### Scheduling Error Correction Operations for a Quantum Computer

Co-authorRobert Carr, Anand Ganti, Andrew Landahl

In a (future) quantum computer a single logical quantum bit (qubit)
will be made of multiple physical qubits. These extra physical qubits
implement mandatory extensive error checking. The efficiency of error
correction will fundamentally influence the performance of a future
quantum computer, both in latency/speed and in error threshold (the
worst error tolerated for an individual gate).

Executing this quantum error correction requires scheduling the
individual operations subject to architectural constraints. Since our
last talk on this subject, a team of researchers at Sandia National
Labortories has designed a logical qubit architecture that considers
all relevant architectural issues including layout, the effects of
supporting classical electronics, and the types of gates that the
underlying physical qubit implementation supports most naturally.
This is a two-dimensional system where 2-qubit operations occur
locally, so there is no need to calculate more complex
qubit/information transportation.

Using integer programming, we found a schedule of qubit operations
that obeys the hardware constraints, implements the local-check code
in the native gate set, and minimizes qubit idle periods. Even with an
optimal schedule, however, parallel Monte Carlo simulation shows that
there is no finite error probability for the native gates such that
the error-correction system would be benecial. However, by adding
dynamic decoupling, a series of timed pulses that can reverse some
errors, we found that there may be a threshold. Thus finding optimal
schedules for increasingly-refined scheduling problems has proven
critical for the overall design of the logical qubit system.

We describe the evolving scheduling problems and the ideas behind the
integer programming-based solution methods. This talk assumes no
prior knowledge of quantum computing.

Sandia is a multipurpose laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the
United States Department of Energy's National Nuclear Security Admininstration under contract DE-AC04-94AL85000.