segments the quantum state representation into multiple smaller tensors connected by bonds, rather than storing the entire state as a single large vector. This segmentation dramatically reduces memory requirements by storing only the essential correlations between subsystems, while maintaining simulation accuracy through proper tensor network architecture.
Solution Approach 2:
The patent changes from storing complete quantum state vectors (requiring exponential memory) to storing tensor network parameters with controllable bond dimensions. This parameter transformation allows accurate simulation of large quantum circuits with manageable memory resources by controlling the level of correlation detail retained.
3Productivity
If efficient tensor network contraction ordering is implemented, then computation time is reduced, but algorithm complexity increases
Solution Approach 1:
The patent applies preliminary action by computing the optimal contraction ordering before performing the actual tensor contractions. By pre-calculating the sequence that minimizes computational work using graph theory algorithms, the system reduces the overall computation time for the simulation, making the increased algorithmic complexity worthwhile.
Solution Approach 2:
The patent introduces an intermediary step of computing the contraction ordering using graph representations of the tensor network. This intermediary algorithm acts as a mediator that translates the tensor network structure into an optimal computation sequence, reducing the complexity of the actual contraction operations that follow.
Data Source
AI summary
A method for reducing computation time while simulating quantum computation on a classical computer by performing an algorithm used to determine the most efficient input contraction, the method including receiving, by a processor, a tensor network representing a quantum circuit, computing, by the processor, an ordering for the tensor network by an ordering algorithm, contracting, by the processor, the tensor network by eliminating indices according to the ordering resulting in a contracted tensor network, and returning, by the processor, the contracted tensor network.