Weighted Quantum Channel Compiling through Proximal Policy Optimization
This addresses the challenge of efficient quantum channel compilation for quantum computing, offering a systematic method with theoretical bounds, though it is incremental in applying reinforcement learning to a specific quantum problem.
The paper tackles the problem of compiling arbitrary quantum channels without ancillary qubits, proving it is impossible to achieve arbitrary precision with finite elementary sets, but shows that for a fixed accuracy ε, a universal set can be constructed with sequence length bounded by O(1/ε log 1/ε), and demonstrates in a Majorana fermion example that their algorithm reduces expensive gate use by incorporating weighted costs into reward functions.
We propose a general and systematic strategy to compile arbitrary quantum channels without using ancillary qubits, based on proximal policy optimization -- a powerful deep reinforcement learning algorithm. We rigorously prove 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 accuracy $ε$ one can construct a universal set with constant number of $ε$-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 $O(\frac{1}ε\log\frac{1}ε)$. Through a concrete example concerning topological compiling of Majorana fermions, we show that our proposed algorithm can conveniently and effectively reduce the use of expensive elementary gates through adding the weighted cost into the reward function of the proximal policy optimization.