Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware

TL;DR

This paper extends quantum homogenization protocols to NISQ hardware, demonstrating their potential for quantum state stabilization and information protection through a shallow circuit implementation.

Contribution

It introduces a ($ exttt{SWAP}$)$^ exttt{ extalpha}$ formulation of quantum homogenization and proves its ability to protect quantum information on NISQ devices.

Findings

Implementation on NISQ processors using shallow circuits

The protocol yields a CPTP map with correctable code subspace

Demonstrates quantum homogenization for state stabilization and protection

Abstract

Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically-equivalent ($\mathtt{SWAP}$)$^\alpha$ formulation. We then demonstrate its applicability on available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of $\mathtt{CNOT}$ and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed ($\mathtt{SWAP}$)$^\alpha$ quantum homogenization protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics.