Simulation of Limited Entangled Quantum Fourier Transform Based on Matrix Product State

Unlike classical computing,qubits in quantum computing can be in the superposition state and entangled state can be formed between multiple qubits.Representing a quantum state composed of <i>n</i> qubits requires storing 2 to the <i>n</i>^th power amplitudes.The exponential memory cost makes large-scale quantum simulation difficult.Using the HIP-Clang language,based on the heterogeneous programming model of CPU+DCU and representing the quantum state with the matrix product state,quantum Fourier transform is simulated.By combining the characteristics of the matrix product state and analyzing the quantum Fourier transform circuit,unnecessary tensor contraction operations and orthogonalization construction are reduced during simulation implementation.Tensor contraction during simulation is analyzed and the TTGT algorithm is used to complete tensor contraction operations while utilizing DCU's parallel processing capabilities to improve efficiency.Simulation results are analyzed and the correctness of the simulation is verified through amplitude error and semi-classical Draper quantum adder results.Analyzing simulation scale,when the entanglement entropy of the quantum state is maximum,using 16GB of memory can simulate up to 24bit quantum states at most,while when the entanglement of the quantum state is limited,it can simulate hundreds of qubits of quantum Fourier transform.