Fault-tolerant embedding of quantum circuits on hardware architectures via swap gates

TL;DR

This paper presents a strategy for embedding quantum circuits onto hardware with limited connectivity using swap gates, aiming to preserve fault-tolerance despite increased noise.

Contribution

It introduces a simple swap scheme design method that maintains fault-tolerant properties during circuit embedding on constrained quantum hardware.

Findings

Embedding surface codes on specific lattices shows minimal noise deterioration.

The method preserves fault-tolerance properties despite added noise.

Provides a practical solution for implementing fault-tolerant circuits on current hardware.

Abstract

In near-term quantum computing devices, connectivity between qubits remain limited by architectural constraints. A computational circuit with given connectivity requirements necessary for multi-qubit gates have to be embedded within physical hardware with fixed connectivity. Long-distance gates have to be done by first routing the relevant qubits together. The simplest routing strategy involves the use of swap gates to swap the information carried by two unconnected qubits to connected ones. Ideal swap gates just permute the qubits; real swap gates, however, have the added possibilities of causing simultaneous errors on the qubits involved and spreading errors across the circuit. A general swap scheme thus changes the error-propagation properties of a circuit, including those necessary for fault-tolerant functioning of a circuit. Here, we present a simple strategy to design the swap scheme needed to embed an abstract circuit onto a physical hardware with constrained connectivity, in a manner that preserves the fault-tolerant properties of the abstract circuit. The embedded circuit will, of course, be noisier, compared to a native implementation of the abstract circuit, but we show in the examples of embedding surface codes on heavy-hexagonal and hexagonal lattices that the deterioration is not severe. This then offers a straightforward solution to implementing circuits with fault-tolerance properties on current hardware.