SWAP-less Implementation of Quantum Algorithms

TL;DR

This paper introduces a SWAP-less method for implementing quantum algorithms on devices with limited connectivity by tracking parity quantum information, reducing circuit depth and qubit overhead for algorithms like QFT and QAOA.

Contribution

It proposes a novel formalism that exploits entangling gates for quantum information transport, eliminating the need for SWAP operations in constrained architectures.

Findings

Achieves circuit depth of 5n-3 for QFT on linear architectures.

Outperforms SWAP networks in QAOA implementation.

Balances qubit count and circuit depth using bi-linear connectivity.

Abstract

We present a formalism based on tracking the flow of parity quantum information to implement algorithms on devices with limited connectivity without qubit overhead, SWAP operations or shuttling. Instead, we leverage the fact that entangling gates not only manipulate quantum states but can also be exploited to transport quantum information. We demonstrate the effectiveness of this method by applying it to the quantum Fourier transform (QFT) and the Quantum Approximate Optimization Algorithm (QAOA) with $n$ qubits. This improves upon all state-of-the-art implementations of the QFT on a linear nearest-neighbor architecture, resulting in a total circuit depth of ${5n-3}$ and requiring ${n^2-1}$ CNOT gates. For the QAOA, our method outperforms SWAP networks, which are currently the most efficient implementation of the QAOA on a linear architecture. We further demonstrate the potential to balance qubit count against circuit depth by implementing the QAOA on twice the number of qubits using bi-linear connectivity, which approximately halves the circuit depth.