Weighted Quantum Channel Compiling through Proximal Policy Optimization

TL;DR

This paper introduces a reinforcement learning-based method for compiling quantum channels without ancillary qubits, demonstrating theoretical limits and practical efficiency improvements in quantum gate decomposition.

Contribution

It presents a novel approach using proximal policy optimization for quantum channel compilation and establishes fundamental limits on arbitrary channel approximation.

Findings

The method effectively reduces the use of costly elementary gates.

A universal set of elementary channels can approximate any channel within fixed accuracy.

The sequence length for decomposition scales as O(1/ε log(1/ε)).

Abstract

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 $\epsilon$ one can construct a universal set with constant number of $\epsilon$-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 $O(\frac{1}{\epsilon}\log\frac{1}{\epsilon})$. 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.