ReDId: simulação de computação quântica baseada em redução e decomposição via Operador Identidade

Abstract

One of the main obstacles for the adoption of quantum algorithm simulation is the exponential increase in temporal and spatial complexities, due to the expansion of transformations and read/write states by using tensor product in multi-dimensional applications. Simulation of these systems is very relevant to develop and test new quantum algorithms. To minimize the problem created by the high complexity of the simulation of quantum algorithms, this paper presents a new strategy named ReDId, which provides optimizations based on the reduction and decomposition via Identity operator. Next, the paper considers the implementation of the algorithm that makes use of the ReDId strategy, exploring the components VPE-qGM and VirD-GM that integrate the D-GM environment. For evaluation, is considered the application of optimization via ReDId strategy in simulations of Hadamard transformations from 21 to 28 qubits and Quantum Fourier Transforms from 26 to 28 qubits. Those algorithms were simulated over CPU, sequentially and in parallel, and in GPU, showing reduced temporal complexity and, consequently, shorter simulation time. Moreover, evaluations of the Shor’s algorithm considering 2n + 3 qubits in the order-finding quantum algorithm were simulated up to 25 qubits. Comparing our implementations running on the same hardware with LIQUi|� - Language-Integrated Quantum Operations, release version by QuArC -Quantum Architectures and Computation Group from Microsoft Research, the simulator via ReDId strategy proved to be faster.