Abstract
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit. Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential. In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes. In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.
- Received 17 August 2021
- Accepted 14 April 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.020334
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
A quantum computer utilizes the rules of quantum mechanics to solve certain problems through special algorithms, that is, a sequence of arithmetical and logical operations, much faster than any classical computer could ever achieve. However, due to interaction with its environment, it is likely that errors occur during the execution of an algorithm. The role of quantum error-correcting codes is to identify these errors and correct them while the algorithm is run. The working principle of error-correction protocols is to extract information about the errors that occurred by measuring the quantum system without corrupting the logical information. To do so, one encodes the information in logical quantum bits (qubits). Logical qubits that are encoded into the continuous degrees of freedom of a quantum system, e.g., the electromagnetic field of light, are known as bosonic qubits. In this case, a destructive measurement can be implemented experimentally by detecting the photons of the electromagnetic field.
In our paper, we perform numerical simulations with realistic measurement models to show that the extraction of information during error-correction protocols limits the reliable operation of quantum computers built from bosonic qubits. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.
