Evolving Quantum Error Correction Codes

Abstract

Ribas Tandeitnik, Daniel; Barbosa dos Santos Guerreiro, Thiago (Advisor). Evolving Quantum Error Correction Codes.

Optimization of tensor network codes with reinforcement learning

“…In order to assess the performance of our RL algorithm, we now apply it to codes that are still small enough to also be found via brute force search, but large enough that the probability of quickly finding the optimal codes by random search is now quite small. We repeat the simulations of the previous subsection with initial codes that include one five-qubit code and either 4 or 5 six-qubit stabilizer states, which correspond to uncontracted [ [29,1,3]] and [ [35,1,3]] respectively. Outputs are summarized in table 5.…”

“…Code with the maximum distance obtained after s fusion steps starting from an initial [ [29,1,3]] (resp. [ [35,1,3]]) code built by combining one five-qubit code and four (resp. five) six-qubit stabilizer states.…”

“…A few days prior to the completion of this paper, a related work appeared on the arXiv [34], where the authors also look at using RL to discover optimal quantum error correction codes using the 'quantum lego' framework. We have also become aware of work exploring the use of genetic algorithms to search for quantum codes [35].…”

“…Average code distance as the RL agent progressively finds the optimal code. This example shows the case of an initial [[35,1,3]] code and s = 5 fusions in order to ultimately find the [[25,1,9]] code. We see the role of the softmax parameter β, one of the parameters controlling the tradeoff between exploration and exploitation.…”

“…Figure 5. Probability of finding the [[19,1,7]] over 1000 trials using the RL agent compared to a random search, when starting with a [[35,1,3]] code and allowing 8 fusions. For the random search probability, a brute force search was first conducted showing only 5 out of the N = 3, 108, 105 possible fusion sequences lead to the maximum-distance [[19,1,7]] code.…”