Quantum homogenization as a quantum steady-state protocol on noisy intermediate-scale quantum hardware

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 (SWAP)α formulation. We then demonstrate its applicability on the available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of 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 (SWAP)α 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. Published by the American Physical Society 2024