Abstract
In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat- and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.
Highlights
To perform useful large-scale quantum computation, fragile quantum states must be protected from errors, which arise due to their inevitable interaction with the environment
We propose an efficient method for faulttolerant syndrome extraction
Note that this eigenspectrum is described in the frame which is rotating at the frequency of the oscillator ωPCO, which implies that the energy gap in the laboratory frame is ωPCO − ωgap; that is, external drives or perturbations at frequency ωPCO − ωgap can cause transitions between jCÆβ i and excited states
Summary
To perform useful large-scale quantum computation, fragile quantum states must be protected from errors, which arise due to their inevitable interaction with the environment. Knill’s method, based on error correction by teleportation, requires two ancillary code blocks prepared in the encoded Bell state j0iEj0iE þ j1iEj1iE These approaches lead to a rapidly growing overhead of computationally expensive entangling gates and ancilla hardware, which forces a more stringent requirement on error rates and pushes large-scale fault-tolerant quantum computation further out of reach. We discuss the fault tolerance of this technique in detail and examine specific examples based on three distinct errorcorrecting codes, namely, qubit-based toric [4], bosonic-cat [9,10], and Gottesman-Kitaev-Preskill (GKP) codes [29] These examples belong to the subclass of quantum codes known as stabilizer codes, the ideas for error syndrome extraction presented here could be extended to other types of codes as well.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
