Quantum deep sets and sequences

Ernesto Rodríguez

Yuanhang Zhang, Pei-Lin Zheng, Yi Zhang +1 more

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep reinforcement learning that compiles an arbitrary single-qubit gate into a sequence of elementary gates from a finite universal set. It generates near-optimal gate sequences with given accuracy and is generally applicable to various scenarios, independent of the hardware-feasible universal set and free from using ancillary qubits. For concreteness, we apply this algorithm to the case of topological compiling of Fibonacci anyons and obtain near-optimal braiding sequences for arbitrary single-qubit unitaries. Our algorithm may carry over to other challenging quantum discrete problems, thus opening up a new avenue for intriguing applications of deep learning in quantum physics.

Satoko Titani, Haruhiko Kozawa

Shouliang Hu, Chunlin Chen, Daoyi Dong

This paper investigates quantum gate control problems using the deep reinforcement learning algorithm, i.e., a model-free machine learning method. We implement the twin delayed deep deterministic policy gradient (TD3) algorithm to search for piece-wise constant control pulses for quantum gates through the trail interaction with the quantum system. Simulation results on four typical gates, including three one-qubit gates and a two-qubit CNOT gate, demonstrate that deep reinforcement learning exhibits improved performance for quantum gate control tasks. By setting punishment for steps in the reward function, DRL can automatically find a shorter control sequence than the traditional gradient-based algorithm (e.g., GRAPE algorithm) and the evolutionary algorithm (e.g., DE algorithm) while maintaining high control precision.

Weiyuan Gong, Si Jiang, Dong-Ling Deng

We rigorously prove a no-go theorem that, in sharp contrast to the case of compiling unitary gates, it is impossible to compile an arbitrary channel to arbitrary precision with any given finite elementary channel set, regardless of the length of the decomposition sequence. However, for a fixed error bound $\ensuremath{\epsilon}$, we find a general and systematic strategy to compile arbitrary quantum channels. We construct a universal set with a constant number of $\ensuremath{\epsilon}$-dependent elementary channels, such that an arbitrary quantum channel can be decomposed into a sequence of these elementary channels followed by a unitary gate, with the sequence length bounded by $O(\frac{1}{\ensuremath{\epsilon}}log\frac{1}{\ensuremath{\epsilon}})$ in the worst case. We further optimize this approach by exploiting proximal policy optimization---a powerful deep reinforcement learning algorithm for the gate compilation. We numerically evaluate the performance of our algorithm concerning topological compiling of Majorana fermions, and we show that our algorithm can conveniently and effectively reduce the use of expensive elementary operations.