Witnessing entanglement in trapped-ion quantum error correction under realistic noise

TL;DR

This paper develops a detailed microscopic error model for two-qubit gates in trapped-ion quantum error correction, quantifies the generated entanglement under realistic noise, and bridges microscopic parameters with phenomenological error rates.

Contribution

It introduces a comprehensive microscopic error model for trapped-ion gates and applies it to analyze entanglement in QEC circuits under realistic noise conditions.

Findings

Effective error models link microscopic gate infidelity to phenomenological error rates.

Quantification of multipartite entanglement under realistic noise conditions.

Analysis of how noise impacts entanglement witnesses in QEC circuits.

Abstract

Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. In current implementations of QEC, sequences of non-perfect two-qubit entangling gates are used to codify the information redundantly into multipartite entangled states. Also, to extract the error syndrome, a series of two-qubit gates are used to build parity-check readout circuits. In the case of noisy gates, both steps cannot be performed perfectly, and an error model needs to be provided to assess the performance of QEC. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We analytically derive leading-error contributions in terms of microscopic parameters and present effective error models that connect the error rates typically used in phenomenological accounts to the microscopic gate infidelities hereby derived. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks. We do so by using entanglement witnesses, complementing in this way the recent studies by exploring the effects of a more realistic microscopic noise.