Distribution of Quantum Circuits Over General Quantum Networks

TL;DR

This paper addresses the challenge of distributing quantum circuits across heterogeneous quantum networks, proposing algorithms to minimize communication costs using entanglement and teleportation, and evaluating their performance through simulations.

Contribution

It introduces heuristic algorithms for distributing quantum circuits over networks with constraints, combining entanglement and teleportation, and provides simulation-based analysis of their effectiveness.

Findings

Heuristic algorithms effectively reduce communication costs in distributed quantum circuits.

Simulation results demonstrate scalability across various network sizes and circuit complexities.

Proposed methods outperform baseline approaches in minimizing communication overhead.

Abstract

Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum programs represented as quantum circuits across a quantum network of heterogeneous quantum computers, in a way that minimizes the overall communication cost required to execute the distributed circuit. We consider two ways of communicating: cat-entanglement that creates linked copies of qubits across pairs of computers, and teleportation. The heterogeneous computers impose constraints on cat-entanglement and teleportation operations that can be chosen by an algorithm. We first focus on a special case that only allows cat-entanglements and not teleportations for communication. We provide a two-step heuristic for solving this specialized setting: (i) finding an assignment of qubits to computers using Tabu search, and (ii) using an iterative greedy algorithm designed for a constrained version of the set cover problem to determine cat-entanglement operations required to execute gates locally. For the general case, which allows both forms of communication, we propose two algorithms that subdivide the quantum circuit into several portions and apply the heuristic for the specialized setting on each portion. Teleportations are then used to stitch together the solutions for each portion. Finally, we simulate our algorithms on a wide range of randomly generated quantum networks and circuits, and study the properties of their results with respect to several varying parameters.