Efficient particle-conserving brick-wall quantum circuits

TL;DR

This paper develops and tests efficient particle-conserving quantum gates within brick-wall circuits, demonstrating their effectiveness for variational quantum optimization, especially on NISQ devices, by comparing different gate types and extending circuit connectivity.

Contribution

It introduces practical methods to construct and optimize particle-conserving gates, including a general four-parameter gate, and extends circuit connectivity beyond nearest neighbors.

Findings

The four-parameter particle-conserving gate performs best in tests.

Generalized gates outperform simpler alternatives.

Extended circuits with non-nearest-neighbor gates improve efficiency.

Abstract

In variational quantum optimization with particle-conserving quantum circuits, it is often difficult to decide a priori which particle-conserving gates and circuit ansatzes would be most efficient for a given problem. This is important especially for noisy intermediate-scale quantum (NISQ) processors with limited resources. While this may be challenging to answer in general, deciding which particle-conserving gate would be most efficient is easier within a specified circuit ansatz. In this paper, we show how to construct efficient particle-conserving gates using some practical ideas from symmetric tensor networks. We derive different types of particle-conserving gates, including the generalized one. We numerically test the gates under the framework of brick-wall circuits. We show that the general particle-conserving gate with only four real parameters is generally best. In addition, we present an algorithm to extend brick-wall circuit with two-qubit nearest-neighbouring gates to non-nearest-neighbouring gates. We test and compare the efficiency of the circuits with Heisenberg spin chain with and without next-nearest-neighbouring interactions.