Abstract
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that, for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as shown in our previous work [Tansuwannont and Leung, Phys. Rev. A 104, 042410 (2021)]. In this work, we develop a notion of distinguishable fault set that captures both concepts of flags and weight parities, and extend the use of weight parities in error correction to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical -gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only two ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill.
8 More- Received 12 December 2021
- Revised 27 May 2022
- Accepted 21 June 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.030322
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
In quantum computation, errors in a quantum circuit arising from its interaction with the environment are one of the biggest obstacles to building large-scale quantum computers. To deal with such errors, we can simulate a quantum circuit using a fault-tolerant error-correction gadget, a method that suppresses error propagation, together with other gadgets for quantum computation. However, achieving a fault-tolerant simulation with low logical error rate can require a large number of additional qubits.
In this work, we develop fault-tolerant gadgets for error correction and quantum computation on certain quantum error correcting codes with promising properties. For the code that can correct up to any number of faults, our protocols require only two additional qubits. Our schemes rely on two techniques: the flag technique that uses a few additional qubits to detect faults, leading to high-weight errors, and the weight parity technique that significantly simplifies the error identification for some codes. A notion of distinguishable fault set that unifies both aforementioned techniques for handling high-weight errors is developed in this work. This notion also leads to a generalization of fault-tolerant gadgets that gives more flexibility when designing fault-tolerant protocols.
In our development, the structure of all circuits involved in fault-tolerant protocols is crucial for achieving fault tolerance with few additional qubits; therefore, all protocols must be designed in tandem. We hope that our protocol designs can be extended to reduce the qubit requirements for other codes.