Quantum Circuit Knitting via Sparsity Prediction
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Solution Overview
Problem
Quantum circuits with more qubits than a target quantum computer can handle require circuit cutting and knitting, which consumes significant computing resources due to high computational overhead in the knitting process, necessitating efficient methods to estimate and minimize this overhead.
Innovation Solution
A recurrent model is used to predict the sparsity index of state vectors, influencing cutting and knitting operations by estimating computational overhead and optimizing the Kronecker product process, thereby reducing the computational burden of circuit knitting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If quantum circuit cutting and knitting is performed to execute circuits with more qubits than available, then the quantum computer can handle larger circuits, but the computational overhead and resource consumption increase significantly
Solution Approach 1:
The patent performs preliminary analysis of the quantum circuit to identify sparsity patterns and predict which cutting configurations will result in sparse state vectors. By predicting sparsity before execution and optimizing cut positions in advance, the system prepares the most efficient knitting strategy beforehand, avoiding expensive computations during actual circuit execution.
Solution Approach 2:
The patent changes the parameter of state vector representation by exploiting sparsity - instead of storing and computing with full dense state vectors, the system represents only the non-zero elements of sparse state vectors. This parameter change from dense to sparse representation dramatically reduces the computational overhead of knitting operations while maintaining accuracy.
2Measurement precision
If traditional knitting operations are used to combine sub-circuit results, then the complete quantum circuit result is obtained, but the computational cost is prohibitively high
Solution Approach 1:
The patent changes the computational parameter by exploiting the sparsity structure of quantum state vectors. Instead of performing full-density matrix operations during knitting, the system performs operations only on non-zero elements, reducing the time complexity from exponential to polynomial in the number of non-zero elements while preserving measurement precision.
Solution Approach 2:
The patent extracts and utilizes the sparsity pattern from the quantum circuit structure. By identifying and extracting the positions of non-zero elements in state vectors before knitting operations, the system creates an optimized computation plan that processes only necessary elements, thereby reducing computational time while maintaining accuracy.
3Reliability
If full state vector computation is performed during circuit knitting, then accurate results are obtained, but the computational complexity becomes intractable for large circuits
Solution Approach 1:
The patent changes the computational approach by parameterizing the state vector representation based on sparsity. Instead of using fixed dense representations, the system adapts the representation to exploit sparsity patterns, reducing device complexity from exponential to manageable levels while preserving result correctness through careful tracking of non-zero elements.
Solution Approach 2:
The patent performs preliminary analysis to identify and record sparsity patterns before executing knitting operations. By pre-computing and storing information about which state vector elements are non-zero, the system reduces the complexity of actual knitting operations while ensuring correctness through the preserved sparsity information.
Data Source
AI summary
Approximating state vector sparsity for quantum computing operations. A recurrent model is trained to predict sparsity indexes (sparsity vector) for a quantum circuit and its subcircuits. The computational requirements of a knitting operation can be estimated or predicted more efficiently using the predicted sparsity indexes. Cutting operations and decisions can also be based on the predicted sparsity indexes.