Developing universal logical state-purification strategy for quantum error correcting codes

TL;DR

This paper introduces a measurement-based protocol for purifying logical states in quantum error correcting codes with high fidelity, using engineered Hamiltonian dynamics and post-selection, applicable to various codes and robust against measurement basis variations.

Contribution

It presents a novel, universal purification protocol for logical states in quantum error correction, combining Hamiltonian evolution, measurement, and post-selection, with demonstrated robustness and applicability.

Findings

Achieves unit fidelity with finite probability starting from thermal states.

Robustness demonstrated with non-optimal measurement bases and multiple iterations.

Feasibility shown for logical qubits in quantum state transfer using spin models.

Abstract

We develop a measurement-based protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability, starting from arbitrary thermal states of each code. The protocol entails a time evolution caused by an engineered Hamiltonian, which results in transitions between the logical and error subspaces of the quantum error correcting code mediated by the auxiliary qubit, followed by a projective measurement in an optimum basis on the auxiliary qubit and an appropriate post-selection of the measurement outcomes. We illustrate the results with the three-qubit repetition code and the logical qubit used in quantum state transfer protocol. We further demonstrate that when the measurement base is not optimal, it is possible to achieve both classical fidelity, and fidelity as high as $90\%$ through several iterations of the purifying procedure, thereby establishing its robustness against variations in the measurement basis. By repeating the purification rounds, we show that purifying the cardinal states of the logical Bloch sphere corresponding to logical qubits in quantum state transfer is feasible utilizing paradigmatic quantum spin models as the generator of the time evolution.