Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Abstract

Shenvi et al. have proposed a quantum algorithm based on quantum walking called Shenvi–Kempe–Whaley (SKW) algorithm, but this search algorithm can only search one target state and use a specific search target state vector. Therefore, when there are more than two target nodes in the search space, the algorithm has certain limitations. Even though a multi-objective SKW search algorithm was proposed later, when the number of target nodes is more than two, the SKW search algorithm cannot be mapped to the same quotient graph. In addition, the calculation of the optimal target state depends on the number of target states m. In previous studies, quantum computing and testing algorithms were used to solve this problem. But these solutions require more Oracle calls and cannot get a high accuracy rate. Therefore, to solve the above problems, we improve the multi-target quantum walk search algorithm, and construct a controllable quantum walk search algorithm under the condition of unknown number of target states. By dividing the Hilbert space into multiple subspaces, the accuracy of the search algorithm is improved from p c = (1/2) – O(1/n) to p c = 1 – O(1/n). And by adding detection gate phase, the algorithm can stop when the amplitude of the target state becomes the maximum for the first time, and the algorithm can always maintain the optimal number of iterations, so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t f = ( π / 2 ) 2 n − 2 .

Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

“…Since the color and position of each image pixel are represented by classical numbers, we can represent the pixel position and color information in image using quantum states and their coefficients according to the quantum image (FRQI) encoding method. [41][42][43] We set the number of iterations to 350 and use the Adam optimizer, and set the initial learning rates of the generator and discriminator to α G = 0.05 and α D = 0.001 respectively. Subsequently, we trained the QGAN following the training procedure outlined in Table 1.…”