Quantum Circuit Optimization with AlphaTensor

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.

Entailment Relations on Distributions

In this paper we give an overview of partial orders on the space of probability distributions that carry a notion of information content and serve as a generalisation of the Bayesian order given in (Coecke and Martin, 2011). We investigate what constraints are necessary in order to get a unique notion of information content. These partial orders can be used to give an ordering on words in vector space models of natural language meaning relating to the contexts in which words are used, which is useful for a notion of entailment and word disambiguation. The construction used also points towards a way to create orderings on the space of density operators which allow a more fine-grained study of entailment. The partial orders in this paper are directed complete and form domains in the sense of domain theory.