A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.

Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers.

We report on the usefulness of using neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we supply further evidence for the usefulness of neural network states to describe multipartite entanglement. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction. In particular, we show that a) neural network states yield quantum codes with a high coherent information for two important quantum channels, the depolarizing channel and the dephrasure channel; b) neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error correction codes. In both cases, the neural network state ansatz provides an efficient and versatile means as variational parametrization of these states.