Quantum Circuit Tensor Elimination for Large-Qubit Simulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing quantum circuit simulation methods face complexity and inflexibility in selecting results to simulate, leading to high computational cost and memory requirements, especially when dealing with large numbers of qubits.
Innovation Solution
A computer-implemented method using RMCS (Reverse Matrix Chain Similarity) to determine an optimal elimination sequence for amplitudes in quantum circuits, reducing computational cost and memory requirements by iteratively selecting intermediate qubits based on a chordal graph representation of the tensor network.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional quantum circuit simulation methods are used, then simulation capability is provided, but computational cost and memory requirements increase exponentially with the number of qubits
Solution Approach 1:
The patent segments the quantum circuit simulation into independent amplitude calculations. Instead of simulating the entire quantum state vector (which requires 2^N complex numbers for N qubits), the method calculates only the amplitudes for a user-selected subset of basis states. This segmentation reduces the computational problem from exponential size to a manageable subset, allowing simulation of circuits with many more qubits than conventional methods permit.
Solution Approach 2:
The patent applies local quality by allowing users to specify which particular amplitudes they want to compute. Different regions of the amplitude space can be selected based on the user's interests (e.g., amplitudes corresponding to specific computational basis states). This selective approach concentrates computational resources on locally relevant amplitudes rather than uniformly processing all amplitudes, thereby reducing overall computational cost while maintaining simulation capability.
2Loss of information
If all amplitudes are simulated, then complete quantum circuit results are obtained, but computational resources and time are excessively consumed
Solution Approach 1:
The patent extracts only the necessary amplitudes from the complete quantum state space. Users can specify a subset of computational basis states for which amplitudes are required. The simulation method then extracts and computes only these specific amplitudes using tensor network contraction techniques, rather than computing the entire state vector. This extraction principle maintains the essential simulation results while eliminating unnecessary computational overhead.
Solution Approach 2:
The patent implements partial action by computing only the portion of the amplitude space that is necessary for the user's needs. Instead of performing excessive action (computing all 2^N amplitudes), the method performs exactly the right amount of computation for the specified subset. This partial computation approach significantly reduces computational time and resources while still providing meaningful simulation results for the selected amplitudes.
Data Source
Figure 1~4g
Figure 5a~6e
Figure 7
AI summary
The present disclosure provides embodiments for simulating a quantum circuit. In particular, an indication of a subset of input and output qubits of the quantum circuit is received. The indicated subset corresponds to an amplitude tensor of the quantum circuit that is to be determined, wherein the amplitude tensor comprises amplitudes for different combinations of states of the qubits of the indicated subset. Using a tensor network of the quantum circuit and Restricted Maximum Cardinality Search, RMCS, an elimination order of intermediate qubits within the quantum circuit is determined. The amplitude tensor is determined by removing, successively in accordance with the elimination order, that indices of the tensors of the tensor network that correspond to the intermediate qubits from the tensor network.