Abstract
Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement (GME) across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify GME that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear number of bipartitions by a number of measurements that also scales linearly, suffices to certify GME. Moreover, our method goes beyond the standard procedure of separating the state from the convex hull of biseparable states, yielding an improved finesse and robustness compared to previous techniques. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version. In particular, we subject the circuits to combinations of three types of noise, namely, uniform depolarizing noise, two-qubit gate depolarizing noise, and bit-flip measurement noise. We numerically compare our method with the standard, yet generally inefficient, fidelity test and to a pair of efficient witnesses, verifying the increased robustness of our method. Last but not least, we provide the full translation of our analysis to a trapped-ion native gate set that makes it suitable for experimental applications.
- Received 3 November 2020
- Accepted 5 March 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.020304
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers run their algorithms on a large number of quantum systems, called qubits, by creating quantum correlations across all of them. Hence, an important minimal checkpoint in making these devices is to verify that the actual computation procedures lead to quantum correlations of desired quality. Such checks are resource-intensive since, in general, they require a number of tests that grows exponentially with the number of qubits, in order to provide strong robustness against experimental imperfections.
In this work, we propose a new technique that overcomes this problem by reducing the number of measurements significantly and maximizing the resilience against noise. Our method offers solution to genuine multipartite entanglement certification. We combine the process of localizing entanglement in subsystems of the qubit register with the construction of the so-called entanglement witnesses, which are observables that can signal the presence of entanglement, to obtain conditional entanglement witnessing. We prove the efficiency of our recipe and discuss why it generically tolerates higher levels of noise. We then use it to certify the entanglement generated by quantum error correction circuits in trapped-ion processors. We numerically simulate and compare our approach with previous entanglement witnesses and show that it yields a significant increase in the noise tolerance whilst being efficient. This is of crucial importance in current technology where the addition of each qubit unavoidably amplifies the complexity of quantum states and experimental imperfections.
Our method can be applied to benchmark entanglement generation in different quantum-processing platforms. It can therefore play an important role in experiments where efficient entanglement certification is necessary.
