# Entanglement bounds on the performance of quantum computing architectures

## TL;DR

This paper introduces an isoperimetric number-based metric to evaluate quantum architecture performance, providing lower bounds on entanglement creation time and demonstrating the potential of hierarchical architectures.

## Contribution

It proposes a new metric based on the isoperimetric number to evaluate quantum architectures and shows how it can be used to compare and optimize connectivity graphs.

## Key findings

- Hierarchical architecture is a promising alternative to grid architecture.
- The isoperimetric number provides a lower bound on entanglement creation time.
- The lower bound can be nearly saturated with a constructive protocol.

## Abstract

There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph's performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states. This metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We use this metric to evaluate the hierarchical architecture proposed by A. Bapat et al. [Phys. Rev. A 98, 062328 (2018)], and find it to be a promising alternative to the conventional grid architecture. We also show that the lower bound that this metric places on the creation time of highly entangled states can be saturated with a constructive protocol, up to a factor logarithmic in the number of qubits.